UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Dropping zinc amalgam electrodes in polarography Coghlan, William Richard Easton 1950

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1951_A8 C6 D7.pdf [ 17.48MB ]
Metadata
JSON: 831-1.0062301.json
JSON-LD: 831-1.0062301-ld.json
RDF/XML (Pretty): 831-1.0062301-rdf.xml
RDF/JSON: 831-1.0062301-rdf.json
Turtle: 831-1.0062301-turtle.txt
N-Triples: 831-1.0062301-rdf-ntriples.txt
Original Record: 831-1.0062301-source.json
Full Text
831-1.0062301-fulltext.txt
Citation
831-1.0062301.ris

Full Text

It 3 37 I<3$I PI a  DROPPING ZINC AMALGAM ELECTRODES IB POLAROGRAPHY  by  Wm. R. E. COGHLM  A t h e s i s submitted i n p a r t i a l f u l f i l m e n t o f the requirements f o r the Degree o f MASTER OF ARTS i n t h e Department of CHEMISTRY  The U n i v e r s i t y o f B r i t i s h Columbia October, 1950.  i ABSTRACT The  general  b r i e f l y and  the  current  compared.  are  the p o i n t s of It  equations for. the polarographic  with r e a l i t y . ideality  The  diffusion  to c o r r e c t i o n terms a r e  t h e a s s u m p t i o n s upon w h i c h t h e  d i f f u s i o n current are  based are not  I t i s a l s o known t h a t t h e  in  departures  e v e n i f i m p e r f e c t l y f u l f i l l e d , may discussed  A complete.  during  he  considered  development o f the  and  noted.  derived  t e n d t o o p p o s e so t h a t , f i n a l l y , t h e b a s i c  faotors are  mentioned  s e v e r a l d e r i v a t i o n s are traced  departure leading  i s known t h a t  t i o n s f o r the  p r i n c i p l e s of polarography are  equa-  accord from  assumptions, valid.  These  equations.  r e v i e w o f amalgam p o l a r o g r a p h y i s e s s e n t i a l l y Publications dealing with  the  subject  are  reported  almost i n e n t i r e t y . The the  preparation  o f d i l u t e amalgams i s d i s c u s s e d  l i g h t of r e s u l t s obtained  i n p r e l i m i n a r y work.  The  in  ideal  n a t u r e o f t h e s e amalgams i s shown i n a r e v i e w o f s e v e r a l p a p e r s dealing with z a t i o n and  E. M.  measurements>.  polymerization  i s discussed  briefly  which e x p l a i n the addition,  F.  along  evidence f o r the  with the h y p o t h e t i c a l  i n s t a b i l i t y of very  i t i s n o t e d t h a t a few  transport  solution.  during passage of the  reactions  d i l u t e amalgams.  In  workers have i n v e s t i g a t e d passage of d i r e c t  e v i d e n c e i n d i c a t e s t h a t a d i l u t e amalgam h a s  a n a l o g o u s to a s a l t  ioni-  o f z i n c metal i n s o l u t i o n i n mercury  b e h a v i o u r o f d i l u t e amalgams d u r i n g The  The  the  current.  properties  P a r t i c u l a r l y , t h e phenomena o f electrical  current  has  been  ii reported.  Further  i n v e s t i g a t i o n o f t h e phenomena i s s u g g e s t e d  s i n c e t r a n s p o r t o f t h e m e t a l i n amalgam d u r i n g p a s s a g e o f e l e c t r i c a l c u r r e n t v i o l a t e s t h e c o n d i t i o n s r e q u i r e d by polarographic  theory.  The  has  the  p h y s i c a l p r o p e r t i e s o f z i n c and  amalgams p e r t i n e n t t c t h e p o l a r o g r a p h i c It i s noted t h a t the  the  method a r e  zinc  tabulated.  d i f f u s i o n c o e f f i c i e n t o f z i n c i n mercury  not been s a t i s f a c t o r i l y  established.  A method f o r s t a b i l i z i n g d i l u t e z i n c amalgams by impressing num  a voltage across  eleotrode The  XXII  t h e amalgam r e s e r v o i r and  plati-  i n a w a t e r l a y e r o v e r t h e amalgam i s d e s c r i b e d . u t i l i z a t i o n o f the Sargent Polarograph  i n c o n j u n c t i o n w i t h a L e e d s and  potentiometer  a  Borthrup  Model  S t u d e n t Type  f o r manually recording polarograms i s described.  Polarograms of standard  zinc solutions i n  O.UJ  p o t a s s i u m c h l o r i d e p l u s a t r a c e o f g e l a t i n were r e c o r d e d m e a s u r e d u n d e r t h e same c o n d i t i o n s i n t e n d e d  for recording  m e a s u r i n g t h e p o l a r o g r a m s o f z i n o amalgams. t a i n e d a g r e e d t o w i t h i n 5$  ported  and  i n G.H  c h l o r i d e p l u s t r a c e s o f maximum s u p p r e s s o r s . the values of the d i f f u s i o n ourrent  lished  The  ob-  reported  constant  re-  potassium  I t was  noted  increased  that  with pub-  c o n t r a r y t o t h e f i n d i n g s o f K a l t h o f f and  d e v i a t i o n i s b e l i e v e d t o be  presence o f t r a c e s o f oxygen. gested.  so  c o n c e n t r a t i o n o f z i n c i n agreement w i t h o t h e r  r e p o r t s but  Lingane.  data  and  t o w i t h i n 2% o f t h e  half-wave p o t e n t i a l f o r zinc s a l t s  decreasing  The  of the values p r e v i o u s l y  f o r the d i f f u s i o n current constant  and  Further  due  i n part to  the  i n v e s t i g a t i o n i s sug-  The electrode  behaviour  found  i n t h e drop  short, raphy  time  has a n e g l i g i b l e accuracy  The  inflection  w h i c h t h e 'wave' f o r z i n c  shown t h a t t h e amalgam  effect  f o r an  on t h e r e c o r d e d  o f t h e same o r d e r o b t a i n e d  stabilizing  polarograms.  In  i n ordinary polarog-  can a p p a r e n t l y be a t t a i n e d .  been o b t a i n e d . diffusion equation fusion  p o l a r o g r a m s o f 0.000288$ z i n c  Calculations f a i l  current constant i s found  coefficient  of zinc  calculated  i n mercury  values  value o f the d i f f u s i o n  reported  coefficient  the  second  has  been c a l c u l a t e d  the  v a l u e s p r e d i c t e d f o r B, f r o m  Choice  term  larger  that  streaming  23.6 dt 2.3.  v a l u e s f o r B. a t the drop  i t i s observed  agreement  diffusion  i s calculated  The Ilkovio  2.4 X  i n the l i t e r a t u r e .  the numerical  10"^cm  2  For t h i s  constant  'B' i n  equation,^  i s w i t h i n range o f  theoretical  the r e s u l t  s u r f a c e i s near  approximations. coefficient i s taken  as  would evidence  minimum.  i n polarography  o f standard  zinc so-  t h a t t h e l i n g a n e - L o ve r i d g e e q u a t i o n g a v e t h e  with accepted  coefficient  error.  The mean v a l u e o f t h e d i f -  This value  here,  amalgam have  the original  values o f the d i f f u s i o n  From t h e d a t a o b t a i n e d lutions  from  of the Strehlow-Stackelberg  of the larger  give  to r e v e a l g r o s s  t o be 5.16 ±. 0.07.  s e c " l a t 25.0°C from  lated  to t h a t o f mercury except  vs p o t e n t i a l curve.  It i s also  Reproducible  best  amalgam a t t h e d r o p p i n g  i n the range o f p o t e n t i a l over  amalgam d e v e l o p s . circuit  zinc  i s shown t o c o r r e s p o n d  inflection is  of dilute  values.  o f zinc  a c c o r d i n g to e q u a t i o n ^ A s  A®oordingly,the v a l u e  i n meroury a t 25.0°C has been 2.58cm sec l±0.09. A value 2  -  f o r the calcui n agree-  ment w i t h t h e l a r g e r o f t h e s e v e r a l r e p o r t e d Consistent  r e s u l t s w i t h amalgams  values.  l e s s t h a n 0.005$  s o l u t e m e t a l have not p r e v i o u s l y been r e p o r t e d graphic provided  literature.  I n t h i s w o r k a n amalgam  0.000288$  not only c o n s i s t e n t r e s u l t s , but a l s o r e s u l t s  w h i c h remarkable agreement w i t h p u b l i s h e d tained.  i n the polaro-  This i s taken  from  d a t a has been ob-  a s e v i d e n c e t h a t t h e method  f o r w o r k o f t h e p r e c i s i o n and a c c u r a c y  has  obtainable  i s suitable i n ordinary  polarography. The c o n d i t i o n s f o r w o r k o f g r e a t e r p r e c i s i o n and accuracy  are set forth with a b r i e f  c u l t i e s and s o u r c e s  discussion of the  of error involved.  The p r a c t i c a l a p p l i c a t i o n s o f amalgam are  suggested.  diffi-  polarography  ACKNOWLEDGMENT. A grant from  t h e C o n s o l i d a t e d M i n i n g and  S m e l t i n g Company o f Canada L t d . t o t h e U n i v e r s i t y o f B r i t i s h Columbia Research Sargent  Polarograph  I'und e n a b l e d  used i n t h i s  Tadanac Z i n c  purchase  of the  work.  (99.99 + $ ) was a l s o s u p p l i e d  b y t h e C o n s o l i d a t e d M i n i n g a n d S m e l t i n g Company. The a u t h o r w i s h e s for  to express h i s a p p r e c i a t i o n  t h e d i r e o t i o n o f t h i s r e s e a r c h b y D r . L.W. S h e m i l t .  T h a n k s a r e a l s o due t o M r . Wm. P y e f o r c o n s t r u c t i n g the a l l g l a s s dropping  electrode assemblies.  Larkham gave a s s i s t a n c e w i t h  photography.  Mr,G.W.  TABLE OF CONTENTS  ABSTRACT  i  INTRODUCTORY NOTE  v  PART A  INTRODUCTION  1  PART B  POLAROGRAPHY. THEORY AND APPLICATIONS  PART C  1.  POLAROGRAPHIC THEORY  2  2.  DROPPING AMALGAM ELECTRODES  27  ZINC AMALGAMS 1.  METHODS OF PREPARING ZINC AMALGAM  31  2.  CHEMICAL and P H Y S I C A L PROPERTIES o f  52  ZINC AMALGAMS PART D  PART E  EXPERIMENTAL 1.  MATERIALS AND SOLUTIONS  41  2.  APPARATUS  45  3.  METHODS  49  RESULTS AND DISCUSSION 1.  POLAROGRAPHY OF STANDARD ZINC SOLUTIONS 51  2.  AMALGAM POLAROGRAPHY  62  3.  SUMMARY OF RESULTS  78  BIBLIOGRAPHY COPY 'THE USE OF D I L U T E AMALGAMS IN THE DROPPING ELECTRODE by HEYROVSKY AND KALOUSES  82  1  f o l l o w i n g page  84  ±7  INTRODUCTORY NOTE The  d i v i s i o n of t h i s t h e s i s into several parts  been found necessary  to o l a r i f y p r e s e n t a t i o n o f the  phases involved i n the work. polarographic  F i r s t l y ^ the equations  d i f f u s i o n c u r r e n t are d e r i v e d .  t i o n f o r the d i f f u s i o n ourrent  have been i n t e g r a t e d f o r comparison.  f o r the  Since an equa-  several derivations Secondly, s i n c e the  l i t e r a t u r e d e a l i n g w i t h amalgam polarography decided  various  i s the law r e q u i r e d i n the  fundamental theory o f polarography,the  was  has  i s limited i t  to gather as much as p o s s i b l e under one  cover.  T h i r d l y i n order to have as much u s e f u l i n f o r m a t i o n as possf  i b l e i n one p l a c e f o r f u t u r e i n v e s t i g a t i o n s , a wide range o f s u b j e c t s i s discussed h e r e i n . t i o n , chemistry  and  These s u b j e c t s a r e the  prepara-  p h y s i c s o f z i n c amalgams d e s c r i b e d  i n the  l i t e r a t u r e as w e l l as c l o s e l y r e l a t e d s u b j e c t s such as  the  t r a n s p o r t o f metal i n an amalgam during passage o f the  eleotric  ourrent.  Unfortunately,  some o f the i n f o r m a t i o n i s fragmentary  due to the f a c t that the o r i g i n a l l i t e r a t u r e was ly available. were not  not  On the other h a n d t h e r e a r e some s u b j e c t s which  covered  }  due  to the f a c t t h a t time d i d not permit  ther l i t e r a t u r e search.  Among the omissions  may  mercury amalgams.  and  dilute  T h i s s u b j e c t ^owever^ appears to be a  i n v e s t i g a t i o n . F o u r t h l y ^ t h e experimental  r e s u l t s o f t h i s work are  presented.  fur-  be mentioned  the e l e c t r o c a p i l l a r y c h a r a c t e r i s t i c s o f mercury and  f o r separate  immediate-  field methods  Due  to the c o n s i d e r a b l e range o f m a t e r i a l  some o v e r l a p p i n g and In a few without  r e p e t i t i o n i s required for c o n t i n u i t y .  i n s t a n c e s experimental  d e t a i l of method.  were u n s a t i s f a c t o r y and the context  covered  evidence  i s given  In these cases, however, the r e s u l t s  d e t a i l was  considered  superfluous since  e x p l a i n s t h e b a s i s o f the method.  It i s r e g r e t t e d that time d i d not permit f u r t h e r i n v e s t i g a t i o n s under the c o n d i t i o n s which experience gained t h i s work had  shown to be  necessary.  in  1.  DBOPPIIG AMALGAM ELECTRODES IS POLAROGRAPHY  A—INTRODUCTION During i n v e s t i g a t i o n f o r s u i t a b l e methods o f a n a l y s i s i n r e s e a r c h on z i n c anodes i n chrornate e l e c t r o l y s i s the p o l a r o g r a p h i c technique was  c o n s i d e r e d . Lingane'sf / )  note on the dropping oadmium amalgam e l e c t r o d e suggested t h a t perhaps a dropping z i n c amalgam e l e c t r o d e i n the polarography o f ohromate s o l u t i o n s wouia a f f o r d some u s e f u l i n f o r m a t i o n w i t h r e s p e c t to t h e e l e c t r o d e r e a c t i o n s i n v o l ves.  F u r t h e r search i n the l i t e r a t u r e a t t h a t time r e v e a l e d  no q u a n t i t a t i v e data  roopeet to the anodio  c u r r e n t o f dropping amalgam e l e d t r o d e s .  diffusion  Consequently,  this  work has been d i r e c t e d towards determining the c h a r a c t e r i s t i c s o f dropping z i n o amalgam e l e c t r o d e s l n polarography w i t h r e s p e c t to the f e a s i b i l i t y o f t h e i r use i n i n v e s t i g a t i n g anode r e a o t i o n s .  Since time d i d not permit & »  the e n t i r e work l n mind, i t was o f the apparent  completion o f  decided that the d e t e r m i n a t i o n  d i f f u s i o n c o e f f i c i e n t o f z i n c i n meroury under  p o l a r o g r a p h i c c o n d i t i o n s would p r o v i d e the most u s e f u l data towards f u r t h e r  investigations.  2  B - Polarography.  Theory and A p p l i c a t i o n s  (l)--POLAROGRAPHIO THEORY The p o l a r o g r a p h i o method o f chemical a n a l y s i s was invented by J . Heyrovsky.  The method i s based on  the  i n t e r p r e t a t i o n o f the c u r r e n t - v o l t a g e carves that  are  o b t a i n e d when s o l u t i o n s o f e l e c t r o - r e d u c i b l e or  e l e c t r p - o x i d i z a b l e substances a r e e l e c t r o l y z e d i n which one e l e c t r o d e c o n s i s t s o f mercury wise from a f i n e bore c a p i l l a r y .  in a  falling  cell drop-  The .solution c o n t a i n s  a minute amount of t h e e l e c t r o c h e m i c a l l y r e a c t i n g substanoe i n the presence o f a r e l a t i v e l y huge amount of an indifferent electrolyte.  The unique c u r r e n t - v o l t a g e  curves obtained by the method i n d i c a t e both the s p e c i e s and c o n c e n t r a t i o n o f t h e r e a c t i v e  substance.  On account o f t h e smallness o f the dropping mercury  e l e c t r o d e , extreme c o n c e n t r a t i o n p o l a r i z a t i o n  occurs so that the current i s determined by d i f f u s i o n o f the  r e a c t i n g substance and t h e area o f t h e mercury  drop.  The d i f f u s i o n c u r r e n t i s thus p r o p o r t i o n a l to the concent r a t i o n of t h e r e a c t i n g substance when a l l o t h e r f a c t o r s i n f l u e n c i n g the d i f f u s i o n c u r r e n t a r e made c o n s t a n t .  That i s  The p r o p o r t i o n a l i t y constant /< i s determined by measuring the tion  d i f f u s i o n current C  .  A* f o r a s o l u t i o n o f known c o n c e n t r a -  Subsequently, an unknown c o n c e n t r a t i o n may be  determined by u s i n g the e x p e r i m e n t a l l y determined v a l u e f o r K  •  However, i t i s more desirable to o a l e u l a t e K ^ o r any  reasonable  variations of the faotors whioh Influence the d i f f u s i o n current. An equation for the polarographic d i f f u s i o n current has been derived by Ilkovic (X)  and substantiated by others (3) (*/)•  The general and t h e o r e t i c a l p r i n c i p l e s of polarography have been discussed i n some d e t a i l b y several authors (S)  {(m) (7).  and the reader i s referred to them for a more  complete treatment than i s given here.  In particular,the more  reoent publications of Lingane and Loveridge (SO and and Staokelberg (J)  Strehlow  have added much to the theory o f the  polarographic d i f f u s i o n current. Before deriving the Ilkovic equations i t may  be  i n order to present a b r i e f summary of t h e i r development.  She  o r i g i n a l Ilkovic equation reads (JL)  where  average current i n microamperes during the l i f e of the drop. //i t number of faradays o f e l e c t r i c i t y required per mole of the electrode reaction. p-z.  d i f f u s i o n c o e f f i c i e n t of the reducible or o x i dizable substance i n the units Cs>n.  x  C " i t s concentration i n mlllimoles per  litre.  /yn-i rate of flow of mercury from c a p i l l a r y i n ?n*n  -^^cT1  "C - drop time i n seconds. S i n o e ^ 5 - ^ O C h a s been chosen as a standard condition d  for polarographic work the values of the physloal oonstants at that temperature must be used.  The Ilkovic d i f f u s i o n current  equation f o r the stanaara c o n d i t i o n ZS-OO  - 6>oj<n. &k By  C  C i e given  C^t  ort^  (ID  c o l l e c t i n g the v a r i a b l e terms  —4^7-^ where JL  r  <*°7^  d i f f u s i o n current constant. ( ) have shown t h a t j f  l o v e r i d g e (£}  ,0  ohanging v a l u e s o f orC^  I  -  v a r i  (in)  However, Lingane  9s  s i g n i f i c a n t l y with  E^* thus demonstrating -  t h a t the  o r i g i n a l I l k o v i o equation, although approximately not completely  satisfactory.  and  correct, i s  They have a l s o shown t h a t the  equation can be d e r i v e d d i r e c t l y from the d i f f u s i o n ourrent equation f o r l i n e a r d i f f u s i o n to a plane e l e c t r o d e . Presumably^ tfee s i m p l i f i c a t i o n s i n intermediate mathematical o p e r a t i o n s became e q u i v a l e n t to a n e g l e o t o f the c u r v a t u r e o f the mercury drop i n the o r i g i n a l I l k o v i o e q u a t i o n . i f i c e Lingane and  *Cjz (.07^ Strehlow  Ioveridge obtained a new  P ^ 6 ^ n %  By a simple  art-  equation (l V).  C I * - 3 ? * . % < 7 r r 4 t t) (IV)  and S t a c k e l b e r g (*?) have derived a s i m i l a r  whioh d i f f e r s o n l y i n the v a l u e o f the n u m e r i c a l  equation(y)  constant  T h e i r d e r i v a t i o n from b a s i c p r i n c i p l e s a l s o gave the equation ft//) for  the p o l a r o g r a p h i c d i f f u s i o n ourrent o f dropping amalgam  eleotrodee.  The problem i n v o l v e d i s to c a l c u l a t e the of  diffusion  the r e a c t a n t a c r o s s an a r e a which i s d e f i n e d by the s u r f a c e  a r e a o f an expanding drop.  Sinoe the d i f f u s i o n ourrent i s the  product o f the q u a n t i t y o f e l e c t r i c i t y r e q u i r e d per mole o f e l e c t r o d e r e a c t i o n and the u n i t f l u x and the area o f the  5. e l e c t r o d e an equation o f the form  (VII) might he expected where sC  •=- d i f f u s i o n c u r r e n t at the time  z  -  -  •  the e l e c t r o c h e m i c a l e q u i v a l e n t ^ the  ^72 *=. the number o f faradays electrode reaction.  J)  <C  faraday^  r e q u i r e d per mole o f  p r o p o r t i o n a l i t y constant  for d i f f u s i o n .  / 9 £ : A ~ r a t e o f change o f c o n c e n t r a t i o n C with {jfT-Slz change o f d i s t a n c e 7^ from a f i x e d o r i g i n % - O at a plane defined by 7^ a t the time t . ( s i n e e the c o n c e n t r a t i o n a t any plane i s dependant on the time} /1^= Such an time  T~  Area o f the drop a t the time  equation would g i v e the instantaneous  c7« c u r r e n t at  the  • However, we have a drop expanding w i t h time which  counteracts  the decrease o f thre u n i t f l u x with time.  the c o n c e n t r a t i o n a t y~  Further,  must be changed s i n c e the plane  i n question  i s i t s e l f moving  due to the r e l a t i v e i n c o m p r e s s i b i l i t y o f l i q u i d .  In view o f  these c o n s i d e r a t i o n s i t i s r e q u i r e d to r e p l a c e / J j ^ ^ and with the a p p r o p r i a t e  been assumed that the  e l e c t r o d e by d i f f u s i o n alone.  o r d i n a r y polarography  /\  c  expressions.  F i r s t l y , i t has reaches the  %--=o  r e f e r r e d to a f i x e d c o o r d i n a t e  reactant  In the case o f  t h i s c o n d i t i o n i s adequately  Although the e l e c t r i c f i e l d and  fulfilled.  the e l e c t r i c t r a n s p o r t o f the  r e a c t a n t are never n i l , the e f f e c t i s immeasurably s m a l l s i n c e the i n d i f f e r e n t  electrolyte i s usually / O  c o n c e n t r a t i o n o f the r e a c t a n t . polarography,  to 10  times the  In the oase o f amalgam  however, the assumption w i l l be  considered  q u e s t i o n a b l e pending f u r t h e r i n v e s t i g a t i o n s .  Here the  question  o f e l e c t r i c t r a n s p o r t o f metals d i s s o l v e d i n mercury a r i s e s . Elsewhere there i s g i v e n some evidence f o r the phenomena* Whether or not the e f f e o t i s measurable i n amalgam polarography cannot be  stated here.  convection  ourrent  In a d d i t i o n to e l e o t r i o a l t r a n s p o r t , a  could a l s o i n t e r f e r e w i t h t r u e  A c t u a l l y , a convection  diffusion.  ourrent o f c o n s i d e r a b l e magnitude does  exist.  According  to Strehlow and  ourrent  i s s u i n g from the c a p i l l a r y p e r s i s t s so as to cause  streaming at t h e mercury s u r f a o e .  Stackslberg  the mexoury  T h i s streaming, o r  rinsing  e f f e c t , i s not as s t r o n g i n o r d i n a r y polarography^where reactant  the  i s i n s o l u t i o n i s i t i s i n amalgam p o l a r o g r a p h y .  She  streaming, or r i n s i n g e f f e e t , 1B shown s c h e m a t i c a l l y i n f i g . l . Thus ,the i n i t i a l assumption f o r the d e r i v a t i o n o f the for  the p o l a r o g r a p h i c  equation  d i f f u s i o n current i s imperfectly  For l i n e a r d i f f u s i o n the number o f moles,  fulfilled.  jLfi^i.  r e a c t a n t d i f f u s i n g a o r o s s a c r o s s s e c t i o n a l plane o f a r e a  A con*-  i n the i n f i n i t e s i m a l i n t e r n a l o f time <s/£"is p r o p o r t i o n a l to the c o n c e n t r a t i o n g r a d i e n t expressible  a t the plane i n q u e s t i o n and  is  by  where j ) , t h e p r o p o r t i o n a l i t y c o n s t a n t , i s the d i f f u s i o n  coef-  ficient.  desig-  nated  The  f l u x at a plane distanoeXfrom the o r i g i n .  ^  In order to o a l o u l a t e the t o t a l amount o f m a t e r i a l t h a t d i f f u s e across a g i v e n plane i n a f i n i t e p e r i o d i t ;  is  will  necessary  to have a knowledge o f the change i n c o n c e n t r a t i o n w i t h time at  FIGURE 1. —  Schematic  representation of  c u r r e n t due to mercury o u t f l o w and  r e s u l t a n t streaming or  rinsing effeot.  the plane i n q u e s t i o n .  The change i n c o n c e n t r a t i o n w i t h  time  between two planes separated by the i n f i n i t e s i m a l d i s t a n c e i s equal to the d i f f e r e n c e between t h e number o f moles whioh enter a c r o s s t h e plane a t  and the number whioh l e a v e  a c r o s s the plane a t ^ d i v i d e d by t h e volume  /4<^cnolosed  between the p l a n e s ; t h a t i s  Sinoe^j i s equal to u n i t y when we speak o f the f l u x we a l s o  S i n c e from we f i n d from equation (X) t h a t the ohange i n o o n o e n t r a t i o n w i t h time a t a g i v e n plane a t a g i v e n i n s t a n t i s expressed  3 "t"  *d y-  d tr  (ziiD  The problem i s to o b t a i n an e x p r e s s i o n f o r the c o n c e n t r a t i o n g r a d i e n t a t any i n s t a n t a t ^ < 2 , r  by means o f equation (EL) can be computed.  the f l u x , and hence the c u r r e n t  A t t h e i n s t a n t the EMP i s applied,(C-=©),  the o o n o e n t r a t i o n a t the e l e c t r o d e , (  in  the body o f t h e s o l u t i o n , ( C ) .  (£70),  i s equal to t h a t  A f t e r the EMJ i s a p p l i e d , 1  CZo i s r a p i d l y decreased by t h e e l e o t r o d e r e a o t i o n .  The i n i t i a l  and boundary c o n d i t i o n s a r e t h e r e f o r e , Co  Co^<-  from whioh  C  or  - C  when  C -0  when  0  t  O  "7  These c o n d i t i o n s h o l d i n polarography  O s i n c e a t an approp-  r i a t e a p p l i e d EMF t h e r e a c t a n t i s e l e o t r o l y t i o a l l y  reduced or )  oxidized^as  f a s t as i t meets the e l e c t r o d e s u r f a c e .  these c o n d i t i o n s the s o l u t i o n of equation  By d i f f e r e n t i a t i n g equation X  - O  we  1 #  under the o o n d i t i o n t h a t  obtain  S u b s t i t u t i n g i n equation  ^Tr  (XIV)  (XIII) i s  Under  =  (VII) we  FA  T h i s i s the equation a f t e r the BMP  have  C fy^  (xvi)  f o r the instantaneous  c u r r e n t at any  i s a p p l i e d where l i n e a r d i f f u s i o n to a  plane electrode- i s c o n s i d e r e d . derived the c o r r e c t e d  Lingane and  I l k o v i o equation  by s u b s t i t u t i n g the values f o r A-  Loverldge  Suoh a d e r i v a t i o n provided  a due  ( £T)  ( I I ) from equation(XVI)  . i n t e g r a t i n g to o b t a i n  average c u r r e n t and m u l t i p l y i n g by a numerical  o r i g i n a l Ilkovio  time  the  constant.  to the inadequacy o f  the  equation*  However, the problem i n v o l v e s a s p h e r i c a l e l e c t r o d e . In the d e r i v a t i o n i t i s assumed t h a t the mercury drop i s a f r e e sphere. case.  Later i t w i l l be shown t h a t t h i s i s not a c t u a l l y the Here we w i l l c o n s i d e r the r e a c t a n t  s p h e r i c a l e l e c t r o d e o f r a d i u s Sl s p h e r i c a l s h e l l surrounding  0  . The  1.  See  diffusion field i s a  the e l e c t r o d e a t d i s t a n c e  measured from the centre o f the sphere. face i s  d i f f u s i n g to a f r e e  The a r e a o f the  LjJfsL -. 1  reference  s o l u t i o n , equation  ( i T ) page 21 f o r a d i s c u s s i o n o f t h i s (XIV).  s\s sur-  9. The number o f moleB which d i f f u s e a c r o s s t h i s surfaoe i n the t i m e < ^ £ " i s g i v e n by the e x p r e s s i o n , analogous to P i c k ' s First  and  Law,  _  the f l u x a t  y  is  S i m i l a r l y t h e number o f moles t h a t d i f f u s e a c r o s s the s u r f a c e ;  at  A.-t-e/'X i n the time d  Ufi^u^ = H'rrc++J^  & is  J>(zk)«~tt^  t  (xix)  and  - ^(^-i)-!-r-*^-  i^l  (XX)  1  The c o n c e n t r a t i o n g r a d i e n t a t /i  and hence equation  i s r e l a t e d to t h a t .  (XIX) may be w r i t t e n as  Expanding and n e g l e c t i n g the terms c o n t a i n i n g i n f i n i t e s i m a l s o f the second and t h i r d o r d e r s , equation  (XXII) becomes  H i r U t + 2*(%=)J* ^  Jth+J-x  ^y^(xxiii)  The change i n c o n c e n t r a t i o n i n the s p h e r i c a l s h e l l i n the time  cl^C  i  s  t^  1 6  d i f f e r e n c e between the number o f moles whioh  enter  the s h e l l a t - i * - * / - ! and the number which l e a v e a t A. d i v i d e d by the volume o f the s h e l l which i s ^ / T ^ 2 * T ^ L ; t h a t i s  Vc - ^ Therefore,the  / — clN**trrst*-  r a t e o f ohange o f o o n o e n t r a t i o n  g i v e n v a l u e s o f A and C i s  i/T^  cist  c{C  (xxiv) w i t h time a t  10, By  s u b s t i t u t i n g the values expressed by equations (XVII)  and  (XXIII) i n t o (XX¥) we o b t a i n  -if?  -  L ^  J  „  .  +^(^7/  (mi)  In order to o a l c u l a t e the t o t a l flow through a g i v e n s h e l l o f i n f i n i t e s i m a l t h i c k n e s s i n a f i n i t e time i t i s necessary to i n t e g r a t e equation  (XXVI).  She i n i t i a l and  boundary c o n d i t i o n s f o r l i n e a r d i f f u s i o n are a p p l i c a b l e that i s :  Co  C-o - C-  when  or  ~  C  Co  C  ~  O  O r' when  V  Under these c o n d i t i o n s the s o l u t i o n i s  C t - c(/-^t) t  y  O  1  fivm £7 *yy y  ^ - ^ o  (xxviD  and  £ ^ ^ That i s with  = C (/-  (xxviii)  i n c r e a s i n g time o f d i f f u s i o n the c o n c e n t r a t i o n  at any g i v e n p o i n t i n t h e d i f f u s i o n f i e l d g r a d u a l l y approaches a constant  v a l u e , a steady s t a t e i s s a i d to e x i s t .  stant concentration and  C  The con-  i n the steady s t a t e i s a f u n c t i o n o f  v a r i e s from zero a t the e l e c t r o d e s u r f a c e at a l a r g e distanoe  from the e l e c t r o d e  (si'-slo)  to  (i>-77/7o and-^? -<?).  T h i s i s an important fundamental d i f f e r e n c e between symmetric a l s p h e r i o a l d i f f u s i o n and l i n e a r d i f f u s i o n , i n which l a t t e r r case a steady s t a t e i s t h e o r e t i c a l l y  1.  See r e f e r e n c e  this solution.  ( 5"  )  unattainable.  Pages 28-29 -for a d i s c u s s i o n o f  11. The at  c u r r e n t a t any i n s t a n t i s governed by the f l u x  the e l e c t r o d e s u r f a o e , i . e . , by t h e c o n c e n t r a t i o n  at^l=-^lo  •  By d i f f e r e n t i a t i n g e q u a t i o n  gradient  (XXVII) the concen-  t r a t i o n g r a d i e n t a t the e l e c t r o d e surfaoe a t any time g i v e n by  The  C is  ,  instantaneous  -cr  value o f the r e s u l t i n g c u r r e n t i s , t h e r e f o r e ,  A M O - - ^ ^ ^ ( i ^-^=.  ) (xxx)  In the case o f the dropping mercury e l e c t r o d e the a r e a o f the d i f f u s i o n f i e l d  ohanges c o n t i n u o u s l y  l i f e o f a drop and d i f f u s i o n takes plaoe  during the  i n a medium t h a t i s  moving w i t h r e s p e c t to t h e c e n t r e o f the drop, i n a d i r e c t i o n opposite  to the d i r e c t i o n o f d i f f u s i o n .  Due to the inoompres-  s i b i l i t y o f a l i q u i d a d i f f u s i o n s p h e r i c a l s h e l l remains t h e same d i s t a n c e from the e l e c t r o d e surfaoe but the s u r f a c e  area  i n c r e a s e s c o n t i n u o u s l y w i t h time during t h e l i f e o f each drop. Therefore the }  equations  that d e s c r i b e d i f f u s i o n to the dropping  e l e c t r o d e d i f f e r from those f o r s t a t i o n a r y s p h e r i c a l d i f f u s i o n by terms whioh d e s c r i b e t h e i n c r e a s e i n the area o f the d i f fusion f i e l d with time. It i s assumed that the mercury drops a r e f r e e  spheres.  A c t u a l l y a s m a l l p a r t i s soreened o f f by the c a p i l l a r y thus decreasing the d i f f u s i o n f i e l d .  However, the drops a r e deformed  by g r a v i t a t i o n and beoome t e a r shaped,thus o r e a t i n g a l a r g e r ./surface a r e a thanr> i s possessed by a t r u e sphere o f equal ume.  Thus ,the s c r e e n i n g e f f e c t and deformation  vol-  oppose each  other w i t h respect to the d e v i a t i o n o f the s u r f a c e a r e a .  18. I t i s assumed t h a t a t C - s O t h e drops have an In r e a l i t y an area i s always  area^.  maintained.  It i s a l s o assumed t h a t the r a t e o f f l o w o f mercury i s constant;  A c t u a l l y ^ a t the b e g i n n i n g o f drop f o r m a t i o n a  v e r y c o n s i d e r a b l e counter p r e s s u r e due to the ourvature o f the drop p r e v a i l s , a l t h o u g h i t i s v e r y q u i c k l y removed.  Thus, at  the b e g i n n i n g o f the drop time the r a t e o f i n c r e a s e i n s u r f a c e a r e a i s c o n s i d e r a b l y decreased  for a brief interval.  This  compensates to some extent the maintenance o f an a r e a a t T ~ o I t i s assumed t h a t the t h i c k n e s s o f the  diffusion  l a y e r i s s m a l l compared to the r a d i u s o f t h e drop.  This i s  not s a t i s f a c t o r i l y the oase as s h a l l be« seen f u r t h e r f u r t h e r d i s c u s s i o n i s based on a t l e a s t d i f f e r e n t l i n e s o f development.  Lingane  o u s s i o n by M a c G i l l a v r a y and R i d e a l { H ). Loveridges  iff)  three  ( f r o m  Secondly,  d e r i v a t i o n w i l l be t r a c e d .  more r i g o r o u s d e r i v a t i o n g i v e n by Strehlow and ( ^  on.  F i r s t l y the d e r i v a t i o n i s  based on t h a t shown by K o l t h o f f and  and  .  a disLingane  T h i r d l y , the Stackelberg  ) w i l l be i n t r o d u c e d . We have seen t h a t the fundamental d i f f e r e n t i a l  equation f o r symmetrical  i n which s t ^ i a  spherical diffusion i s  r a d i a l distanoe measured on a f i x e d  coordinate  system whose o r i g i n i s a t the oentre o f the s p h e r i c a l e l e c t r o d e . In o r d e r to apply t h i s equation to d i f f u s i o n a t the e l e c t r o d e the f i x e d  ooordinate/*"must  c o o r d i n a t e , ^ ) , to take i n t o account  dropping  be replaoed by a moving the i n c r e a s e i n area o f t h e  13. diffusion  field  d u r i n g the growth o f the mercury drops.  moving c o o r d i n a t e , /  3  The  i s d e f i n e d as the r a d i u s o f a h y p o t h e t i c a l  sphere whose volume i s the same as the volume enclosed between the s u r f a c e o f the growing mercury drop and a s p h e r i o a l s u r faoe o f r a d i u s s l i g h t l y l a r g e r than the r a d i u s o f the drop.  *  3  -  or  (XXXI) y)'*  — /to  (XXXII)  where A* i s the r a d i a l d i s t a n c e from a p o i n t i n the s o l u t i o n to the centre o f the drop, and / ) i s the r a d i u s o f the drop a t any 9  instant • I f we assume t h a t the mercury  drop i s t r u l y s p h e r i c a l ,  then i t s volume a t any time 'C measured from the beginning  of i t s  formation i s  V where  * vn  $ -  W  = ^  = etc-  weight o f mercury f l o w i n g from per second.  m  i  >  capillary  <^ •= the d e n s i t y o f mercury. cpi -z p r o p o r t i o n a l i t y constant r volume o f mercury f l o w i n g from the c a p i l l a r y . p e r second. For a g i v e n c a p i l l a r y and a constant v i r t u a l l y constant  pressure <m~ and ad are  and independent o f the i n t e r f a o i a l t e n s i o n  at the m e r c u r y - s o l u t i o n  i n t e r f a c e (/? )•  However, d u r i n g the  formation o f a s i n g l e drop there i s a very c o n s i d e r a b l e i n pressure.  ohange  Assuming/>rvconstant then the volume o f t h e drop  i s d i r e c t l y p r o p o r t i o n a l to i t s age, but i t s r a d i u s i n c r e a s e s with the oube root o f i t s age; t h a t i s  irr  14. / I n view o f these r e l a t i o n s , ana equation (xxxii) expressed  can be  as a f u n c t i o n o f the age o f the drop by  /O*  -  ^1^-  (xxxv)  (ft  The f l u x o f the d i f f u s i n g substance g i v e n v a l u e o f su  at a given instant  and  is  From equation (XXXV) f o r a g i v e n value o f tr 1^  -  '  (XXXVII)  and henoe equation (XXXVI) becomes  where/4^, i s  the a r e a o f the d i f f u s i o n f i e l d  i n s t a n t , a n d ^ His  atsv-  the number o f moles t h a t d i f f u s e  i n the time e/t~.  D i f f e r e n t i a t i n g equation  low i n terms o f f l u x o f the d i f f u s i n g substance (XXVI) may  at  any through  (XXXVIII)  equation  be w r i t t e n  By s u b s t i t u t i n g the f o r e g o i n g r e l a t i o n s f o r i n t o t h i s equation and  and  "^^-v  simplifying  T h i s i s the fundamental d i f f e r e n t i a l equation f o r d i f f u s i o n to the dropping mercury e l e c t r o d e . We a r e i n t e r e s t e d i n the r e g i o n very c l o s e to the surfaoe o f the dropping e l e c t r o d e and s i n c e i n t h i s r e g i o n Sis i s only s l i g h t l y larger t h a n ^ o i t follows that ^ ^ i s much s m a l l e r t h a n ^ ' C ana  ^  a  .  (y ) t  W h e n } f t  very  we have  3  T h e r e f o r e , f o r t h i s r e g i o n very near to the surfaoe o f the  -~i  15. dropping  e l e c t r o f e ' ei-aat'idfi" VX&l) beoomes  In o r d e r to o b t a i n a s o l u t i o n o f t h i s equation i t i s convenient to perform a s u b s t i t u t i o n o f v a r i a b l e s to s i m p l i f y the a l g e b r a . Let  y-  ^  Then  = 3 / ° ^  <  2  4^  r ^ -  <s£y . 3 - r- %  ana  In terms o f these new v a r i a b l e s  *y  ^Tr ~ 3 <-  3  5 y  (XLIII)  -  Substituting  the r e l a t i o n s expressed by equations  (XLIV) ana (XLV) i n t o  where  (XLIV)  ^  (XLII) l e a d s to  -  A s o l u t i o n o f equation  (XLVI) i s  - A T - 5 -j/fr J ^y  ^  (XLIII)  If <?( y  o  where ^Kis an i n t e g r a t i o n v a r i a b l e ,  (xivn)  ana  £3 a r e c o n s t a n t s  ana the v a l u e o f the i n t e g r a l aepenas o n l y on the v a l u e o f the upper l i m i t . The  !•  i n i t i a l ana boundary c o n d i t i o n s Co -  C  C  Q  Co  ~  O  XT - -O i when  "C  ^  (C, i s the c o n c e n t r a t i o n i n . the body o f the s o l u t i o n ,  where and (C  Q  When t 1.  or  C- when  the o o n o e n t r a t i o n a t the surfaoe o f the meroury ? 0  }  ^  - O and s i n o e X ' / ^ t 7 ^  See r e f e r e n c e (S~) page 35  i s  a  l  s  o  s ^ * ! *° 11  drops.  16. Hence when^ "70  the upper l i m i t o f the i n t e g r a l i n equation  ;  (XLVII) and the i n t e g r a l i t s e l f , become e q u a l to z e r o . Co i s also equal to zero when tzpoit  Since  f o l l o w s t h a t K must be  On t h e other hand,when C - O s i n c e  e q u a l to z e r o .  ^ '• P  the upper l i m i t o f the i n t e g r a l beoomes i n f i n i t y and the v a l u e o f the i n t e g r a l becomes it  •  f o l l o w s that the constant  C  Since  J3l& equal  a  — C-when  simply to C.  C7 ~ °  Henoe ,  equation (XLVII) becomes Co Sinoe  -  j  ¥• - /O^  and  ^ y  ^ -  l  ^  »l f  C %  and  (XLVIII) - ^2 /  ~=  J?  and hence equation (XLVIII) may be w r i t t e n  ~-  Co  ^Tftfo*^~ ^r r  The r e s u l t a n t ourrent a t any i n s t a n t is  111  during the l i f e o f a drop  governed by t h e fLux o f the d i f f u s i n g substance  face o f the drop From equation  a t the s u r -  (^-.o), and i s g i v e n by  (XXXVIII) j<y.  •  D£  By d i f f e r e n t i a t i n g equation (L) w i t h r e s p e c t to so  we o b t a i n  t  or i n view o f equation (XLIX)  - ^ y ^ ) T>/O - -^th 3w C  i: *  t  dm)  ^  (  (1IV) x  17. Hence from equation  ( U V ) , the f l u x at t h e surface o f t h e drops  i s g i v e n by  r  a  /JZ—) (IV)  and  the e x p r e s s i o n f o r the c u r r e n t i n equation  Since  —  equation  ^  r  3^-  ^  3 ^ ^  ( L I ) becomes  (LVII)  7  (LVI) becomes  - £>• 732L ^  F  ~  <  r  n  % C"^  (LVIII)  where 0.732 i s simply a combination o f t h e n u m e r i c a l  constants . 1  T h i s r e l a t i o n was o r i g i n a l l y derived by I l k o v i c . It i s more convenient  to express the c u r r e n t i n micro-  amperes, t h e c o n c e n t r a t i o n i n m i l l i m o l e s per l i t e r and m as milligrams/second of F  The  2  and on t h i s b a s i s when the n u m e r i c a l  i s introduced  into  equation  value  (LVIII) we have  average c u r r e n t during the l i f e o f a drop i s defined as t h e  h y p o t h e t i c a l constant  c u r r e n t which, f l o w i n g f o r a l e n g t h o f  time equal to the drop time, would produce the same q u a n t i t y o f e l e c t r i c i t y as t h e q u a n t i t y a c t u a l l y a s s o c i a t e d with Mathematically  the average c u r r e n t ,  each drop.  »,is d e f i n e d by  where C ^ ^ i s  the drop time.  By performing  t h e ' ^ n t e g r a t i o n we f i n a l l y o b t a i n  In view o f equation (LIX)  yoc^ p^c^^jW- ^ f ^ / r (Lxi)  1. The value f o r d i s taken here as 13.6 g/om . 2. The v a l u e f o r F i s taken here as 96500 coulombs. 3  When the d e n s i t y o f mercury a t 25.0°C i s taken as 13.53 the equation  becomes  ^T-  3  1  r i :  D z 6 ^ ^  £>o7^  Lingane and  gm.cm"  Loveridge  ( %  ( L X I I D  ) s u b s t i t u t e d the r e l a t i o n f o r the  area o f a s p h e r i c a l meroury drop into equation i n t e g r a t i n g found that the equation  (XVI) and a f t e r  f o r the d i f f u s i o n  current  was J  ~  3^7  I f the constant 607  397  i s obtained.  represents  ^  V^-  C  %  i s m u l t i p l i e d by |/J"the " I l k o v i o Constant"  In the  I l k o v i c d e r i v a t i o n the f a c t o r  the decay o f the c o n c e n t r a t i o n g r a d i e n t at  e l e c t r o d e s u r f a c e andjhence,the f a c t o r has T h e r e f o r e ^ t h i s f a c t o r was  f o r the instantaneous cal  (LXIV)  the f a c t t h a t the expansion o f the mercury drops  counteracts  ficance.  ZTT  the  theoretical signi-  s u b s t i t u t e d i n the  equation  d i f f u s i o n c u r r e n t at a s t a t i o n a r y s p h e r i -  electrode  ^r - ^ r  F D C A C^i  S u b s t i t u t i o n and  TrSr)  i n t e g r a t i o n gave the equation  (xxx) f o r the  diffusion  current From equation  (LXV)  the t r u e d i f f u s i o n c u r r e n t c o n s t a n t , l o , i s  Strehlow and equation  S t a c k e l b e r g have a l s o derived a  f o r the p o l a r o g r a p h i c  i s s i m i l a r to that obtained  d i f f u s i o n current.  by Lingane and  new  Their  Loveridge's  equation  somewhat  1. The p u b l i c a t i o n d e a l i n g with t h i s c o r r e c t i o n has not b een l o c a t e d so f a r .  19. a r b i t r a r y procedure. In t h e d e r i v a t i o n shown by K e l t h o f f and Lingane we  have  and However,the r e l a t i o n from equation (XXXV) was  not s u b s t i t u t e d f o r t h e term r  Strehlow and Staokelberg  4  /O 2*i"  i n equation  %t  ~  (XLI).  have made t h i s s u b s t i t u t i o n and o b t a i n  J>((^rO*f£^  +- zL«>*-rr> | % 7  with t h e c o n d i t i o n s f o r C^  z  ^ C^ D  {  m  /*»o Cv^0  = C  i  I  , o ~ ®  Equation (LXVII) i s expanded to  ,3 is  the p r o p o r t i o n  o f d i f f u s i o n volume to drop volume  and,under p o l a r o g r a p h i c  conditionsjSmall  compared to 1.  Then,  i n d i c a t i n g the middle v a l u e o f the d i f f u s i o n l a y e r by'd' so that  Sl--^o  and  s£=^U*  , (djLtf^2i^  rv  ft  + ol  rr  3  ^  d-t  Since the d i f f u s i o n l a y e r d i s p r o p o r t i o n a l p r o p o r t i o n a l to (  L  ) then 3  - §MLXIX) jjD'C and SIo i s  i s proportional  tol/' 2'^7?  The v a l u e o f ^rCTis about 0.15 and t h e r e f o r e not t o be d i s r e g a r ded- . 1  Hence,both terms l i n e a r i n -TT^are kept, t h e higher  terms are n e g l e c t e d .  1. See r e f e r e n c e  The approximation i s then  ( *f ) page 56.  20. T h i s equation i s not  exactly solvable.  s o l u t i o n assume that  ^.j-  p o s i t i v e , and average  For an approximate  i s s m a l l compared to 1 and  d u r i n g the drop time a t every p o i n t has a constant  value  .  As  grows w i t h £~M;he average  from the c e n t r a l v a l u e i s s m a l l .  /  -t  Then equation (LXX) reads  Equation  '  - ^ s = C  (LXXI)  2)^  can be transformed  yy  '  deviation  Set  and  -frf  i s always  ^~  ^  7)^J  (LXXI)  to an equation o f the type  ?>y^-  (LXXII) ufa  with c o o r d i n a t e s  —\\  y., so"**-, y ^ r * ^  I f one n e g l e c t s the terms that m u l t i p l y with t h e r e f o r e s m a l l compared to the r e s t  i s then  and  are  then  The boundary c o n d i t i o n s are g i v e n as b e f o r e .  (LXXIII)  (a-rl)  0  The s o l u t i o n o f  I  (LXXIV)  with  e c u r r e n t i s g i v e n Dy Ft*  2^To  r^,  ^^ ^<LXXVI) 7  3 ^ c _ C J ± _ _ —  S u b s t i t u t i n g i n equation  7)cTl  (LXXVI)  flow  _J  -  '  >.  ~~zJ~^0  "^"3""^)  (LXXVIII)  21. I f a l l powers o f e except  the f i r s t a r e n e g l e c t e d one o b t a i n s from  (LXXVII)  ,  When  .  y' i s expressed  1  i / ,  "  \  by 'nu' i n mgm/sec. and ' C i n m i l l i -  m o l e s / l i t r e and ' i ' i n microamperes a f t e r oompiling t h e c o n s t a n t s and  integrating  From equation ^ and  ^  (LXIX) %T4  ^  -^n~3  upon s u b s t i t u t i n g i n equation  (LXXXI)  (LXXX)  From t h i s i s shown t h a t t h e d i f f u s i o n constant  A =•  whioh was found not to be a constant p r a c t i c a l l y not a constant  ITT--^  {/o ) i s a l s o  theoretically.  In order to c a l o u l a t e t h e constant A we make use o f the d e r i v a t i o n o f the I l k o v i o equation as g i v e n by M.van S t a c k e l b e r g (W).  % ~ -^V^=r )  Here two d i f f u s i o n l a y e r s were d e f i n e d  (ixxxin) /  and  S  >  f  (^-C0)  (LXXXIV)  The c u r r e n t d e n s i t y i s now  ^°  -  looo  E - r -  %  where q i s the drop a r e a  /\  i s p r o p o r t i o n a l to the d e c r e a s i n g p a r t s  By combining these  then  equations  .  (ixxxv)  22. For  l i n e a r d i f f u s i o n , t h e d i f f u s i o n laws y i e l d  &  ~ ^jf  Substituting The  £ By  %  (LXXXIX)  ^^-^  i n equation ( U X X V I I )  solution i s  1  j0  ^''o/t  2  (zo)  = \J ^TTDr  a combination o f equations (LXXXV) (LXXXVIII) and (XC) and  converting  to t h e u n i t s proposed by K a l t h o f f and Lingane one  o b t a i n s t h e I l k o v i c equation ( I I ) . The  s i m p l i f i c a t i o n i n these d e r i v a t i o n s  assumption that  l i e s i n the  d i f f u s i o n to a plane s u r f a o e t a k e s p l a c e .  s i m p l i f i c a t i o n s a r e equivalent  These  to t h e assumption that t h e d i f -  f u s i o n l a y e r i s very s m a l l oompared to t h e r a d i u s o f t h e mercury drop.  The r e l a t i o n ""^ must a l s o be c a l c u l a t e d  to a s p h e r i c a l s u r f a o e .  for diffusion  The p l a c e and time dependanoe f o r  dif-  f u s i o n to a sphere i s g i v e n by  l^^'^Y  Co--c^ --cO-1f)+^ c  That i s  S\ — //<>  ^  (xxvii)  y~  i s a c c o r d i n g to d e f i n i t i o n (XCI) Setting  (XXVII) i n (XCI)  "  J  r  This the  ^.-r^lfr  ^  >o  .  _  7  ^  'Heifer 5  +  logarithmic  terms i n s e r i e s  W  (XCII)  'Z^o^djyi  i n t e g r a l would s o l v e i n an approximate manner by p u t t i n g Integra"  (<si° - ^ s i o — 1. See equation (XCV). Wa.en.yto fusion exists. 2. See e q u a t i o n (XCVIII)  ^ ^ 'J^-^rXr becomes i n f i n i t e , l i n e a r  dif-  23. I f X i s very small compared to SI* then t h e sum o f the f i r s t two terms o n l y a p p l i e s 4 ^  ^  f ^ f b X C^^'  "^y)-^ <?/?  i s a c c o r d i n g to d e f i n i t i o n  £ -  "T§^)  By i n s e r t i n g G from  (LXXXIII)  (XXVII) (XOIV)  from (XOIII) and (XCIY)  ,J^r-.  ,  S u b s t i t u t i n g (XOV) i n (LXXXVII) one o b t a i n s the i n t e g r a l equation  v. Assuming that the term term i n the time O  Vj^Jjf^l  to ZT  as the smallest  correction  , a constant average v a l u e JZ' i s  assumed.  Equation (XOVI) becomes  A solution i s Substituting  ^  f**"  Z/^/^'X^-^j  ^  £ - / - 2 - —  T O Since the e x p r e s s i o n on the l e f t  i s a constant then  and i t f o l l o w s  A For  -  -  £-  i from equations (LXXXV) (LXXXVIII) and (XCVIII)  ^-77 —  V  24. I YfiTir .  was l ^ - ^ a n d  \Tiny£^-  w _  Then  S u b s t i t u t i n g f o r the constant  u^cm^zrz  jjzco^ The  constant  Z^QTZT)  f o r a growing drop  3  - 3 V- / A i n equation  (i+  3  (LXXXII)  n p ^ ^ i ' ^  c±)  <iv)  A may also be d e r i v e d from the geometry o f the  mercury drop and the d i f f u s i o n l a y e r as shown i n F i g i 2 .  A is  the mercury drop, B i s t h e c y l i n d r i c a l d i f f u s i o n volume that i s alone considered  i n t h e d e r i v a t i o n o f t h e I l k o v i o equation.  However the r e a c t a n t d i f f u s e s to the curved  s u r f a c e ab through  the r e g i o n C ( i n c r o s s s e c t i o n a l view - wedge shaped). Instead o f equation  -CJ  r  6o7—  D ^ C ^  ( i i ) may a l s o be considered 3  ^  ~C±  C l + ~ > )  (0).  Where X i s the r e l a t i o n o f volume C to t h e volume B. r s  r a d i u s o f mercury drop  d ?  t h i c k n e s s o f the d i f f u s i o n l a y e r .  Volume B ( f o r the whole drop) Volume B*0 The  -  correction factor  Sinoe  )+ X  d under p o l a r o g r a p h i c  the term -^-z-can p o r t i o n a l to I/DV  3 TT/h  ~0  -<7  3  i s g i v e n by  y  c o n d i t i o n s i s s m a l l compared to r  be disregarded.« as d i f f u s i o n l a y e r i s pro%  r as drop r a d i u s i s p r o p o r t i o n a l to (syr\  cL Therefore the c o r r e c t i o n term - ^ T . can be giv«n  FIG.  Z.  Schematic Diagram o f Mercury Drop and the D i f f u s i o n Layer  •  25.  From these simple ways equation (LXXXII) i s o b t a i n e d . To c a l c u l a t e t h e v a l u e o f A approximately we assume a l i n e a r decrease o f the c o n c e n t r a t i o n and s e t c/~ i s g i v e n by Therefore  %7 7 ^ ~  3/-  f~y TT^C^  % -  ^ IT 3S5T" 3T ^0  1  .  ,  ,  .  Though t h e c l o s e r to the surfaoe extends t h e s o l u t i o n so that more i s c o n t r i b u t e d to the c u r r e n t d e n s i t y i t must be averaged  over d.  A  For A by l i n e a r decrease o f c o n c e n t r a t i o n  -^-^  -  iv- %  T h i s v a l u e i n view o f the omissions i n t h e I l k o v i c is satisfactory.  still  derivation  From t h e p r e v i o u s d e r i v a t i o n A » 17 which i s  i n b e t t e r agreement with experiment  and jtherefore^ s h a l l be  assumed v a l i d . For a reaotant w i t h a d i f f u s i o n c o e f f i c i e n t i.ox.to~  the c o r r e c t i o n term i s Hi/To Since the q u a n t i t i e s ^ !  ^r^with  lO ^~3 3  commonly used  =. 0.OS^^C^ capillaries  v a r i e s perhaps about 0.5 to 1.2 t h e c o r r e c t i o n term amounts to 2.7$ to 6.5$ and i s by no means to be n e g l e c t e d . It may be mentioned t h a t t h e Lingane and Loveridge value o f A = 39 amounts to a c o r r e c t i o n f a c t o r o f 6.2$ to 15$ which appears  to be somewhat l a r g e r than t h e experimental  v a r i a t i o n demands.  When c a p i l l a r i e s o f v e r y s m a l l outflow, m,  and very l a r g e drop times a r e used longer a p p l i c a b l e sinoe larger.  the I l k o v i c equation i s no  then becomes comparable to 1 o r  The improved I l k o v i c equation may then be w r i t t e n -  K on % r - f e C 1 -h^^-'i  +- aJ^ ^ n ' H r i  )  1. The value 13530 i s taken as the d e n s i t y o f mercury i n m i l l i g r a m s per cm^ a t 25° C.  26. I f ^7?  ' then the f i r s t two  third.  For very l o n g drop times the c u r r e n t d e n s i t y should be .  terms become s m a l l compared to t h e  i  p r o p o r t i o n a l to C^as  G.S.Smith ( I S )  found  experimentally.  However, w i t h t h i c k d i f f u s i o n l a y e r s t h e r e i s g r e a t e r r i s k o f c o n v e c t i o n and the assumption o f l i n e a r d i f f u s i o n i s no  longer  admissable. The d i s s o l u t i o n o f a base metal  from an amalgam at  the dropping e l e c t r o d e as anode g i v e s a current d e n s i t y whioh i s l i k e w i s e expressed expression  by the I l k o v i c equation.  However the  used i n the p r e v i o u s d e r i v a t i o n s must be  oed by-/3.  repla-  T h i s change o f s i g n merely r e s u l t s i n a n e g a t i v e s i g n  i n the c o r r e c t i o n term.  By an approximation  Strehlow  and  STACK £/.  Schlcoinger ( faotor 1.5  B  have evaluated the value o f the c o r r e c t i o n  i n the term  /—  S J)~7-<^n  ~C  to 2 times the v a l u e o f A i n the term / -f-  to be  A  D'T-  -Tvt " -  5  Since A has been accepted as 17 then B would l i e i n the range o f values  25-35. A second e f f e c t causes the value o f B to be  than A i n that the r a t i o  i s no longer very s m a l l .  larger In view  o f the c o n c l u s i o n s drawn with respect to the t r a n s p o r t o f metals  d i s s o l v e d i n mercury t h e n ^  In r e a l i t y t h e streaming }  =• / i s not  e f f e o t caused  inadmissable.  by the o u t f l o w current  from the c a p i l l a r y complicates the problem c o n s i d e r a b l y . Strehlow and  S t a c k e l b e r g have determined  the v a l u e o f B as  when a cadmium amalgam i s used as the dropping e l e c t r o d e .  28.5  27 (2)~DROPPING AMALGAM  In 1939,J.J.Lingane  ELECTRODES  ( / ) p u b l i s h e d a note  reporting  the q u a l i t a t i v e behaviour o f a dropping cadmium amalgam e l e c trode In polarography o f cadmium s u l f a t e s o l u t i o n . 0.01$ cadmium amalgam dropping i n a i r f r e e O.IW  Using  potassium  c h l o r i d e s o l u t i o n c o n t a i n i n g 0.04 M cadmium s u l f a t e h e ob;  t a i n e d c a t h o d i c and anodic d i f f u s i o n c u r r e n t s f o r the reduct i o n o f the cadmium i o n i n s o l u t i o n and f o r the o x i d a t i o n o f the cadmium metal i n t h e amalgam r e s p e c t i v e l y . branohes formed a s i n g l e p o l a r o g r a p h i c wave.  The two The anodic  d i f f u s i o n c u r r e n t showed a •maxima' which was e l i m i n a t e d by the a d d i t i o n o f 0.1 ml. o f 0.1$ methyl  r e d . He s t a t e d  that  t h i s i s evidence that the p o l a r o g r a p h i c 'maxima' i s a phenomena o f the s o l u t i o n s i d e o f t h e s o l u t i o n metal  interface.  In 1940 M.v.Staokelberg and H.v.Freyhold ;  ( l~T)  included a paragraph on the dropping z i n c amalgam e l e o t r o d e i n t h e i r paper on t h e d e t e r m i n a t i o n o f the c o o r d i n a t i o n number o f metal ions i n complex f o r m a t i o n by the s h i f t o f the p o l a r o g r a phic  'half-wave' p o t e n t i a l .  Using 0.005$ z i n c amalgam dropping  i n 0.01M z i n c s a l t s o l u t i o n s w i t h potassium  c h l o r i d e o r potas-  sium n i t r a t e as s u p p o r t i n g e l e c t r o l y t e t h e y obtained a s i n g l e ;  wave f o r the anodic and c a t h o d i c branches currents.  o f the d i f f u s i o n  The s i n g l e wave i n d i c a t e d almost  l i t y o f the e l e o t r o d e r e a c t i o n s .  complete  reversibi-  However, w i t h IN potassium  hydroxide the anodic wave and the c a t h o d i c wave were separated thus i n d i c a t i n g an i r r e v e r s i b l e e l e c t r o d e r e a c t i o n .  38. Although no q u a n t i t a t i v e data was presented i n the above papers, K o l t h o f f and l i n g a n e (If?) s t a t e that the anodic d i f f u s i o n c u r r e n t s obtained w i t h the dropping amalgams were o f the order o f magnitude expected on the b a s i s o f t h e assumpt i o n t h a t the I l k o v i c equation h e l d good. Late i n 1940, J.Heyrovsky  and M.Kalousek ( )°J)  p u b l i s h e d an account o f t h e i r work with very d i l u t e amalgams o f copper, cadmium, lead and z i n c .  This work had been announ-  ced i n 1938 thus c r e d i t i n g these workers with the i n i t i a l i n v e s t i g a t i o n s o f amalgam polarography.  (Since t h e i r paper i s  not immediately a v a i l a b l e a copy i s i n c l u d e d w i t h t h i s work). However, they added nothing to the q u a n t i t a t i v e data with respect to the a n o d i c d i f f u s i o n c u r r e n t . oontinued  Heyrovsky's  (2.0)  i n v e s t i g a t i o n s have l e d to an o s c i l l o g r a p h i c  techni-  que f o r r e c o r d i n g c u r r e n t - v o l t a g e curves a t dropping o r streaming mercury e l e c t r o d e s .  Electrodepositions  involving  s i n g l e e l e c t r o n t r a n s f e r s and some few E - e l e c t r o n t r a n s f e r s show the anodic and c a t h o d i c d e p o l a r i z a t i o n wave at the same potential.  However, f o r most e l e c t r o d e p o s i t i o n s  involving  £-electron t r a n s f e r s the p o t e n t i a l o f the anodic wave i s d i f f e r e n t from the p o t e n t i a l o f the c a t h o d i c wave.  I t may  be noted that the c a t h o d i c wave i s due to the r e d u c t i o n o f t h e i o n i n s o l u t i o n to form a d i l u t e amalgam.  The r e v e r s a l o f the  p o t e n t i a l sweep i s so r a p i d that the amalgam formed by the cathodic sweep i s discharged on the anodic sweep even when a streaming mercury e l e c t r o d e i s used.  Prom the r e s u l t s o b t a i n e d  so far^Heyrovsky has deduced that a 2 - e l e c t r o n t r a n s f e r i s a two step p r o c e s s .  One e l e c t r o n i s accepted: i n an e l e c t r o l y t i c  29. process: The  ^  ^  + +~  ^  —  o t h e r e l e c t r o n i s acquired  ^  ^  +  by d i s m u t a t i o n :  U n f o r t u n a t e l y ,t he r e s u l t s a r e reported  more o r l e s s q u a l i t a -  t i v e l y and the s i g n i f i c a n c e o f Heyrovsky's deduction cannot presently  be a p p r e c i a t e d .  amalgam e l e c t r o d e s  Comparisons o f the behaviour o f  i n the p o l a r o g r a p h i c  and o s c i l l o g r a p h i c  techniques should be u s e f u l . In 1947, J.E.B.Randies ( A / ) used a form o f the polarographic of electrode  c a p i l l a r y electrode reactions  amalgam e l e c t r o d e s  i n h i s study o f the k i n e t i c s  with a l t e r n a t i n g c u r r e n t .  (copper, cadmium, t h a l l i u m and z i n c ) were -  used where an a u x i l i a r y d i r e c t current a c r o s s the amalgam r e s e r v o i r . a siphon from the r e s e r v o i r . circuit  Dropping  c i r c u i t was maintained  The c a p i l l a r y was a t t a c h e d to The purpose o f the a u x i l i a r y  i s to s t a b i l i z e the d i l u t e amalgams. A s i m i l a r technique has been used i n t h i s work and  i l l u s t r a t i o n s are shown elsewhere. Also the  i n 1947, T.Erde Graz and E.Varga (XX)  e f f e c t o f non e l e c t r o l y t e s on the e l e c t r o d e  amalgams.  reported  potentials of  The p o t e n t i a l s o f r e s t i n g and dropping amalgams o f  bismuth, copper, t h a l l i u m , l e a d and z i n c were dsetermined i n solutions of various dine, o - o r e s o l ,  isoamyl a l c o h o l , b e n z y l a l c o h o l , o - t o l u i -  p-cresol butyric  make the s o l u t i o n s  r  a o i d and v a l e r i c a c i d i  To  e l e c t r i c a l conductors^ sodium s u l f a t e was  added and the s o l u t i o n s and apparatus were c a r e f u l l y f r e e d o f oxygen.  When the amalgam c o n c e n t r a t i o n s were above 1 0 ~ to 5  10-4 gram atoms per l i t e r ^ t h e e l e c t r o d e reproducible  to m i l l i v o l t s .  p o t e n t i a l s were  The p o t e n t i a l s a r e determined  30. p a r t l y b y t h e a d s o r p t i o n o f i o n s and n e u t r a l d i p o l e m o l e c u l e s on t h e l i q u i d  side o f the solution - metal i n t e r f a c e , partly  by t h e a d s o r p t i o n o f m e t a l i o n s o n t h e amalgam s i d e o f t h e double l a y e r .  The a d s o r b e d m e t a l i o n s f o r m t h e p o s i t i v e p a r t  o f t h e d o u b l e l a y e r c r e a t e d w i t h i n t h e amalgam. part consists o f diffusely t a l technique  and d a t a  distributed  The n e g a t i v e  electrons.  (Experimen-  i s not a v a i l a b l e since only the abstract  o f t h e i r paper i s p r e s e n t l y o b t a i n a b l e ) . In 1948, F . L . E n g l i s h  (23) reported  c h a r a c t e r i s t i c s o f copper, gold, s i l v e r , at polarographic cury  electrodes.  t h e drop time  t i n and z i n c  amalgams  Z i n c m e t a l was d i s s o l v e d i n mer-  and t h e amalgam a f t e r f i l t e r i n g t h r o u g h c h a m o i s was washed  w i t h m e t h a n o l and a c e t o n e t o remove g r e a s e a n d o i l .  0.01$ and  0.0001$ z i n c amalgams g a v e t h e u s u a l t y p e o f d r o p t i m e  versus  voltage curve i nt h e negative  similar  voltage range.  However,  t o p u r e m e r c u r y , i n t h e v o l t a g e r a n g e - f - 0 . 3 v o l t t o -0.6 v o l t a h i g h degree o f d i s c o r d a n c e found.  among r e p e a t e d  In the positive voltage  d r o p were e x c e e d i n g l y  irregular  determinations  was  r a n g e the p e n o s c i l l a t i o n s p e r i n both shape and  amplitude.  The e l e o t r o l y t e s u s e d i n t h i s w o r k w e r e 0.11 p o t a s s i u m c h l o r i d e and  0.1N t e t r a m e t h y l ammonium c h l o r i d e w i t h  sometime a d d i t i o n  of methyl red or g e l a t i n . A f t e r t h i s w o r k had s t a r t e d a p a p e r b y S t r e h l o w a n d Stackelberg  (9) reported  cadmium amalgam accuracy.  the d i f f u s i o n current f o r dropping  eleotrodes.  A m a n u a l c i r o u i t was e m p l o y e d f o r  A l l m e a s u r e m e n t s were made i n 0.1H p o t a s s i u m c h l o r i d e  w i t h 0.01$ g e l a t i n a t 25.0°C ±;0.4° a f t e r t h e s o l u t i o n was swept out w i t h n i t r o g e n .  The t e m p e r a t u r e was m e a s u r e d t o 0.1° and t h e  30a d i f f u s i o n c u r r e n t c o r r e c t e d by c a l c u l a t i o n to 25.0°. values f o r ' i '  and ' t ' were determined  The  i n the solution a t the  same time the d i f f u s i o n current was measured.  A cadmium  amalgam 13.92 m i l l i r n o l a r was used w i t h d i f f e r e n t  dropping  c a p i l l a r i e s where the pressure was v a r i e d from 37 cm - 110 cm ^  -r  The d i f f u s i o n c u r r e n t constant J. = ^  o f mercury.  ^rzr_z so d e t e r -  mined v a r i e s up to 2% f o r d u p l i c a t e d e t e r m i n a t i o n s . I and  i s found  to v a r y c o n s i d e r a b l y with changing v a l u e s o f 'm'  ' t ' . F o r d i f f e r e n t c a p i l l a r i e s the values o f 3  p l o t t e d versus y, where asymptotic and  However,  to a s t r a i g h t  c <- .  were  The ourves beoame  l i n e f o r the l a r g e r v a l u e s o f 'm*  ' t ' . From t h e d i f f u s i o n c u r r e n t equation f o r amalgam  anodes (Equation V/) can be obtained Therefore,a plot o f I  versus y would y e i l d  the v a l u e o f  607 n Dg- from the i n t e r c e p t and t h e v a l u e o f BD-J from t h e slope.  Since the curves were asymptotic to a s t r a i g h t  line,  Strehlow and S t a c k e l b e r g used t h e values o f i t s i n t e r c e p t and slope f o r t h e determination of the d i f f u s i o n c o e f f i c i e n t of cadmium i n merojiry and t h e value of t h e n u m e r i c a l constant B. T h e i r experimental v a l u e f o r the d i f f u s i o n c o e f f i c i e n t a t 25.0°G  1.52 X 10~5 cm  2  sec-1 i s i n e x c e l l e n t agreement w i t h  the v a l u e reported i n t h e l i t e r a t u r e 1.520 X 10*5 c m s e c - l a t 2  20.0°G.  The value o f B i s determined  as 28.5.  When t h e value o f B i s c a l c u l a t e d from the g i v e n data it  i s found  that the values vary c o n s i d e r a b l y .  which l i e c l o s e to t h e s t r a i g h t  For those p o i n t s  l i n e B v a r i e s from 24 to 29.  As t h e d e v i a t i o n i n c r e a s e s the v a l u e f o r B becomes more n e g a t i v e and a value -90.'9 has been c a l c u l a t e d .  I t i s shown that the  30b v a l u e o f B d e c r e a s e s w i t h i n c r e a s i n g p r e s s u r e o f t h e amalgam column.  Assuming t h a t t h e ' r i n s i n g ' e f f e c t  i s t h e major  of error^then as t h e outflow current decreases c u r r e n t becomes more t r u l y r e l a t e d and  to a d i f f u s i o n p r o c e s s  alone  The l i m i t i n g  l i e s w i t h i n t h e r a n g e 25-35 a c c o r d i n g t o t h e o r e t i c a l a p p -  roximations. all  thee l e c t r i c a l  t h e value o f B approaches a l i m i t i n g v a l u e .  value  source  Actually,  a r a n g e 21-35 i s o b t a i n e d  the t h e o r e t i c a l approximations  Stackelberg.  i f one c o n s i d e r s  g i v e n by S t r e h l o w and  I n o u r own w o r k i t w i l l b e c o n s i d e r e d t h a t t h e  larger  values f o r B indicate  t h a t t h e o u t f l o w c u r r e n t does not  unduly  d i s t u r b t h e d i f f u s i o n p r o c e s s a t t h e amalgam d r o p s u r f a c e .  I t s h o u l d b e m e n t i o n e d t h a t S t r e h l o w a n d S t a c k e l b e r g do n o t d e s cribe any  t h e p r e p a r a t i o n o f t h e cadmium amalgam n o r do t h e y  technique  mention  f o r o v e r c o m i n g t h e i n s t a b i l i t y o f t h e d i l u t e amalgam.  Heyrovsky  ( 6 4 ) n o t i c e d t h a t t h e r e i s no d i f f e r e n c e  b e t w e e n t h e maximum o n t h e c u r r e n t - v o l t a g e c u r v e s o f cadmium amalgam a n d t h e maximum e x i s t i n g o n t h e c a t h o d i c w a v e s . I s made t o e x p l a i n t h e e v i d e n c e o f t h e p o l a r o g r a p h i c maxima. an  mercury.  i n the l i g h t o f Ilkovic's  This theory  inhomogeneous e l e c t r i c f i e l d  to t h e t h e o r y . c a p i l l a r y zero  theory  i s based on t h e i d e a o f  at a potential  corresponding  c a p i l l a r y z e r o ^ t h e maximum c a n n o t e x i s t  according  However, t h e e x p l a n a t i o n i s g i v e n t h a t t h e e l e c t r o i s s h i f t e d by t h e a n i o n s ^ w h e r e a s t h e r e d u c t i o n o r  oxidation potential the observed  attempt  due t o t h e c h a r g i n g o f t h e d r o p p i n g  S i n c e cadmium i s r e d u c e d  to t h e e l e c t r o  An  o f cadmium r e m a i n s u n c h a n g e d and t h e r e f o r e  maximum.  31  C - ZING AMALGAMS (1)—METHODS OF PREPARING ZINC AMALGAM The l i t e r a t u r e  (24) r e p o r t s many v a r i a t i o n s o f t h r e e  b a s i c methods used i n t h e p r e p a r a t i o n o f z i n c amalgams. methods may be  These  enumerated: 1.  Simple contaot o f z i n c metal and mercury.  2.  E l e c t r o l y t i c r e d u c t i o n of z i n c s a l t s a t the mercury cathode.  3.  Chemical r e d u c t i o n o f zino s a l t s by a l k a l i metal amalgams.  In a d d i t i o n , t h e r e i s the method o f H u l e t t and De Lury (25)(26) where z i n c metal i s i n contact w i t h the mercury  cathode  under  a l a y e r o f d i s t i l l e d water which c o n t a i n s the p l a t i n u m anode. D i s s o l u t i o n of t h e z i n c metal proceeds r a p i d l y when t e n v o l t s d i r e c t ourrent a r e impressed.  P r e l i m i n a r y experiments,  reported elsewhere, showed that the method o f H u l e t t and De Lury i s by f a r the b e s t f o r p r e p a r i n g standard z i n o amalgams.  32.  C (8)—CHEMICAL AID PHYSICAL PROPERTIES OP 2IIC AMALGAMS The  s o l u b i l i t y o f z i n c i n mercury has been reported  as 2.2199 grams o f z i n o i n 100 grams o f mercury a t 25°C.  Ho  evidence o f i n t e r m e t a l l i o compounds i s shown by the f r e e z i n g p o i n t diagram. med  The non  e x i s t e n c e o f such oompounds i s c o n f i r -  by o b s e r v a t i o n s on the s o l u b i l i t y , e l e c t r i c a l r e s i s t a n c e ,  s p e c i f i c volume, vapour p r e s s u r e and v a r i o u s o b s e r v a t i o n s on the e l e o t r o m o t i v e f o r c e o f z i n c amalgams ( 2 V ) . (2.7)  Forbes  suggested  R i c h a r d s and  t h a t the d e v i a t i o n o f the e l e c t r o m o t i v e  f o r c e v a l u e s from the v a l u e s c a l c u l a t e d by the l e r n s t  equation  could be e x p l a i n e d by p o l y m e r i z a t i o n of the z i n c atoms.  Hulett  and Crenshaw {2-L) r e p o r t t h a t i n the range 0.006IU - Q. 000003 S^WJ,  where I = mole f r a c t i o n the p o t e n t i a l d i f f e r e n c e between  any two  amalgams conforms to the laws o f a p e r f e c t  solution.  However, the v a l u e s reported by Richards and Forbes did not agree  with the v a l u e s r e p o r t e d by H u l e t t and  t i o n a l l y , no two  f a u l t could be found  groups o f c a r e f u l workers.  Crenshaw.  i n the methods used by  Hildebrand  Addithe  (2.^) measured the  vapour pressure o f zino amalgam and found that the data o f R i c h a r d s and Forbes  conformed to the laws o f i d e a l  solutions  when the presence o f a diatomic molecule,Zn2,was p o s t u l a t e d . P i e r c e and E v e r s o l e (Z°f ) repeated the e l e o t r o m o t i v e f o r c e measurements and and F o r b e s .  found good agreement w i t h the data o f Richards  Crenshaw (3<5)  then showed t h a t the d a t a o f the  t h r e e papers could be made to agree by c o n s i d e r a t i o n o f a s i n g l e a r b i t r a r y constant.  L i e b h a f s k y (31  ) r e p o r t e d t h a t the data o f  33. a l l the papers were i n agreement when the measurements were r e f e r r e d to the p o t e n t i a l o f the two phase z i n c amalgam* Furthermore, he showed that the amalgams conform to  ideality  over the e n t i r e range o f composition s t u d i e d when i t was p o s t u l a t e d that z i n c metal i n s o l u t i o n was atomic, diatomic and t r i a t o m i c z i n c .  present as mono-  He proposed t h a t the  c o n c e n t r a t i o n s o f extremely d i l u t e amalgams c o u l d he  oaloulated  a c c u r a t e l y by means o f the Nernst equation from the v a l u e s o f E.M.F. measurements.  T h i s p r o p o s a l may  f i n d some f u r t h e r  a p p l i c a t i o n i n determining the c o n c e n t r a t i o n o f the amalgams used i n polarography. shown t h a t  However, from the f o r e g o i n g i t has been  d i l u t e z i n c amalgams a r e unique  to the laws f o r i d e a l  i n t h a t they  conform  solutions.  A l l o f the above quoted papers a s w e l l as s e v e r a l o t h e r s {/^ ) U 4 ) z i n c amalgams.  (3x) (33) r e p o r t on the i n s t a b i l i t y o f d i l u t e W.G.Horsoh (32.) gave up the study o f the app-  a r e n t l y anomalous behaviour o f d i l u t e z i n c amalgams. reported t h a t between two varied  samples o f the same amalgam the E.M.F.  i n an e r r a t i c m a n n e r , f a l l i n g and r i s i n g r a p i d l y .  own work i t was  impossible to f i n d  evidence o f z i n c  polarograms o f amalgams whioh had been exposed night .  He  In our  from  to a i r o v e r -  (Although the l i m i t s o f d e t e c t i o n have not been reaohed  at 0.1 ppm  there i s reason to b e l i e v e that i t w i l l be found o f  the o r d e r 0.001 the waveheight  ppm.  T h i s l a t t e r f i g u r e b e i n g estimated from  shown by a v e r y d i l u t e amalgam and  v i t y s e t t i n g s o f the r e c o r d i n g apparatus.) (2-7) found that when oxygen was  the s e n s i t i -  R i c h a r d s and  removed from t h e i r  solutions  the E.M.F. v a l u e s f o r the very d i l u t e amalgams f i t t e d  I  Forbes  i n with  34. the  data obtained w i t h more concentrated amalgams.  t h i s i s evidence t h a t oxygen p l a y s some p a r t l e a d i n g to i n s t a b i l i t y ^ l i e b h a f s k y  Although  i n the r e a c t i o n s  ( 3 3 ) s t a t e s that even i n the  absence o f oxygen the amalgams tend i n c r e a s i n g l y to l o s e z i n c as they become more d i l u t e .  I t i s also known t h a t hydrogen gas  i s not r e a d i l y evolved from d i l u t e z i n c amalgams immersed i n a c i d s o l u t i o n s UH ). rate o f oxidation  A c c o r d i n g to l i e b h a f s k y j t h e  i n c r e a s e s only  centration of zinc.  absolute  s l i g h t l y w i t h i n c r e a s i n g con-  He has p o s t u l a t e d  the f o l l o w i n g  reaotions  to e x p l a i n the experimental evidence obtained with d i l u t e z i n c amalgams i n s u l f u r i c a c i d s o l u t i o n s .  A rapid  e x i s t s between the amalgam and amalgam Amalgam The  0  -h  2  surfaoe:  ~h  y Amalgam s u r f a c e  r a t e determining  equilibrium  electrons  step:  J- 2H~^  2 electrons  ^  HgOg  A rapid follow reaction: Amalgam s u r f a c e 1 The  )  =  Amalgam surfaoe  e l e c t r o n d e n s i t y at the amalgam s u r f a c e  -/-  i s regarded as a  constant depending on space and charge f a c t o r s .  Thus^in  clean-  i n g mercury the removal o f z i n c becomes p r o g r e s s i v e l y  e a s i e r as  the c o n c e n t r a t i o n  instabi-  lity  o f z i n c decreases.  In view o f t h i s  i t i s not s u r p r i s i n g t h a t few papers r e p o r t  o f d i l u t e amalgams a t the c o n c e n t r a t i o n s polarographic  required  investigations i n the  technique.  There i s some c o n s i d e r a b l e  l i t e r a t u r e which  deals  with s u b j e c t s p e r t a i n i n g to o r a p p l i c a b l e to t h i s work. normal e l e c t r o d e p o t e n t i a l o f z i n c has been determined by s e v e r a l workers as shown i n Table 1.  The  35. TABLE 1. THE NORMAL ELECTRODE POTENTIAL OP ZINC INVESTIGATOR Hor8Ch  E.M.F.Volts 0.758  REP.  TETT  Scatchard and T e f t  0.7610(corr.)  (3V)  Getman  0.7613  (3b~)  Shrowder.Cowperthwaite and LeMer  0.7614(corr.)  (34):  The c o r r e c t i o n s noted  i n Table 1 r e f e r to the c o r r e c t i o n f o r t h e  E.M.P. between z i n c metal and the two phase z i n c amalgam i n z i n c salt solutions.  The v a l u e s determined by v a r i o u s workers a r e  shown i n Table 2. TABLE 2 i THE ELECTROMOTIVE FORCE OF ZINCZINC AMALGAM INVESTIGATOR Cohen  E.M.F.MILLIVOLTS 0.570  Puschin Clayton and Vosburgh  REF. (37 )  -2.0  ( 3S")  0.0  ( 39 )  For the v a l u e o f the p o t e n t i a l d i f f e r e n c e between z i n c amalgams H u l e t t and Crenshaw found t h a t i n the range 0.006IN-0.00000307N, where N - mole f r a o t i o n , t h e simple equation h e l d t r u e E:Et  nF  where  E R T n F In C s  5 = = = « a  l n Ci  %  electromotive force t h e gas constant a b s o l u t e temperature e l e c t r o e q u i v a l e n t s p e r mole Faraday n a t u r a l loganthm c o n c e n t r a t i o n s o f r e s p e c t i v e amalgams.  35(a)  Richards  and Forbes (27) have p u b l i s h e d a t a b l e showing t h e  e l e c t r o m o t i v e f o r c e between z i n c amalgam and amalgamated z i n c i n z i n c s u l f a t e s o l u t i o n as determined by e a r l i e r workers. The only r e f e r e n c e they g i v e i s "Lindeck  1888".  The values are shown i n Table 3.  TABLE 3. EMF Z i n c Amalgam v s . Amalgamated i n Zinc S u l f a t e S o l u t i o n . % Zinc 1.860 0.467 0.064 0.028 0.0014 0.0010 0.00038 0.00027 0.00020 0.00015  Zino  E.M.F. 0.003 v o l t 0.022 0.047 0.057 " 0.096 " 0.11 0.13 " 0.14 " 0.15 0.16 n  36. Hildebrand ^O)  from h i s f i n d i n g s on the vapor pressure  amalgams p l u s the data p u b l i s h e d  by R i c h a r d s and  the f o l l d w i n g equation f o r the eleotromotive 2.• ^Q'L  amalgams, where  -Z F  N  L  0  zinc of  zino  Forbes^ g i v e s  f o r c e between zino  /Tv^T//  A/, r 2-  s u b s c r i p t - mole percent  of  respective  amalgam the remaining symbols having the p r e v i o u s l y meaning. P i e r c e and  Eversole  (2*?) g i v e the f o l l o w i n g E = RT In nF  where Ag,  ag = a c t i v i t y o f z i n o i n the  r e s p e c t i v e amalgam. f o r the a c t i v i t y o f z i n c  o f mercury i n z i n o amalgams as w e l l as f o r f r e e energy,  entropy and  temperature  Liebhafsky hed  relation  A2 a2  These workers have g i v e n t a b l e d v a l u e s and  given  coefficients.  (SlJ^by r e c a l c u l a t i n g previously p u b l i s -  data^has e s t a b l i s h e d the  relation  E s 0.09922 T l o g ^ Z m ^ *2 z  where  isLZn sub  - terms f o r e q u i l i b r i u m oonstants and c o n c e n t r a t i o n t i v e amalgams.  The  l o g terms are based on the assumption o f a r a p i d  between monoatomic, diatomic 2n The  o f z i n c i n the  best values  and Zn  respecequilibria  t r i a t o m i c z i n c i n the amalgam. 2n3  2  o f the e q u i l i b r i u m constants  s o l u t i o n o f the equation are g i v e n  required  i n Liebhafsky's  Although the e l e c t r o m o t i v e  for a  paper.  f o r c e o f z i n c amalgam  37. e l e c t r o d e s appears to be w e l l e s t a b l i s h e d , t h e r e a r e few r e p o r t s on the behaviour o f z i n o amalgams d u r i n g conduction city.  of electri-  Lewis and h i s co-workers C-U ) found that a l k a l i metals  i n d i l u t e amalgams a p p a r e n t l y migrate to the anode d u r i n g the passage o f e l e c t r i c a l  current.  behaviour f o r a l l base metals.  G.Mayr {NZ) reported a s i m i l a r F.Skaupy ( £ / 3 ) (  ) concluded  that s i n c e the a d d i t i o n o f z i n c i n c r e a s e s the c o n d u c t i v i t y o f mercury c o n s i d e r a b l e i o n i z a t i o n o c c u r s .  He p o s t u l a t e d t h a t the  s o l v e n t metal and s o l u t e metal a r e i n e q u i l i b r i u m w i t h a common ion,  the e l e c t r o n .  He e x p l a i n s that the change o f e l e c t r o n  c o n c e n t r a t i o n d u r i n g the passage o f c u r r e n t induces v e l y charged metal ions t o migrate. drag along n e u t r a l atoms* i n amalgams,  t = /V U  the p o s i t i -  The p o s i t i v e ions  apparently  He g i v e s an e x p r e s s i o n f o r t r a n s p o r t  (1 + Z)  (_C_ ) (100 )  u = m o b i l i t y o f mercury c a t i o n V r " " electron Z - number o f n e u t r a l mercury moles f o r each cation G - c o n c e n t r a t i o n o f a l k a l i metal amalgam According  to K.Sohwarz (VH) and G.Wagner  during t h e passage o f e l e o t r i o i t y mercury i s almost dissociated  i n t o Eg " 1  h  ions but Hgg^ " 11  Zinc i s d i s s o l v e d i n mercury as i o n s . the i o n w i t h  i o n s cannot be  . completely excluded.  Schwarz (yC>) s t a t e s t h a t  the g r e a t e r charge d e n s i t y m i g r a t e s to the cathode.  Prom the t r a n s f e r e n c e number he has determined the d i f f u s i o n constant 3.  o f z i n c i n mercury a t 25°C and 35°G as shown i n Table  More r e c e n t l y , G . B i a n c h i  (^7) has presented  h i s f i n d i n g s on  the d i s s o l u t i o n o f metal e l e c t r o d e s i n d i l u t e amalgam s o l u t i o n s . The  r e s u l t s he obtained  i n d i c a t e some s i m i l a r i t y to the d i s s o l u -  t i o n o f metal e l e c t r o d e s i n s a l t  solutions.  Anomalies a r e  38. evident - f o r i n s t a n c e a t temperatures over 150°C t h e anode corrodes f a s t e r than the cathode, a t lower temperatures t h e oathode corrodes f a s t e r .  T h i s r e s u l t was obtained f o r the  passage o f d i r e c t c u r r e n t through copper e l e c t r o d e s i n mercury. He has a l s o found t h a t the s o l u b i l i t y o f copper i n mercury i s g r e a t l y reduced when z i n c i s p r e s e n t i n the meroury. A c c o r d i n g to Meyer (^£Q the d i s s o l u t i o n o f z i n o i n meroury lowers the s u r f a c e tensioni^of mercury water lowers i t s surfaoe t e n s i o n .  as some s a l t s i n  The a v a i l a b l e data i s g i v e n  i n Table 4 . ( . ^ TABLE 4 SURFACE TENSION OF ZINC AMALGAMS WEIGHT % ZINC  $ dynes/cm  0.661  437.1  1.221  440.4  1.750  440.0  The p u b l i s h e d v a l u e s f o r t h e d i f f u s i o n constant o f z i n c i n mercury employed.  a r e somewhat c o n f u s i n g w i t h respect to t h e u n i t s  The data has been r e c a l c u l a t e d  u n i t 8 cm2 sec-1 f o r Table 5.  f o r e x p r e s s i o n i n the  39. TABLE  5.  DIFFUSION CONSTANT OF ZINC IN MERCURY TEMPERATURE 150 C  INVESTIGATOR G.Meyer  DIFFUSION CONSTANT 2.42 x: io- Pom' eeo"" 3  35° C  10" 5 3.36 X 10" 5 2.00 X 10" 5 2.13 X 10 • 5  15° C  1.15 X 10" 5  Wogan  11*5°C  n  99.2°C  2.52  25° C  Sohwarz  n Guthrie  x  r  REF.  1  rf  (so)  tf  (so  t»  (^k)  it  ( tJL>)  Tl  )  ( Si)  Some c o n s i d e r a b l e v a r i a t i o n i s shown between the values r e p o r t e d .  For t h i s r e a s o n i t i s somewhat d o u b t f u l t h a t ;  at 25°C has  the value o f the d i f f u s i o n oonstant F u r t h e r , Samarin and  Shvartsman (53)  been e s t a b l i s h e d .  have c a l c u l a t e d the  coef-  f i c i e n t o f d i f f u s i o n o f s e v e r a l metals i n mercury from atomio r a d i i and v i s c o s i t y data by Stokes - E i n s t e i n law. - - — — — - — - ted and  For the a l k a l i and  experimental  v a l u e s were i n agreement to 10%.  f o r g o l d , l e a d , t h a l l i u m and 50$.  T h i s discrepancy  s o l u t i o n polymerize  a l k a l i n e earth metals the  i s explained  However,  i f z i n c atoms i n mercury  to form diatomic and }  triatomic  molecules.  i s apparent t h a t a s o l u t i o n o f  be considered  s o l u t i o n o f s a l t i n water.  calcula-  z i n c the d i s c r e p a n c i e s were up to  From the f o r e g o i n g i t z i n c i n mercury may  —  i n some ways s i m i l a r to a  I t i s an i n t e r e s t i n g analogy which,  perhaps, could bear f u r t h e r i n v e s t i g a t i o n . So f a r as t h i s work i s concerned the e l e c t r i c a l t r a n s p o r t o f the s o l u t e metal i s most important,sinoe process  alone.  considered  polarographic  Provided  theory demands a  diffusion  t h a t e l e c t r i c a l t r a n s p o r t may  n e g l i g i b l e then the determination  o f the  be  diffusion  40. c o e f f i c i e n t would be s t i l l complicated by the p o l y m e r i z a t i o n of zinc  i n amalgam as p o s t u l a t e d by s e v e r a l workers.  In t h i s  oase the d i f f u s i o n c o e f f i c i e n t would become a f u n c t i o n o f the concentration. the  Such a r e l a t i o n would e x p l a i n the v a r i a t i o n i n  experimental v a l u e s f o r the d i f f u s i o n c o e f f i c i e n t as w e l l  as the d e v i a t i o n o f the value c a l c u l a t e d Einstein  Law.  by the Stokes-  41. J> ~  EXPERIMENTAL  I - M a t e r i a l s and S o l u t i o n s Mercury a l l y very d i r t y .  The mercury used The mercury was  i n t h i s work was  origin-  f i l t e r e d at a o a p i l l a r y  f u n n e l and then aerated under 5$ n i t r i c a c i d f o r s e v e r a l The supernatant l i q u i d b e i n g siphoned o f f and f o u r times f o r each batch. passed  days.  renewed t h r e e or  F o l l o w i n g a e r a t i o n ^the mercury  was  i n a f i n e spray through f o u r scrubbing columns c o n t a i n i n g  5% n i t r i c a c i d , 5$ sodium hydroxide, 2.5$ n i t r i c a c i d d i s t i l l e d water i n t h a t o r d e r .  The mercury was  d i s t i l l e d at least three times. mercury s t i l l was  and  then vacuum  A f t e r each d i s t i l l a t i o n  cleaned with n i t r i c a o i d v.  the  f l u s h e d with tap  water, r i n s e d w i t h d i s t i l l e d water and f i n a l l y  dried  in a  r  stream o f dry a i r . Polarograms showed no  unexpected  mercury p u r i t y remained  ( 5^  curves.  recorded w i t h t h e f i n a l product  The D.S.Pharmaooepia t e s t f o r  )was a p p l i e d .  In t h i s work the meroury  b r i g h t l y m e t a l l i c one minute and t e n seconds  to  one  minute and t w e n t y - f i v e seconds a f t e r the appearance o f b o i l i n g at  the s u r f a o e o f t h e Zinc —  solution.  Tadanao z i n c  (99.99 +• $) was  fractured  the loosened c r y s t a l s were p r i e d o f f with h o r n - t i p p e d and weighed immediately. pure  tweezers  taken to be that o f  zino. Potassium  was  The weight was  and  chloride —  Reagent grade potassium  chloride  r e o r y s t a l l i z e d t h r e e times from doubly d i s t i l l e d water and  f i n a l l y d r i e d o v e r n i g h t at 110°C.  42. O.IN Potassium c h l o r i d e — potassium c h l o r i d e was d i s s o l v e d to  2000 ml.  14.822 gm. o f r e c r y s t a l l i z e d  i n d i s t i l l e d water and made up  C a l c u l a t e d 0.0994 I  KGL  Standard z i n c s o l u t i o n s r— Z i n c c r y s t a l s were d i s s o l v e d i n 5 ml. H i c h o l ' s H y d r o c h l o r i c A c i d ,0.P., i n a covered 250 ml. beaker.  Very l i t t l e ,  i f any, s p r a y i n g was observed.  t i o n was evaporated j u s t to dryness on a hot p l a t e a t  The s o l u 1  low heat.  The z i n c c h l o r i d e c r y s t a l s were washed i n t o a 2000 ml, v o l u m e t r i c f l a s k c o n t a i n i n g 14.822 gm,of potassium c h l o r i d e and made up to the mark w i t h d i s t i l l e d water.  A l i g u a t s were made up to the  mark with O.IH potassium c h l o r i d e s o l u t i o n . are  The z i n c standards  reoorded i n Table 6. TABLE 6. Standard Z i n c S o l u t i o n s .  lo. 1 2 3 4 5 6 7  MAKE UP  Molarity m i l l i m o l e s / l i t e r  0.0809 gm.Zn i n 2000 ml. 0.0440 " " " " 0.02695 " " " " 0.0136 " " " 25.0 ml #2 to 500 ml. 25.0 ml #2 to 1000 ml. 10.0 ml #3 to 500 ml. n  Z i n c Amalgam —  0.6187 0.3365 0.2061 0.1040 0.0168 0.0084 0.0041  In p r e l i m i n a r y work d i l u t e  amalgams prepared by simple c o n t a c t o f the metals unsatisfactory.  zinc  'proved  Whether prepared i n a i r , i n n i t r o g e n atmos-  phere, i n vacuum or under z i n c s u l f a t e s o l u t i o n a s u r f a c e f i l m was e v i d e n t .  In a i ^ a b l a c k f i l m o f z i n c suboxide appeared on  the s u r f a c e o f the mercury.  In n i t r o g e n o r i n vacuum a  c r y s t a l l i n e m e t a l l i c f i l m appeared.  The e x i s t e n c e o f these  f i l m s p r e v e n t s the p r e p a r a t i o n o f amalgams o f known c o n c e n t r a -  43. t i o n by simply weighing the two Amalgams prepared  metals before amalgamation.  under zino s u l f a t e s o l u t i o n were covered  by  c o n s i d e r a b l e amounts o f a white f l o c c u l e n t p r e c i p i t a t e which i s presumed to be a mixture o f basio z i n c s a l t s and hydroxide.  Upon exposure to a i r the amalgam was  a b l a c k f i l m almost immediately.  zino  covered  with  A l l o f these amalgams showed  a marked tendency to adhere to g l a s s .  When a s m a l l g l o b u l e  was  r o l l e d around on a c l e a n watch g l a s s s t r e a k s o f amalgam would be l e f t s t i c k i n g to the g l a s s .  On  the whole, amalgams  prepared  by these methods were not s u i t a b l e f o r use i n g l a s s apparatus nor did the method a l l o w q u a n t i t a t i v e p r e p a r a t i o n s . Amalgams prepared  by the method o f H u l e t t and  c l o s e l y resembled pure mercury so long as they were not to  a i r f o r more than a few  seconds.  exposed  However, i t i s a d v i s a b l e  that oxygen does not come i n contact with t h e amalgam at time.  DeLury  any  U n f o r t u n a t e l y , H u l e t t ' s (z (*) paper on the p r e p a r a t i o n o f  z i n c amalgam i s not  immediately a v a i l a b l e .  However, H u l e t t  and  DeLury have shown t h a t cadmium metal d i s s o l v e s q u a n t i t a t i v e l y i n mercury under the same c o n d i t i o n s .  In t h i s work  polarography  o f the water l a y e r a f t e r amalgamation gave polarograms ( F i g . STC ) which could not be d i s t i n g u i s h e d from polarograms o f water.  I t has been found that 0.008 m i l l i m o l a r z i n c s o l u t i o n s  can be d i s t i n g u i s h e d from d i s t i l l e d water by methods.  distilled  polarographic  Thus i t can be s a i d t h a t the water l a y e r a f t e r amal-  gamation c o n t a i n s l e s s than 0.5  /  per m i l l i l i t e r .  For  an  amalgam made up with 30 m i l l i g r a m s o f z i n c metal w i t h a water l a y e r o f 25 cm^  i n volume an e r r o r of the order o f O.lfo  c o n c e n t r a t i o n may  be p o s s i b l e .  in  The method o f f e r s the most  44. s a t i s f a c t o r y r e s u l t s f o r p r e p a r a t i o n o f t h e amalgams used i n polarography. The method f o r making up a standard z i n c amalgam i s described  i n t h e s e c t i o n d e a l i n g w i t h the amalgam c e l l . Calomel E l e c t r o d e Paste —  Mercurous  chloride, CP.,  was mixed with p u r i f i e d mercury to form a powdery p a s t e . Gelatin — dropped  0.2 gm.of Knox S p a r k l i n g G e l a t i n was  into 10 ml.O.II potassium c h l o r i d e and heated j u s t to  b o i l i n g or u n t i l the g e l a t i n d i s s o l v e d .  Immediately  after  d i s s o l u t i o n 20 ml.of 0. IN potassium c h l o r i d e was run i n .  This  make up i s approximately 0.6% g e l a t i n i n 0.1! potassium c h l o r i d e . 1 ml. d i l u t e d to 125 m l . i s approximately 0.005% g e l a t i n . I I Potassium c h l o r i d e —  75 grams reagent grade  potassium c h l o r i d e was made up to 1 l i t e r . Saturated potassium o h l o r i d e — sium c h l o r i d e was added to d i s t i l l e d remained  Reagent grade p o t a s -  water  u n t i l an excess  a f t e r s t a n d i n g s e v e r a l days. Saturated potassium c h l o r i d e  zinc chloride  App-  roximately 100 grams o f z i n c c h l o r i d e was added to 100 ml,of s a t u r a t e d potassium  chloride.  Saturated potassium n i t r a t e —  zinc n i t r a t e —  Pot-  assium n i t r a t e , reagent grade, was added to 109 ml, d i s t i l l e d water hours. the  u n t i l an excess remained  u n d i s s o l v e d on s t a n d i n g s e v e r a l  Approximately 150 grams o f z i n c n i t r a t e were added to  s a t u r a t e d potassium n i t r a t e . A l l chemicals used were reagent grade as s u p p l i e d by  the  U n i v e r s i t y o f B r i t i s h Columbia,  Chemicals  Storeroom.  Doubly d i s t i l l e d water was used throughout t h e e x p e r i mental p r o c e d u r e s .  45  II - Apparatus , the  A Sargent Model XXII Polarograph was  used to record  polarograms. A manual method was a l s o devised which employed  the  r e c o r d i n g polarograph to measure the c u r r e n t a t constant a p p l i e d E.M.F. the  A Leeds and l o r t h r u p Student Type Potentiometer measured  p o t e n t i a l a c r o s s the dropping e l e c t r o d e and t h e O.HJ  electrode.  The c i r c u i t diagram i s shown i n P i g . 3  oalomel  .  Opening and c l o s i n g the s t a b i l i z i n g c i r c u i t d i d not cause any d e f l e c t i o n o f the potentiometer galvanometer thus i n d i c a t i n g that the p o s s i b i l i t y o f e r r o r from t h i s source i s negligible.  The e f f e c t o f switching on the c u r r e n t  could not be determined. magnitude the  The e r r o r involved here depends on the  o f the c u r r e n t and the shunt r e s i s t a n c e s s e l e c t e d by  sensitivity  settings.  Por a c u r r e n t o f 6 microamperes  a s e n s i t i v i t y s e t t i n g o f 0.04  and  mioroamps/mm an e r r o r o f the  order o f 0.0015 v o l t can be expected. g i b l e i n most p o l a r o g r a p h i c work. the  recorder  Such an e r r o r i s n e g l i -  The method appears to o f f e r  same degree o f accuracy as the simple manual c i r c u i t  des-  c r i b e d by Lingane (5^5"). The amalgam c e l l — Pig.  H  .  The amalgam c e l l i s shown i n  The c o n t a i n e r was weighed  f i l l e d w i t h mercury  weighed a g a i n to determine the weight o f mercury. h o l e rubber stopper c o n t a i n s a contact e l e c t r o d e  and  The f o u r , C, which  extends to t h e bottom o f the c e l l , a platinum wire  coil  e l e c t r o d e , B, which i s p o s i t i o n e d about 1 cm. above the mercury s u r f a c e , a siphon tube, A, which extends to w i t h i n 1-2  mm  Sketch o f Apparatus Showing S t a b i l i z i n g C i r c u i t and Leads to Potentiometer and Polarograph. A P E W 'B S B DE -  Amalgam Platinum c o i l e l e c t r o d e Mercury contact e l e c t r o d e s Water l a y e r Reference e l e o t r o d e Electrolyte Anode p o o l Dropping e l e c t r o d e  Figure 4 The Amalgam  Cell  A.  Siphon  tube  B.  Platinum o o i l e l e c t r o d e  C.  Contact e l e c t r o d e to bottom o f mercury  D.  Pressure tube  TO  POTENT  Figure  5.  Polarographic  Cell  A.  Reference  Electrode  B.  Platinum c o i l layer  C.  Polarographic c e l l pool container  T.  Thermometer  M.  Nitrogen  R.  Amalgam  gas  e l e c t r o d e i n water  line  reservoir  showing  anode  46. o f t h e bottom o f the c e l l and a short tube, D, which i s used to  exert p r e s s u r e f o r s t a r t i n g t h e siphon.  After positioning  the stopper,a weighed z i n c c r y s t a l was dropped through the hole for coil  t h e pressure tube, D.  D i s t i l l e d water was added t i l l the  e l e c t r o d e was covered.  The p r e s s u r e tube was r e p l a c e d .  F i n a l l y , 10 v o l t s were impressed  across the c e l l making t h e c o i l  e l e c t r o d e the anode and t h e mercury t h e cathode. agitated  The c e l l was  so as to r o t a t e t h e mercury a t i n t e r v a l s .  e r a l days e l e c t r o l y s i s the amalgam was siphoned  A f t e r sev-  i n t o t h e drop-  ping e l e c t r o d e assembly. Although no r e a l evidence  has been obtained  i n this  work j i t i s b e l i e v e d that the z i n c amalgam i s ready f o r use i n the dropping  e l e c t r o d e s h o r t l y a f t e r t h e m e t a l l i c zino  dis-  appear S i The P o l a r o g r a p h i c cell  i s shown i n F i g , S  Fig. 3 •  •  ( C e l l Assembly —  The p o l a r o g r a p h i c  The c i r c u i t connections  a r e shown i n  A 250 ml. beaker was used a s t h e e l e c t r o l y s i s v e s s e l .  A l a r g e rubber stopper was bored so that the dropping  capillary,  the contact e l e c t r o d e , t h e n i t r o g e n l i n e , the thermometer and the calomel  e l e c t r o d e , A, could be i n s e r t e d i n t h e e l e c t r o l y t e i  The  e l e c t r o d e dipped  contact  into a mercury p o o l contained  in a  g l a s s d i s h , C, p o s i t i o n e d so that the f a l l i n g drops d i d not f a l l into the p o o l .  The 0.IN calomel  potassium o h l o r i d e , calomel placed  paste and mercury.  I t was always  i n t h e e l e c t r o l y t e so that the s o l u t i o n flowed  c e l l towards the calomel level.  e l e c t r o d e was made up with O.IN  from t h e  e l e o t r o d e before coming to the common  The thermometer i s graduated 0.1°C per s c a l e d i v i s i o n .  The n i t r o g e n l i n e was a p i e c e o f 4mm, g l a s s t u b i n g drawn to a  47.  f i n e t i p connected to the p u r i f i c a t i o n t r a i n by rubber t u b i n g . Dropping E l e c t r o d e Assemblies  The s o f t g l a s s c a p i -  l l a r y t u b i n g , S - 29350, s u p p l i e d with the Sargent  Polarograph  was cut to lengths 7.0 - 7.5 cm and j o i n e d to 8 mm s o f t g l a s s tubing. for  F i g . <o shows the r e g u l a r dropping  mercury a l o n e .  e l e c t r o d e assembly  The mercury r e s e r v o i r A, i s connected to  the c a p i l l a r y and column, B, by neoprene rubber t u b i n g . t u b i n g was cleaned  by p a s s i n g steam through i t f o r two hours  followed by d r y i n g i n a stream o f a i r . s m a l l q u a n t i t y o f mercury was allowed  Before  connecting^  to flow through i t to  c a r r y out any loose m a t e r i a l remaining.  The contact  C, d i p s i n t o the mercury r e s e r v o i r through a rubber Air  entered  attached to  The  eleotrode, stopper.  the r e s e r v o i r and the c a p i l l a r y column through the  d r y i n g tubes, D.  1 mm,by a s l o t The  i n the marker E.  dropping  gam polarography  The mercury l e v e l was c o n t r o l l e d  e l e o t r o d e assemblies  a r e shown i n F i g s . 7 B~. t  f o r use i n amal-  The c a p i l l a r y i s  connected to the r e s e r v o i r s by 8 mm.soft g l a s s t u b i n g . r e s e r v o i r s have a c a p a c i t y o f about 100 ml. o f the assemblies  The t o t a l  The height  i s about 45 om^thus a l l o w i n g an amalgam  column o f about 35 cm.  A platinum  contact  electrode i s set  into the 8 mm.glass t u b i n g about 1 cm^below the r e s e r v o i r s . The assembly shown by i t s e l f had a second c o n t a c t e l e c t r o d e about 1 cm.above t h e c a p i l l a r y . i s h e l d i n the rubber stopper  The platinum  coil  eleotrode  shown a t t h e top o f t h e r e s e r -  voirs. Before the mercury was siphoned  i n t o t h e amalgam  r e s e r v o i r s they were swept out f o r two o r three hours with  Figure Dropping  6  Electrode  Assembly  A.  Mercury r e s e r v o i r  B.  M e r c u r y column c o n n e c t e d t o r e s e r v o i r by n e o p r e n e t u b i n g .  C.  Contact electrode  D.  Drying  tubes  E.  Marker  f o r mercury  level.  r  Figure All  7  g l a s s dropping e l e c t r o d e assembly f o r amalgam p o l a r o g r a p h y .  *  C.  Capillary  E.  Contact e l e c t r o d e s  P.  P l a t i n u m c o i l e l e c t r o d e (Dips i n t o w a t e r l a y e r i n amalgam reservoir.)  48. nitrogen.  A 4 mm.glass tube was  the upper part o f the c a p i l l a r y n i t r o g e n stream.  The n i t r o g e n  lowered t i l l  so as to sweep out a i r by the stream was maintained as  as p o s s i b l e w h i l e the mercury was  siphoned i n .  g l a s s tube was withdrawn i t was manipulated entrapped gas bubbles. was  i t was r e s t i n g on  long  As the t h i n  so as to remove  As q u i c k l y as possible^ d i s t i l l e d  water  l a y e r e d on the amalgam surface and the c o i l e l e c t r o d e i n -  serted to c l o s e the s t a b i l i z i n g Nitrogen p u r i f i c a t i o n out d i s s o l v e d oxygen was  Tank n i t r o g e n  used to sweep  p u r i f i e d i n a vanadous s u l f a t e t r a i n  a f t e r the method d e s c r i b e d t r a i n consisted  circuit.  by Meites (SO.  The p u r i f i c a t i o n  of four scrubbing b o t t l e s containing  O.IN  vanadous s u l f a t e s o l u t i o n and a f i n a l b o t t l e c o n t a i n i n g  O.IN  potassium c h l o r i d e made b a s i c by the a d d i t i o n o f one or two p e l l e t s o f potassium hydroxide to which 1-3 grams o f sodium s u l f i t e were added.  49.  t  III-METHODS The mass o f mercury f l o w i n g from t h e c a p i l l a r y  was  determined i n a i r and i n the e l e c t r o l y t e .  In a i r t h e mercury  drops were caught on a t a r e d watch g l a s s .  As a drop f e l l the  stop watch was watch was In  s t a r t e d and the next drop was  stopped as the l a s t drop f e l l  caught.  The stop  i n t o the watch  glass.  the e l e c t r o l y t e the timing,was made i n the same manner,  however, the mercury  drops were caught i n a g l a s s l a d l e .  c o l l e c t e d mercury was washed with a stream o f d i s t i l l e d The excess water was  water.  decanted and the spoon and mercury dipped  into acetone and s w i r l e d around. with f r e s h acetone*  The  This p r o c e s s was repeated  The excess acetone was decanted and the  mercury g l o b u l e t i p p e d  into a weighed watch g l a s s .  A f t e r the  acetone had evaporated,the watch g l a s s and mercury was  weighed  and the weight o f mercury determined by d i f f e r e n c e . For  p o l a r o g r a p h i c work the room was warmed to 23°C-  27°G by means o f a hot p l a t e . by means o f thermometers mercury was  The temperature b e i n g determined  d i s t r i b u t e d about the room.  f i l t e r e d at a c a p i l l a r y f u n n e l into the anode con-  t a i n e r and about 125 ml,of standard s o l u t i o n added. quired amount o f g e l a t i n was  then added.  The r e -  A f t e r s e t t i n g up the  dropping e l e c t r o d e assembly,the s o l u t i o n was nitrogen.  The  swept out with  The temperature o f t h e e l e c t r o l y t e was  brought to  25.0°G by h o l d i n g the s i d e s o f the beaker by hand or rubbing with dry i c e . during the run. withdrawn  The temperature was  found to hold w i t h i n  0.1°C  When ready f o r the run the n i t r o g e n tube was  so t h a t i t would m a i n t a i n a blanket over the s o l u t i o n .  50  U s u a l l y the drop time was ing.  determined  In some cases the drop time was  a stop watch graduated to 0.1  second.  from the r e c o r d -  determined by t i m i n g with It was  found t h a t the  drop times could o n l y be reproduced i n the absence o f v i b r a t i o n . Even movements i n o t h e r p a r t s o f the b u i l d i n g seemed to have some e f f e e t .  For t h i s reason p o l a r o g r a p h i c runs were made a t  such times o u t s i d e i n t e r f e r e n c e was  at a minimum.  In amalgam polarography the d i a l s e t t i n g s and  electrode  connections were set so that the p o t e n t i a l o f the dropping e l e c trode became more p o s i t i v e .  The d i a l s e t t i n g s f o r the amalgam  runs are as f o l l o w s : RANGE 1.500 OPPOSED, DME was  0,  V o l t s , SPAN 1.500  DAMPING 1, SENSITIVITY 0.06>^amp.  set 10.0 and zero c u r r e n t s e t a t 40 mm.  apparatus was  Volts  calibrated  zero c u r r e n t check.  fo RANGE  chart r e a d i n g .  The  (see manual o f i n s t r u c t i o n s ) during  The r e c o r d e r was  run a t E.M.E.CONSTANT u n t i l  the pen reached the l i n e chosen f o r the s t a r t o f the polarogram then the switch was thrown to E.M.E.INCREASING. For a manual run the Polarograph was  set E.M.F.CONSTANT  and the p o t e n t i a l a c r o s s the c e l l v a r i e d by s e t t i n g % RANGE. the chart showed steady c u r r e n t the r e c o r d e r was  When  switched o f f  (the a p p l i e d E.M.F. i s maintained) and the p o t e n t i a l o f the dropp i n g e l e c t r o d e determined v s . O.IN the potentiometer.  calomel r e f e r e n c e e l e c t r o d e by  The potentiometer was  a g a i n s t a Weston Standard  frequently  calibrated  Cell.  The potentiometer reading i s that s e t t i n g f o r which the galvanometer  (Leeds and Northrup  ^/sec. s e n s i t i v i t y 0.3 s ^ ^ J )  CAT.  NO.  i s deflected  Z.  330-D  period  e q u a l l y from z e r o .  51 E - R e s u l t s and D i s c u s s i o n I - Polarography o f Standard  Zinc Solutions.  Determinations o f the c a p i l l a r y constant  'm'  f o r the  r e g u l a r dropping mercury e l e o t r o d e a r e recorded i n Table  7.  The mean v a l u e 2.595 mgm/sec. TABLE 7. The Rate o f Meroury Flowing from C a p i l l a r y  into A i r .  Room Temperature 21°C ±. 3° Date  Mass o f %  Feb*13 Apr.16 " 16 " 25  Outflow  Time  3201.2 mgm 442.0 " 476.5 " 823.7 "  has been used  in calculations.  i s not s t r i c t l y v a l i d  s i n c e 'm'  the dropping  electrode.  K o l t h o f f and  Lingane  *m'  1231 seo 170.7 sec 183.9 " 316.7 "  2.601 mgm/sec 2.589 " 2.591 2.601 "  Mean Value  2*595  The  "  use of t h i s value f o r  'm*  v a r i e s w i t h the p o t e n t i a l o f  From r a t h e r meager data shown by an e r r o r of the o r d e r o f Zfo i s  (.57)  expeoted. The n i t r o g e n was  removal o f d i s s o l v e d oxygen by p u r i f i e d  tank  t e s t e d with the r e g u l a r p o l a r o g r a p h i c apparatus.  The r e s u l t s a r e shown i n Table  8.  TABLE 8. Removal o f D i s s o l v e d Oxygen by l i t r o g e n Sweep Electrolyte IK KCL EMF a p p l i e d 1 v o l t . Time o f HgSweep 0 min 5 n  ]_Q  ti  Sensitivity 0.04^amp/mm " «t  Damping ' Current #1 5.8>^amp " 0.64 "  n  ii  027  o!24  15 "  tt  n  n  20  "  n  II  n  " " " " "  "  25  " 0.01 n 0.003  ,f  " " " "  0.04  lgm l a 2 S0 added 3  "  " " it " " "  "  none #1 n  o  n  e  #1 none #1  "  Q  #  2  "  5  0.25 0.245 0.245 0.255 0.255  Pen T r a v e l 21mm 2.0mn M  v  >N t h*t* ^K^s.  O  " rt n  " " " "  0.25  "  0.18  "  »•  2.25mm 0.25 " 6.0 " 0.25 " 14.0 " M » N I ^ M - ? C  1.0  mm  52. It i s seen that a f i f t e e n minute n i t r o g e n sweep i s s u f f i c i e n t f o r p r a o t i c a l purposes.  However, t r a c e s o f oxygen remain d i s -  solved i n the s o l u t i o n .  A f t e r a n i t r o g e n sweep o f one hour  a small -1.10  'wave' appeared on t h e polarograms a t approximately  v o l t versus  O.IH calomel e l e c t r o d e when maximum s e n s i t i -  v i t y o f the r e c o r d i n g instrument was used. that t h i s  It i s believed  'wave' i s due to d i s s o l v e d oxygen. Oxygen i s reduced stepwise a t the dropping e l e c t r o d e i  The  f i r s t wave i s due to the r e d u c t i o n o f oxygen to hydrogen  peroxide, 0)  equation  0 ^ 2 H 0 + 2e 2  2  1.  The h a l f wave p o t e n t i a l i n O.IK > HgOg i- 20H"  potassium o h l o r i d e i s g i v e n versus  E i - O.lv  S.C.E.  The second wave  corresponds to the r e d u c t i o n o f the hydrogen peroxide (2.)  HgOg +- 2e  >  20H"  (5~Sf) •  E i - 0.9v.  It i s seen t h a t i n the presence o f d i s s o l v e d oxygen i n a neut r a l s o l u t i o n , t h e d i f f u s i o n l a y e r about t h e mercury drop becomes a b a s i c s o l u t i o n c o n t a i n i n g hydrogen peroxide* n o t i c e d a t - 1.1 v o l t versus  The s m a l l wave  O.I! calomel e l e o t r o d e  work i s presumably due to t h e r e d u c t i o n o f hydrogen  in this peroxide.  The wave h e i g h t s v a r i e d somewhat between 0.03^amps to 0.09/^amps. Results of a test  f o r r e p r o d u c i b i l i t y o f the i n s t r u -  ment s e t t i n g s a r e shown i n Table 9A. d i a l s were thrown o f f and r e s e t b e f o r e reading.  A f t e r each reading the t a k i n g the potentiometer  53  TABLE 9A R e p r o d u c i b i l i t y o f Instrument Dropping mercury e l e c t r o d e  i n standard z i n c  D i a l Settings Span  % Range  49$ II n " " n  n it " " "  n  solution  Calculated  Initial add 0.1 v o l t  1.5 v o l t s n it " "  Settings  Potentiometer  Voltage 0.8350 K ^ - * -  ti ?n " " II  Reading  0.8346 I / « * T 0.8344 0.8349 " 0.8343 0.8345 •• 0.8350 ••  .. • .. " ••  Since one s c a l e d i v i s i o n i s 0.0150 v o l t s the v a r i a t i o n o f the potentiometer readings 0.0006 v o l t s r e p r e s e n t s 4$ o f one s c a l e division.  I t i s evident  duplicated  accurately.  that the instrument s e t t i n g s can be I t was found, however, that t h e pen  p o s i t i o n on the chart v a r i e d by as much a s 0.2 chart d i v i s i o n . That i s t h e c h a r t v o l t a g e value.  reading varied  from t h e d i a l s e t t i n g  T h i s v a r i a t i o n i s due to b a c k l a s h i n the chart  mechanism.  Fortunately the }  discrepancy i s noticeable  drive as the  instrument operates and consequently the e r r o r can be estimated when the instrument i s stopped.  For an e r r o r o f 0.1  d i v i s i o n a t a span s e t t i n g o f 1.500  chart  v o l t s an e r r o r i n the measure  ment o f the half-wave p o t e n t i a l o f 0.0015 v o l t s r e s u l t s . When the polarograph was used i n c o n j u n c t i o n potentiometer f o r p o i n t by p o i n t was c a l c u l a t e d  readings the a p p l i e d  with the potential  from the d i a l s e t t i n g s and checked a g a i n s t the  potentiometer reading.  The r e s u l t s a r e shown i n Table 9B.  54 TABLE 9B Polarograph v s . Potentiometer Polarograph S e t t i n g 1.350 v o l t 1.005 " 0.900 " 0.750 " 0w525 " 0.300 0.015 " w  Readings.  Potentiometer Reading 1.347 v o l t 1.003 " 0.900 " 0.753 " 0.531 " 0.309 " 0.021 "  Deviation -0.003 v o l t -0.002 " 0.000 " 0.003 " 0.006 " 0.009 0.006 ,T  n  It i s seen that the potentiometer readings become i n c r e a s i n g l y h i g h e r than the instrument s e t t i n g with d e c r e a s i n g a p p l i e d p o t e n t i a l by an amount o u t s i d e the l i m i t o f e r r o r from Table 9A.  determined  I t i s assumed t h a t t h e d e v i a t i o n i s e n t i r e l y  due to inherent e r r o r o f the potentiometer* s i m i l a r degree o f e r r o r i s expeoted  Consequently,  a  i n t h e d e t e r m i n a t i o n o f the  p o t e n t i a l o f the dropping e l e c t r o d e f o r p o i n t by p o i n t p o l a r o grams. In order to o b t a i n i n f o r m a t i o n with respect t o t h e r e l i a b i l i t y , r e p r o d u c i b i l i t y and accuracy o f the method polarograms  used,  o f standard z i n c i n O.IN potassium c h l o r i d e w i t h  added g e l a t i n were recorded. T y p i c a l polarograms  The data i s g i v e n i n Table 10.  a r e shown i n P i g s *  A  }  10A^  55.  TABLE 10 Polarographic C h a r a c t e r i s t i c s (1) Recorded w i t h Sargent Standard  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  Concentration m molar(c) " (o)  0.6187 n IT  II  n  n  ti  ti  tt  ii  tt  tt it  0.3365 tt  ti  n  rt  it  it it  0.2061 ii  if  ii  tt  Tl tt ii  "  IT  11  n it it  ii ti it  ii tt  (d)  1.66 0.828 0.837  it it it  nil  it  it  ii  0.035  ti  TTa~) 1(h)  Concentration 0 . 6 1 8 7 mmolar 11  tt  2(a)  0.2061  11  3(a)  0.1040 n  11  2(h)  3(h)  it  ii  it it  n it it  IT ti it it it it tt  n ti Tt  1.105 volt tt  It.  11 It It  11 It IT  tl It tt IT If  11  nil  it  ti  Tl  1.098 1.093 1.095 1.095 1.084 1.090 1.092 1.090 1.098 1.095 1.098 1.093 1.101 1.107 1.105 it  II  1.113  Zinc i n O.IN KCL with 0.0001$ g e l a t i n , p l u s 0.1 gm Na£ SOg per 100 ml. Temperature 25.1°C  No.  Ei(b)  sec  ( b ) Applied voltage reading (d) I d e n t i c a l wave found i n O.IN KCL a l o n e .  (a) Corrected to 25.0°C (c) Oxygen present Standard  2.84 2.70 2.89 2.70 2.91 3.04 2.98 2.62 2.58 2.49 2.49 2.95 2.92 2.70 2.52 2.70 2.70 2.70 2.70  it  4.51 4.89 4.71 4.83 4.83 4.74 2.68 2.62 2.63 2.62 1.67  0.2° t.  id(a) 4 . 4 4 X <amp.  it  it  0.1040 n 0.0168 0.0084 0.0041  Polarograph.  Zino i n O.IN KCL with 0.0001$ g e l a t i n . Temperature 25.2°C  Mo  o f Zinc Solutions  tt  tt  id 2.64 0.67 0.61 0.51 0.44  0.2° t.  •• •• •• "  2.95 2.89 2.91 2.95 2.73 2.79  sec  (a) A p p l i e d v o l t a g e r e a d i n g .  IT  11 It It II  Ei(a) volt  0.895 0.877 0*858 0.891 0.930 0.918  n  " " " "  56.  (2) Manually  Beoorded  Standard Z i n c i n O.IH  KGI w i t h 0.0001$ G e l a t i n .  Temperature 25.0°C. Concentration 0.2061 mmolar  id 1.40/^amp (b)  (a) (b)  t 3.15  sec.  E i (a) ~1.095volt  E i v s . O.IN calomel e l e c t r o d e . oxygen i n d i c a t e d .  Standard Z i n c i n O.IH KCL with 0.0001$ g e l a t i n p l u s 0.1 gm Hag SOg per 100 ml. Temperature 25.2°C Concentration 0.6187 mmolar 0.2061 "  id 2.6lXamp 0.65 "  (a)  E i v s . O.IH  0.2° t 3.04 2.70  sec n  =Ej (a) -1.095 v o l t -1.098 "  calomel e l e c t r o d e .  The d i f f u s i o n c u r r e n t and drop time were measured by the method d e s c r i b e d i n the Sargent Manual o f I n s t r u c t i o n s f o r the P o l a r o g r a p h . ( S^f )  w  a  The temperature  coefficient  2.0$  per  degree  used to c o r r e c t the measured value to the v a l u e at  s  25.0°C where n e c e s s a r y . negligible.  In most cases the c o r r e c t i o n term i s  The maximum c o r r e c t i o n i s shown i n the following  calculation. id  measured a t 25.3°C  id corrected  =  4.74>^/amp.  = 4.74^amps. - 0.3 X:2 Z 4.74^amps 100 = 4.71  "  a t 25.00C.  The h a l f wave p o t e n t i a l f o r z i n c i n O.U c h l o r i d e i s determined as - 1.095 electrode. ( CO).  v o l t versus O.IN  potassium calomel  The v a l u e g i v e n i n the l i t e r a t u r e i s - 1.084  I t i s seen that the h a l f wave p o t e n t i a l s  from the instrument s e t t i n g s agree with the v a l u e  volt  determined determined  57. w i t h i n the l i m i t o f e r r o r .  On the other hand i n the presence  o f s u l f i t e the E i values c a l c u l a t e d from the i n s t r u m e n t a l  set-  t i n g s do not  correspond  volt  and  v o l t versus O.U.  1.098 The  to the determined v a l u e s — calomel  electrode.  runs made w i t h s u l f i t e present were d u p l i c a t e s ,  that i s run b was  made immediately f o l l o w i n g run a.  a c o n s i d e r a b l e degree o f discordance  The  further during  The decrease o f the d i f f u s i o n c u r r e n t upon the a d d i t i o n  o f s u l f i t e i s not It was creased  There i s  among the r e s u l t s .  o n l y c o n s i s t e n c y i s t h a t the c u r r e n t decreased run b.  1.095  satisfactorily  explained.  noted t h a t the presence o f oxygen a l s o  the d i f f u s i o n c u r r e n t f o r z i n c .  Fig.  de-  shows p o l a r o -  grams o f 0.6187 mmolar z i n c i n O.II potassium c h l o r i d e w i t h 0.0001$ g e l a t i n .  F i g . ^ (a) was  obtained w i t h oxygen p r e s e n t .  The pen t r a v e l before the z i n c wave i n d i c a t e s the presence o f a r e d u c i b l e substance.  Fig. ^(b)  shows t h a t the oxygen has  removed to i t s minimal c o n c e n t r a t i o n . detectable.  According  I t s presence i s not  to the e l e c t r o d e r e a c t i o n o f d i s s o l v e d  oxygen the d i f f u s i o n l a y e r becomes b a s i c and peroxide.  The  c o n t a i n s hydrogen  c o n d i t i o n s t h e r e f o r e f a v o r the f o r m a t i o n  z i n c a t e or z i n c peroxide, most l i k e l y the former. complex i s not and,  The  of zinc  r e d u c i b l e except at a more n e g a t i v e p o t e n t i a l  t h e r e f o r e , does not  c o n t r i b u t e to the d i f f u s i o n c u r r e n t a t -  -1*095 v o l t half-wave p o t e n t i a l .  I t may  t o t a l c u r r e n t i s approximately  the same.  be  been  be n o t i c e d t h a t the Such behaviour could  expected on the b a s i s t h a t the amount o f z i n c removed by  complex formation The  i s p r o p o r t i o n a l to the c o n c e n t r a t i o n o f oxygen.  disappearance o f the z i n c wave a t a  concentration  FT --150  50-  T/!«r.s  Q-1*131-* MOLAR  CL-iJHum  O* O /  HEr^ATtD  :  AFTER.  ^ A M P / A I M  1  CURRENT  4.  d i —60 et  in.  ICMRijr^r.  2 H »  OURllflir-  5,  Figure Polarograms chloride Drop  o f 0.6187  plus  times  millimolar  0.0001% g e l a t i n .  zino  Figure  8a t h e presence  by  pen t r a v e l  preceding  i n 0.1U p o t a s s i u m  Sensitivity  ( 8 a ) E . 8 4 s e c , ( 8 b ) 2.89  In  reduction  8  sec.  of dissolved  the current  oxygen  increase  i s shown due t ot h e  o f zinc.  8a  Residual  0.04/^amp/mm.  current plus oxygen ourrent Z i n c c u r r e n t a t E4T o t a l o u r r e n t a t Bj.  a t E§- 0.92/"amp 4.44 " 5.36 "  8b 0.36/^amp 4.88 " 5.24 "  F i g u r e 8C Polarogram o f supernatant water l a y e r from amalgam o e l l w i t h added potassium c h l o r i d e , A , compared w i t h polarogram o f O.lil potassium c h l o r i d e , B , s o l u t i o n s swept out with n i t r o g e n . 0.003y^amp/mm without damping.  Both  Sensitivity polarograms  are s i m i l a r to polarograms o f 0.0041 m i l l i m o l a r i n 0.1U potassium c h l o r i d e p l u s 0.0001$ g e l a t i n swept out w i t h n i t r o g e n . V o l t a g e - 1.15 v o l t v e r s u s O.M  Both  calomel  e l e c t r o d e read from instrument s e t t i n g s .  zinc  58. 0.0168 mmolar z i n c i s b e l i e v e d due to the f a c t t h a t t h e oxygen remaining i n s o l u t i o n t i e d formation.  up most o f t h e z i n c i n complex  The polarograms o f 0.0084 mmolar z i n c resembled  those o f 0.0168 mmolar z i n c i n t h a t a r e d u c i b l e substance was i n d i c a t e d to be present by the pen t r a v e l d u r i n g drop tion.  forma-  However, polarograms o f 0.0041 mmolar z i n c could not  be d i s t i n g u i s h e d from polarograms o f O.IS potassium c h l o r i d e alone.  These l a t t e r were found to correspond to t h e p o l a r o -  grams o f t h e supernatant water from t h e amalgam c e l l a f t e r a s m a l l amount o f potassium c h l o r i d e had been added polarographic a n a l y s i s .  f o r the  Thus i t i s evident that t h e super-  natant water c o n t a i n e d l e s s than 0.0084 mmolar  zinc  A p l o t o f d i f f u s i o n current v s . concentration i s l i n e a r i n the range o f c o n c e n t r a t i o n 0.1040-0.6187 mmolar zinc.  The s t r a i g h t l i n e passes extremely c l o s e to the o r i g i n  upon e x t r a p o l a t i o n ,  f i g . v*5  The d i f f u s i o n c u r r e n t constant and t h e apparent p o l a r o g r a p h i c d i f f u s i o n c o e f f i c i e n t o f z i n c i n O.IS potassium c h l o r i d e have been c a l c u l a t e d by the I l k o v i c equation  -  Xj  D^- c /*n?z  L>oy^K  (in)  C-c  The v a l u e so determined f o r 3 i has been s u b s t i t u t e d  i n the  second terms o f the equations proposed by Lingane and l o v e r i d g e , and Strehlow and S t a c k e l b e r g and t h e v a l u e f o r D# i n t h e f i r s t term redetermined.  The r e s u l t s a r e shown i n Table 11.  T h e o r e t i c a l l y the 'D' v a l u e s should corcespond to the value o f the d i f f u s i o n c o e f f i c i e n t o f z i n c a t i n f i n i t e d i l u t i o n , 7.2  1  l'O" cm2 s e c " 6  1  (C  /),  58(a) The c a l c u l a t i o n s have been performed suggested  by l i n g a n e and Loveridge  that a knowledge o f J) t h e i r new e q u a t i o n .  i n t h e manner  ( 8 ) . These authors  state  i s necessary f o r the p r a c t i o a l use o f  Late i n t h i s work i t was r e a l i z e d  that  the equation i s a simple q u a d r a t i c and i t i s d i f f i c u l t to understand  why the authors have disregarded t h i s f a c t i n t h e i r  paper. The s o l u t i o n o f the equation o f Lingane and Loveridge  is  , r j r_  -/  +  1/ l + O-0Hf5l  % f=P_DIV\  when m = 2.595 mgm  sec-1 as i n t h i s work and c=£ Strehlow and  Staokelberg's  CL  The f o l l o w i n g v a l u e s c a l c u l a t e d from these  formulae  may be compared with those shown i n Table 11. Ho. 3 4 5 6 7 Average  J?s X 10 7.71 cma sec--*7.32 n 7.51 tt 7.40 it tt 7.26 it 7.44 c  7.03 cm^ s e c 6.78 n 6.85 Tt 6.75 tt 6.57 ft 6.79  The v a l u e s o f  1  J?t_ here are about 0.10 cm** s e c " h i g h e r  those shown i n Table 11.  1  The v a l u e s P$  than  are about 0.03 om2seo-l  higher. It should have been stated t h a t t h e g e n e r a l s o l u t i o n is  V/) 2 A  >3  t  '  L  F i g u r e 9A P o l a r o g r a m s o f z i n c i n 0.1H p o t a s s i u m 0.0001^ g e l a t i n height  versus  swept o u t w i t h  concentration.  chloride plus  nitrogen  s h o w i n g wave-  Sensitivity  0.04X'amp/mm.  Compare p o l a r o g r a m o f 0.0168 m i l l i m o l a r z i n c w i t h 8a.  The p r e s e n c e o f o x y g e n  travel  as i n F i g u r e 8 a .  Figure  i s n o t i n d i c a t e d here by pen  O-Ooo  O./oo  O.soo  o.*-oo C ON  C EN  TRA  T I ON  OMOO A7 /U t / M  O'SOO OJ-AR.  a. coo  0.700  r [•( 1 t.| [ I I i +j-r i | j | \\ \\ | i l l  tttmf IOA A F i g u r e IOA Polarogram o f 0.1040 m i l l i m o l a r z i n c i n O.lfl potassium c h l o r i d e p l u s 0.0001$ g e l a t i n swept out with n i t r o g e n . Sensitivity  0.006/^amp/mm.  D i f f u s i o n c u r r e n t 0.83 , y amp.  ff:  ijiiilsi,  /0B F i g u r e 10B Polarogram run immediately a f t e r that shown i n F i g u r e IOA a f t e r a d d i t i o n o f sodium Concentration  sulfite.  0.1040 m i l l i m o l a r z i n c i n 0.1U  potassium c h l o r i d e p l u s 0.0001$ g e l a t i n p l u s 0.1 gm sodium s u l f i t e Sensitivity  /lOO oc.  0.006^" amp/mm.  D i f f u s i o n ourrent 0.44 .y?'amp.  59.  TABLE 11 The D i f f u s i o n Current Constant and the Apparent D i f f u s i o n C o e f f i c i e n t o f Zino i n 0.113 Potassium C h l o r i d e No. 3 4 5 6 7 8 9 10 11 12 13 14 15 16  Concentration 0.6187 mmolar  n it n  II  n  0.3365 II  0.2061  n tt  0.1040  ii  n it it it it it it it it n it tt  I 3.51 3.42 3.46 3.43 3.38 3.59 3.52 3.56 3.54 3.58 3.68 3.61 3.61 3.61  D X 10 8.34cm 7.92 " 8*12 " 8.00 " 7.76 " 8.75 " 8.41 8.57 " 8.51 " 8.71 " 9.16 8.87 " 8.90 " 8*86 "  D i X l O <aJ 1 6.92 'see  6  6  £  6.61 6.75 6.66 , 6.47 7.25 7.00 7.13 7.08 7.19 7.54 7.33 7.34 7.32  n  n  tt ft n  rt tt it tt it ft it it tt n  D X 106 (b) 7.68 cm ^sec~ S  - 1  7.31 7.48 7.37 7.16 8.05 7.75 7.90 7.80 8*00 8.40 8.14 8.15 8.13  it tt n  tt it tt it ft tt tt it n  Average Values Concentration 0.6187 mmolar 0.3365 0.2061 " 0.1040 " (c)1.00 " n  (a) (b) (o)  I 3.44 3.55 3.62 3.61 3.41  D X 10 8.03 c m 8.56 8.91 8.88 7.91 6  DiX 1 0 ( a ) 6.68 cm^sec-1 7.11 " 7.35 " 7.33 "  DsX 1 0 l b ) 7.40 cm sec-l 7.91 8.18 " 8.14 "  6  2  see-l " " " "  6  £  n  D-i from equation by Lingane and Loveridge D " " Strehlow and S t a c k e l b e r g Values r e p o r t e d i n l i t e r a t u r e n  g  The v a l u e s f o r D a r e seen to i n c r e a s e with d e c r e a s i n g concentration of zinc.  K o l t h o f f and Lingane  (£Z)  mention  s i m i l a r d e v i a t i o n s have been r e p o r t e d f o r other m e t a l s . themselves found no such behaviour when the work was However, t h e i r p u b l i s h e d data f o r lead i n O.IN shows some evidence o f t h i s d e v i a t i o n .  that  They  repeated.  potassium  chloride  Suoh a d e v i a t i o n can be  e a s i l y e x p l a i n e d , i n f a c t ^ s u c h a d e v i a t i o n i s expected when the current  i n the mercury drop i s c o n s i d e r e d ;  A c c o r d i n g to Strehlow  and S t a c k e l b e r g (Cj>), A n t w e i l e r has shown evidenoe o f the c u r r e n t  60.  and  r e s u l t a n t streaming  are used a t a dropping  o f the drop s u r f a c e when a dye and water capillary.  Consequently,,: such behaviour  i s presumed to he c h a r a c t e r i s t i c o f t h e dropping mercury. polarographic  Under  c o n d i t i o n s i t may a l s o be presumed that the c u r r e n t  along the a x i s o f t h e c a p i l l a r y  i s constant  f o r a given set of  c o n d i t i o n s o f temperature, mercury head and back p r e s s u r e . However, s u r f a c e streaming conditions.  would be governed by t h e s u r f a o e  One o f these c o n d i t i o n s would be the c o n c e n t r a t i o n  o f the amalgam formed by r e d u c t i o n to a mercury s o l u b l e Assuming t h a t t h e s u r f a c e streaming  metal.  i s reduced by i n c r e a s i n g ia  c o n c e n t r a t i o n o f amalgam then the r a t i o  t?cF  o r the values f o r D  would i n c r e a s e with inorease i n r a t e o f streaming,  that i s  with decrease i n c o n c e n t r a t i o n o f t h e r e d u c i b l e i o n .  Such id  behaviour has been denied a p p a r e n t l y because the r a t i o ~~C" has again decreased  a t very low c o n c e n t r a t i o n s .  decrease a t v e r y low c o n c e n t r a t i o n s  The nature o f thiss  could be e x p l a i n e d by the  e f f e o t o f the minimal oxygen c o n c e n t r a t i o n . The f o r e g o i n g e x p l a n a t i o n appears v a l i d f o r t h e r a t h e r l i m i t e d number o f papers s t u d i e d so f a r .  On the o t h e r h a n d t h e f  phenomena i s d i r e c t l y r e l a t e d to the occurrence  o f current  maxima which a r e s t i l l t h e s u b j e c t o f c o n t r o v e r s i a l p a p e r s ( ^ V ) * Further review o f reported ment o f an adequate  data should a s s i s t  i n the e s t a b l i s h -  explanation.  I f , as r e p o r t e d by K o l t h o f f and Lingane, t h e r e l a t i o n id (T~ i s s t r i c t l y to w i t h i n 15$.  l i n e a r then t h i s work agrees with p u b l i s h e d id I f the r a t i o 0  a c t u a l l y i n c r e a s e s with  i n g c o n c e n t r a t i o n o f z i n c t h e agreement i s w i t h i n 5$. maximum d e v i a t i o n i s considered  i n both  cases.  data  decreasThe  61. It i s evident t h a t the method does not produce g r o s s d e v i a t i o n s and f o r t h i s reason i t i s assumed that the same order o f accuracy can he obtained i n amalgam polarography.  Provided,  o f course, t h a t i t can be shown t h a t a dropping amalgam has same dropping c h a r a c t e r i s t i c s as pure mercury. English  the  A c c o r d i n g to  the p r o p e r t i e s mentioned do agree over the range  o f p o t e n t i a l necessary f o r p o l a r o g r a p h i c measurements.  62.  II - Amalgam  Polarography.  A few t e s t s were made to show t h a t the d i l u t e amalgam behaved s i m i l a r l y to mercury a t the dropping c a p i l l a r y and t h a t the s t a b i l i z i n g c i r c u i t had no e f f e o t on the recorded  polarograms.  The data from these t e s t s i s g i v e n i n Tables 12 - 14. TABLE 12 The Rate o f Amalgam Plowing from the C a p i l l a r y into V a r i o u s Media Amalgam: 0.0148 gm Zn i n 791.9 gm Hg Stabilizing c i r c u i t closed. Uo.  1 2 3 4 5 6 7 8 9 10 11 12 13 14  Time  Media Air  162.2 seo n 161.1 n Water 113.2 rt tt 113.2 rt Sat KCL 107.7 tt n tt 107.5 n Air 174.0 it 166.2 rt Sat KCL Zn 01 108.9 it n n tt 128.4 tt Sat KH0*Zn(]S0,z)p(a) 124.3 n 119.0 ti Air 68.4 it ti 159.0 rt o  C  (a) Swept out with I The  Amalgam  2  Collected  287.7 mgm 284.9 rt 200.9 it 201.1 tl 191.4 tl 190.6 n 306.8 rt 290.8 it 191.2 rt 224.8 it 216.0 n 207.5 it 12022 it 275.4 tt  1.774  'm' mgm/sec  1.768 1.775 1.777 1.777 1.773 1.763 1.750 1.756 1.751 1.738 1.744 1.757 1.732  n rt it rt it rt it rt it tt it tt it  f o r 15 minutes.  s u c c e s s i v e v a l u e s f o r 'm' determined  f o r a i r show the e f f e c t  o f the d e c r e a s i n g amalgam head - about 2 mm d u r i n g the t e s t . Comparison with a s i m i l a r t a b l e f o r the r a t e o f mercury flow( i s s t r o n g evidence that the r a t e o f amalgam flow i s independant o f the media i n which the drops  form.  The d e t e r m i n a t i o n o f 'm' a t the c a p i l l a r y e l e c t r o d e i s shown i n Table 13.  ^)  63.  TABLE 13 The Bate o f Amalgam Flowing  from the C a p i l l a r y E l e c t r o d e  Amalgam 0.0042 gm Zn i n 1457.7 gm S t a b i l i z i n g c i r c u i t closed Group  Media Air  Amalgam Time 173.5sec 301.6 175.2 * 303.1 297.4 176.8 " 178.7 299.6 179.8 306.3 178.4 " 303.9 179.3 " 301.9 179.4 '* 304.1 177.2 " 301.9 177.0 " 301.5  Applied Voltage  if  IT If  2 it  IT  11  O.U  KCL  n  -0.45 n  IT  v  nil  Air If  IT  IT  ff  IT  IT  ff  It  -0.22 it  -0.60 it  it  w i t h respect to the v a r i a t i o n of electrode.  determined  i n a i r may  v a r i a t i o n appears be determined of  any  conclusions  w i t h t h e p o t e n t i a l o f the  However, i t i s seen that the value f o r be used  to be about  'm  1  i n t h e c a l c u l a t i o n s s i n c e the -t 3%,  The v a l u e o f 'm'  should  i n the e l e c t r o l y t e a t t h e a p p r o p r i a t e p o t e n t i a l  the dropping e l e c t r o d e .  u t i o n o f the amalgam i t s e l f the v a r i a t i o n o f 'm' The  'm'  n  it  Here the data i s not e x t e n s i v e enough to warrant  dropping  1.738mgm /se 1.730 " 1.682 " 1.677 " 1.704 " 1.704 1.684 " 1.695 " 1.704 1.703 "  lgm ^  ri  it  O.Iin KCL  Hg.  In the case o f amalgam the  dissol-  i s an a d d i t i o n a l c o m p l i c a t i o n to  with p o t e n t i a l .  e f f e c t o f the s t a b i l i z i n g c i r c u i t was  determining the drop time w i t h the c i r c u i t  t e s t e d by  open and c l o s e d .  The drop time i s a f u n c t i o n o f s u r f a c e t e n s i o n which i n t u r n i s a f u n c t i o n o f the e l e c t r o c a p i l l a r y p o t e n t i a l . z i n g c i r c u i t had any  14.  stabili-  e f f e c t there should be some d e v i a t i o n o f  the drop times on open and c l o s e d c i r c u i t . recorded i n Table  I f the  The data i s  64 TABLE 14 Drop times with S t a b i l i z i n g C i r c u i t Open and C l o s e d . Amalgam 0.0148 gm 2n i n 791.9 gm H g . E l e c t r o l y t e IE KCL. Stabilizing circuit  10 v o l t s a p p l i e d .  Drop Time Dropping E l e c t r o d e P o t e n t i a l (a) 0.00 v o l t s " " " " " -0.40 " -1.60  n  Circuit  Stabilizing Closed  5.98 seo 5.99  n  n  Stabilizing Open  5.98 sec 5.98 " 6.01 *' 5.99 " 6.08 " 4.21  "  6.08 " 4.84 "  ti  n  4 > 2 2  " " 4.25 " " " (a) A p p l i e d p o t e n t i a l reading a c r o s s dropping and e x t e r n a l S.C.E. The  Circuit  r,  4.24 " 4.24 electrode n  drop times on open and c l o s e d c i r c u i t a r e seen to c o i n c i d e  w i t h i n the l i m i t o f d e t e r m i n a t i o n . A more extended range o f p o t e n t i a l v s drop time determinations  i s shown i n P i g . /I  .  and a t p o t e n t i a l s more n e g a t i v e time was h i g h l y  In the p o s i t i v e v o l t a g e range  - 1.80 v o l t s v s . S.C.E.the drop  erratic.  A polarogram obtained  manually i s a l s o shown i n P i g . / / .  It i s seen that t h e i n f l e c t i o n i n t h e drop time versus p o t e n t i a l curve c o i n c i d e s with the i n f l e c t i o n i n the c u r r e n t - v o l t a g e In both cases oxygen was present  i n the s o l u t i o n .  By breaking and c l o s i n g the s t a b i l i z i n g a polarographic  curve.  circuit  during  run i t was found t h a t the e f f e o t on the recorded  polarogram i s n e g l i g i b l e .  At a s e n s i t i v i t y s e t t i n g 0.003/^amp/mm  with no damping the average current was decreased  0.0022/^amps.,  a n e g l i g i b l e q u a n t i t y compared to a total d i f f u s i o n c u r r e n t o f  r mm  Hi:11  F i g u r e 12 Recordings o f d i f f u s i o n current o f 0.000288$ z i n c amalgam a t constant  E.fll.f, values.  o i r c u i t was opened and c l o s e d on  instrument r e a d i n g .  The s t a b i l i z i n g  to determine e f f e o t  Sensitivity  0.06>^amp/mm.  At 0.600 v o l t a p p l i e d E.M.F. the c u r r e n t 0.06yVamps when t h e s t a b i l i z i n g c i r c u i t T o t a l current  6.45/^amps.  This  indeterminate.  i s closed.  i s t h e maximum  d e v i a t i o n shown by s e v e r a l t e s t s . d e v i a t i o n was  i s deoreased  In most cases the  65.  the order o f even O.iy^amp.  In the working range o f s e n s i t i v i t y  s e t t i n g s with damping no d e v i a t i o n o f t h e d i f f u s i o n c u r r e n t could be detected when the s t a b i l i z i n g c i r c u i t was opened and closed.  ( P i g . )Z~).  The breaking o f the c i r c u i t , however, does  cause an immediate d e f l e c t i o n o f the r e c o r d i n g pen which then d r i f t s back to the o r i g i n a l v a l u e . To sum up, t h e data so f a r i n d i c a t e s t h a t  dropping  amalgam e l e o t r o d e s behave s i m i l a r l y to dropping mercury e l e c t r o d e s i n c a p i l l a r y outflow and droptime c h a r a c t e r i s t i c s .  The  s t a b i l i z i n g c i r c u i t has no a p p r e c i a b l e e f f e c t on t h e r e c o r d i n g c i r c u i t nor on the c a p i l l a r y c h a r a c t e r i s t i c s . c o n d i t i o n s a r e such that accuracy o r d i n a r y polarography By adding  o f t h e same o r d e r obtained i n  could be expected  increments  i n amalgam  polarography.  o f g e l a t i n s o l u t i o n and compar-  ing the polarograms i t was found  t h a t a c o n c e n t r a t i o n o f about  0.005% was optimum f o r amalgam polarography. amalgam c o n c e n t r a t i o n s and d i f f e r e n t it  In s h o r t , the  capillary  For d i f f e r e n t characteristics  i s p o s s i b l e that the optimum g e l a t i n c o n c e n t r a t i o n may v a r y . Polarograms o f 0.0003% z i n c amalgam a r e shown i n  P i g s . /3 ,  Af  .  P i g . 12> i s a polarogram  addition of gelatin. P i g . Jljls obtained  a polarogram  obtained b e f o r e t h e  The maxima i s seen to be very c o n s i d e r a b l e . a f t e r the a d d i t i o n o f g e l a t i n .  f o r t h i s amalgam i s recorded  The data  i n Tables 15 and 16.  F i g u r e 13 Polarogram  o f 0.000288% z i n o amalgam i n O.IN p o t a s s i u m  c h l o r i d e swept o u t w i t h n i t r o g e n . Sensitivity Diffusion The he  rapid  decrease  0.06/^/amp/mm.  current  i n o u r r e n t s t a r t i n g a t 5 0 % span, may  due t o a ohange i n d r o p  was this  almost reason  a maxima  streaming  from  time. 70% span  i t i sd i f f i c u l t  exists.  11.Stamps.  The d r o p p i n g e l e c t r o d e t o end o f r u n .  to determine  For  whether o r n o t  w  r  A  1  Art*  - to % - y»  8.  *PAH  -tob-  J F i g u r e 14 Polarogram o f 0.000288$ zino amalgam i n 0.1N potassium c h l o r i d e p l u s 0.005$ g e l a t i n swept out with  nitrogen.  Sensitivity  0.06^amp/mm  D i f f u s i o n c u r r e n t 5.5>7amp. The a d d i t i o n o f g e l a t i n has a marked e f f e o t on the ourrent  oompare with F i g u r e '-^  r -4 iinin.i.  y  Figure  Polarogram chloride  plus  solution. ourrent and  of  due  0.000288% 0.005%  There  zinc  gelatin  i s no  clear  to reduction  the current  due  . ••.•TTTT  till:  15 amalgam with  in  oxygen  0.1H  potassium  present  i n  d i s t i n c t i o n between t h e  o f oxygen  o r hydrogen  to o x i d a t i o n o f t h e zinc  peroxide  i n amalgam,  5 MM, LINES ACCENTED,CM. LINES H E A V Y  HADE  IN  CANADA  66. TABLE 15 Polarographic  C h a r a c t e r i s t i c s o f Zinc  (1) Recorded with Sargent Amalgam:  (a)  Ho. 1 2 3 4 5  Polarograph  0.0042 gm Zn i n 1457.7 gm H g  Electrolyte: Date June 5 " 6 " 6 " 7 " 7  Amalgam  O.IN KCL  D i f f u s i o n Current 5.37^/amp 5.55 5.64 " 4.88 ** 4.98 " n  a  0.005$ g e l a t i n . Droptime Meroury Outflow 2.64 s e c . 1.750 mgm/sec. 4.12 " 1.734 4.12 " 1.734 2.03 " 1.703 " 2.42 " 1.703 "  The c o n c e n t r a t i o n o f z i n c i s c a l c u l a t e d from the molecular  weight o f z i n c , 65.38, and the d e n s i t y o f mercury at 25.00°C, 13.53 gm/cm , to he 0.5963 m i l l i m o l a r on the assumption that 3  the z i n c l o s t  i n making up the amalgam was n e g l i g i b l e .  grams o f the supernatant  Polaro-  water l a y e r could not be d i s t i n g u i s h e d  from polarograms o f d i s t i l l e d water ( F i g . ^  c  ).  TABLE 15 * v i  (2) Manually Recorded. Date June 7 "  Ho. 6 7  D i f f u s i o n Current 5.23>famp 5.27 "  Droptime 2.75 5 £ " ^ 2.75 "  Mercury Outflow 1.703 mgm/seo 1.703  Due to d i s t o r t i o n o f the wave where t h e c u r r e n t i n creases r a p i d l y the measurement o f t h e d i f f u s i o n c u r r e n t was not made i n the same manner as i n o r d i n a r y polarography.  Instead  the v e r t i c a l d i s t a n c e between the average c u r r e n t - a t a p o i n t before and f o l l o w i n g the c u r r e n t i n c r e a s e was taken as a measure o f the d i f f u s i o n c u r r e n t .  Provided  the same r e l a t i v e p o i n t s a r e  chosen on d i f f e r e n t polarograms the values a r e as c o n s i s t e n t a s those determined a t the half-wave p o t e n t i a l .  The r e s u l t a n t  v a l u e s , however, a r e s l i g h t l y l a r g e r than those  taken a t the  half-wave p o t e n t i a l .  The d i f f e r e n c e i n v a l u e s i s l e s s than 5%  i f t h e v a r i a t i o n o f 'm' and ' t i s n e g l e c t e d .  A comparison may  1  be made w i t h the v a l u e s shown i n Table 15 which g i v e s the data obtained by the method used i n o r d i n a r y p o l a r o g r a p h y .  These r e -  s u l t s were obtained from polarograms where d i s t o r t i o n o f the -wave form d i d not i n t e r f e r e w i t h an a c c u r a t e d e t e r m i n a t i o n of the  half-wave p o t e n t i a l .  I t i s seen t h a t the two methods o f  measurement g i v e r e s u l t s which vary by zfo-5%. However, when 'm' and ' t ' a r e a l s o measured a t the p o t e n t i a l o f the current measurements, the r e s u l t s by e i t h e r method should agree w i t h i n  2%. TABLE 16 P o l a r o g r a p h i c C h a r a c t e r i s t i c s o f Zinc Mo. 2 6 7 (a)  Diffusion Current(a)Ej 5.46-^amp 1.070 v o l t 5.13 " (b) 1.072 " 5.06 " (b) 1*068 "  Droptime 4.12 sec 2.75 " 2.75 n  Amalgam  Mercury Outflow 1*750 mgm/sec 1.703 " 1.703 "  measured by method d e s c r i b e d i n "Sargent Manual o f I n s t r u c t i o n s f o r the P o l a r o g r a p h " .  (b) note order o f d i f f e r e n c e from Table 14. It  i s noted t h a t t h e order o f d i f f e r e n c e f o r the d i f -  f u s i o n c u r r e n t s o f No.6 and 7 i s o p p o s i t e i n Table 16. r e s u l t has been shown to i l l u s t r a t e t h a t the measurement may be somewhat  i n error.  This itself  Unless the polarogram has an i d e a l  form t h e r e i s a c e r t a i n amount o f c h o i c e i n the e x t r a p o l a t i o n o f the  average c u r r e n t as determined from the midpoint o f the pen  t r a v e l during the formation o f each drop.  Since i t has been  shown that the drop time v a r i e s c o n s i d e r a b l y short p o t e n t i a l ranges t h e r e i s l i t t l e an i d e a l polarogram.  ( P i g . I' ) over  likelihood o f obtaining  T h i s f a c t i s evidence t h a t the method f o r  68 measuring the d i f f u s i o n c u r r e n t s as g i v e n i n the book o f i n s t r u c ts  T  t i o n s has-been chosen f o r s t r i c t a c c u r a c y .  A c t u a l l y , measuring  the c u r r e n t a t p o t e n t i a l s preceding and f o l l o w i n g the wave as w e l l as 'm' and ' t ' a t t h e same p o t e n t i a l s and c a l c u l a t i n g t h e value o f t h e r e s i d u a l c u r r e n t by the I l k o v i c equation appears to o f f e r a more a c c u r a t e method f o r t h e d e t e r m i n a t i o n o f the diffusion current. Before using the values shown i n Table 15 f o r c a l c u l a t i o n s i t should be shown t h a t the c o n d i t i o n s under which the d i f f u s i o n c u r r e n t equations can be a p p l i e d have not been v i o l a t e d to a degree g r e a t e r than expected. d  F i r s t l y , a rough approxima-  t i o n o f the order o f r , where d i s the d i f f u s i o n l a y e r and r i s the r a d i u s o f the amalgam drop, may be o b t a i n e d . Ho. 1, i d = 5.37^amp,  t = 2.64 s e c , m = 1.750mgm sec"- - where 1  the amalgam i s 0.5963 m i l l i m o l a r z i n c . tained  From Table 14,  From t h i s data i s ob-  the number o f moles r e a c t i n g i n a f i n i t e p e r i o d , 5.37Xamp. X 2.64 sec = 2 equivalents/mole X 96500  coulombs/equivalent = 7.52 X 1 0 "  and  the number o f moles o f z i n c contained 1.750 mgm/seo X 2.64 sec  x  13530 mgm/cm  moles.  i n the drop*  _i  Y  1000 cm /  s  1 1  5  0.5953 *  1000  molar  = 20.4 X 1 0 - H moles. That  i s approximately  one t h i r d o f the amalgam i n each drop  reacts electro chemically. gross  Thus i t i s shown t h a t there i s no  discrepancy. Assume t h a t the r e a c t i n g z i n c i s contained  d  0  at the outer s u r f a c e o f t h e drop  i n a layer  from whioh  -  } —  \J  -  O •/ 3  The volume o f the drop can be c a l c u l a t e d from t h e v a l u e o f 'm' and thus the v a l u e o f 'd ' may be found d  = 0.13 \ / 3 , 1 . 7 5 0 mgm/sec X 2.64 sec V 4 rf 13.53 mgm/mm 3  0  3  —  0.055 mm  T h i s value f o r d  Q  and  r =  0*43 mm  agrees w i t h the v a l u e f o r t h e t h i c k n e s s o f  the d i f f u s i o n l a y e r around the mercury drop i n o r d i n a r y  i  i polarography.  I t i s not shown t h a t the r a t i o . r does not  equal 1. The d i f f u s i o n current constant l a t e d to show the order o f p r e c i s i o n .  'I'  has been c a l c u -  The v a l u e s o f I a r e  shown i n Table 17. TABLE 17 The D i f f u s i o n Current Constant f o r Z i n c Amalgam id Ho. I = cm 2 t 1 3 6 1 2 3 4 5 6 7  Average value  5.28 5.09 5.17 5.10 5.06 5.20 5.24 5.16  ±- O.OjJ  The v a r i a t i o n between extreme v a l u e s i s l e s s than bfo which i s s l i g h t l y g r e a t e r than the v a r i a t i o n between the extreme v a l u e s f o r I f o r the 0.6187 m i l l i m o l a r z i n c s o l u t i o n where t h e extremes  1. See Ref.5, p.144  70. vary by l e s s than  4$.  In order to show the a c c u r a c y o f the method i t i s necessary to know the v a l u e o f the d i f f u s i o n c o e f f i c i e n t z i n c i n mercury.  However, the v a l u e s r e p o r t e d i n the  t u r e (see Table 5) and  show c o n s i d e r a b l e v a r i a t i o n .  Schwarz v a l u e s temperature  deg."  1  and 0.013  cm  2  1  are c a l c u l a t e d .  p e r a t u r e increments a r e such that a temperature 0.01  litera-  From Wogan's  increments 0.0096 em^  s e c " l degT  of  sec  The  - 1  tem-  coefficient  would not i n t r o d u c e any gross e r r o r i n determining the  v a l u e o f the d i f f u s i o n c o e f f i c i e n t a t 25.00°C from the t a b l e d values.  The r e s u l t a n t v a l u e s a r e shown i n Table  18  TABLE 18 The D i f f u s i o n C o e f f i c i e n t of Z i n c i n Mercury at 25.00°C Investigator 0. Meyer Wogan Schwarz  Reported Value Value 150C-2.42 Z 10- cm«sec--L 2.52 11.50C-2.52Z 10-5 « 2.65 25OC-2.00 X 10" " 2.00 b  5  Mean Value  2.39  C a l c u l a t e d f o r 25.0QQC X 10-°cm«sec-l X 10-5 » Z 10-5 » Z 10-5  «  A c c o r d i n g to the f i n d i n g s o f Strehlow and  Stackelberg  streaming at the amalgam s u r f a c e r e s u l t s i n l a r g e d e v i a t i o n s from c a l c u l a t e d v a l u e s f o r d i f f e r e n t v a l u e s o f 'm' However, they found t h a t a p l o t o f I v s . y, where produced  curves which were asymptotic  to a s t r a i g h t  the i n t e r c e p t o f the l i n e they determined  and ' t . 1  line.  the value o f the  From dif-  f u s i o n c o e f f i c i e n t o f oadmium i n mercury s i n c e From the slope o f the l i n e they c a l c u l a t e d the v a l u e o f B to be 28.5.  This value i s i n agreement with the  theoretical  approximation  that the v a l u e o f B i s about 30.  Assuming that the d i f f u s i o n c o e f f i c i e n t o f z i n c i n mercury i s 3.4 X 10"^ c m s e c 2  constant  - 1  the value o f the n u m e r i c a l  'B' may be c a l c u l a t e d d i r e c t l y .  The v a l u e s are  shown i n Table 19 TABLE 19 Approximation o f the n u m e r i c a l Constant 'B' i n the Strehlow-Stackelberg Equation f o r the D i f f u s i o n Current o f a Dropping Amalgam Electrode Ho. 1 2 3 4 5 6 7 Average  B 19.4 83.1 80.9 85.4 26.0 26.0 24.7 23.6  Since t h e v a l u e s f o r B l i e w i t h i n the range o f t h e o r e t i c a l approximation  i t i s assumed t h a t the s u r f a c e streaming o f  the amalgam drop was no more s e r i o u s than that a t the mercury drop i n r e g u l a r polarography. A c c o r d i n g to the c a l c u l a t i o n s shown i n Table 11 the d i f f u s i o n c u r r e n t equation a f t e r Lingane and Loveridge gave values o f 'D' best i n agreement with D , the d i f f u s i o n 0  c o e f f i c i e n t o f z i n c at i n f i n i t e graphy the equation merely  dilution.  For amalgam p o l a r o -  r e q u i r e s a change o f s i g n i n the  second term thus  The v a l u e f o r D may be determined The r e s u l t s a r e shown i n Table 80  f  /  i n the manner used p r e v i o u s l y .  71(a) A f t e r completion o f t h i s work i t was r e a l i z e d that the new equations f o r the d i f f u s i o n c u r r e n t were simple q u a d r a t i c s with D"§" as the unknown q u a n t i t y . \f~f)~ -  equation  Prom the l i n g a n e - I o v e r i d g e  / — ]f~^ ~ O • }Z  it^ru  The v a l u e s o f D computed by t h i s formula a r e g i v e n i n Table 21. TABLE 21. The Apparent  Polarographic D i f f u s i o n C o e f f i c i e n t o f Z i n c i n Mercury a t 25°C.  Ho . 1 2 3 4 5 6 7  D X 10-5 3.01 cm s e c " 1.59 " 1.65 2.69 " 2.68 " 2.93 " 2.99 " a  1  n  There i s c o n s i d e r a b l y more discordance among these v a l u e s x among those shown i n Table 20.  Here the term t  denominator o n l y and consequently has a l a r g e r However, the value o f 'm' was not determined it  should be.  L  than  occurs i n t h e  influence.  i n t h e s o l u t i o n as  A c t u a l l y t and m should be determined  simultan-  eously f o r a c c u r a c y . The s o l u t i o n o f t h e q u a d r a t i c i s the most a c c e p t a b l e method f o r determining the value of t h e d i f f u s i o n  coefficient.  The method a l s o p r o v i d e s a b e t t e r i n d i c a t i o n o f t h e p r e c i s i o n obtained. In view o f the discordance among t h e v a l u e s shown i n Table 21 i t i s evident t h a t f u r t h e r work under c a r e f u l l y trolled  con-  c o n d i t i o n s i s necessary to e s t a b l i s h h t h e technique  i n t h i s work.  used  72 TABLE  20  The Apparent P o l a r o g r a p h i c D i f f u s i o n C o e f f i c i e n t o f Z i n c i n Mercury a t 25°C. lo _I_ 1 5.28 2 5.09 3 5.17 4 5.10 5 5.06 6 5.20 7 5.24 Average 5.16  D X 10 1.89 c m 1.76 1.81 1.77 1.74 1.83 1.86 1.81  V% X 1 0 ( a ) 2.70 om^sec 2.56 " 2.66 2.47 " 2.45 2.63 " 2.68 2.58  5  5  2  seo " " " " " " "  - i  n  (a) D^ from l i n g a n e - I o v e r i d g e equation, n Do The mean v a l u e i s agreement with the v a l u e s r e p o r t e d by Wogan and Meyer r a t h e r than the v a l u e reported by Schwarz. It i s d i f f i c u l t  to draw any c o n c l u s i o n s with r e s p e c t  to the accuracy o f these r e s u l t s s i n c e the a v a i l a b l e v a l u e s reported i n the l i t e r a t u r e vary by an amount g r e a t e r than t h e experimental e r r o r  involved.  F u r t h e r , i t i s o n l y assumed that  the experimental e r r o r i n amalgam polarography  i s o f the same  o r d e r as t h a t found  Unfortunately,  i n o r d i n a r y polarography.  time d i d not a l l o w f u r t h e r experimentation  under the c o n d i t i o n s  r e q u i r e d to e s t a b l i s h the techniques It has been shown that a d i l u t e amalgam can be stabilized  f o r p o l a r o g r a p h i c measurements. The amalgam used  to o b t a i n the data shown i n Tables 14 and 15 was used  from  June 4-7, 1950, or over a p e r i o d o f 85 hours.  Polarograms  obtained i n the f i r s t hour were approximately  duplicated i n  the l a s t hour.  Due to a decrease i n the h e i g h t o f t h e mercury  column s m a l l d i f f e r e n c e s were observed.  The d i f f e r e n c e s ,  however, were o f the same order as the v a r i a t i o n s shown i n Table 14.  T h i s amalgam was made up 0.000288$ Zn. Heyrovsky and  Kalousek (f )) found t h a t amalgams l e s s than 0.005$ were too 0  unstable f o r use.  Strehlow and S t a c k e l b e r g have o b t a i n e d  measurements which a r e i n b e t t e r agreement f o r d u p l i c a t e d e t e r minations than have been obtained i n t h i s work. 13.93 of  m i l l i m o l a r cadmium amalgam o r 0.01157$ Cd.  They used T h e i r method  p r e p a r i n g the amalgam has not been g i v e n and presumably i t  was not p r o t e c t e d from the atmosphere i s mentioned.  s i n c e no s p e c i a l technique  Unfortunately, t h e i r tabled  r e s u l t s (L C) do not  show the time that each measurement o r each group o f measurements was made. of  That i s they have not shown t h a t the c o n c e n t r a t i o n  the amalgam remained  constant.  Therefore the d e v i a t i o n of I  vs y could be due i n p a r t to a decrease i n c o n c e n t r a t i o n . E a r l y i n t h i s work an amalgam 0.000127$ Zn gave more or l e s s c o n s i s t e n t  r e s u l t s a t the beginning and  120 hour period.March 4-9, s i d e r a b l e t r o u b l e was  1950.  end o f a  At t h a t time, however, con-  experienced with t h e c a p i l l a r y becoming  clogged thus causing h i g h l y e r r a t i c drop times which v a r i e d from a drop time o f 14 seconds to constant streaming under the same c o n d i t i o n s a t d i f f e r e n t times.  This c l o g g i n g has  been presumed due to the presence o f z i n c oxide which  since resulted  from the i n t e r a c t i o n o f zinc i n amalgam w i t h oxygen which r e mained adsorbed on the g l a s s w a l l s o f the e l e c t r o d e  assembly.  A c c o r d i n g to the manufacturers, t h e Sargent P o l a r o graph Model XXII i s a c c u r a t e to 0.1$ when the temperature i s c o n t r o l l e d 25.00°C£0.05°  at the p o l a r o g r a p h i c c e l l and room  temperature i s 25°C±10.  I t i s suggested that  temperature  c o n t r o l be extended to i n c l u d e the e n t i r e apparatus, r e c o r d e r , dropping e l e c t r o d e assembly, p o l a r o g r a p h i c c e l l and p o t e n t i o m e t e r .  74. The meroury column should he c o n t r o l l e d to ±. 0.5 by a convenient marker and mercury r e s e r v o i r .  a screw device to r a i s e or lower  the  It i s e s s e n t i a l t h a t the mercury column i s  not s u b j e c t to v i b r a t i o n . umn  mm  In order to c o n t r o l the mercury  col-  i t i s l a d v i s a b l e to immerse the c a p i l l a r y t i p to a marker. For c o n s i s t e n t r e s u l t s the e x t e r n a l e l e c t r o d e appears  to be b e t t e r than the i n t e r n a l anode p o o l . The  e l e c t r o l y t e should be e s s e n t i a l l y oxygen f r e e .  There i s no doubt t h a t t r a c e s o f oxygen s e r i o u s l y i n t e r f e r e w i t h the d e t e r m i n a t i o n o f the d i f f u s i o n c u r r e n t at low c o n c e n t r a t i o n s . The measurement o f the d i f f u s i o n c u r r e n t i s perhaps more convenient  by the method d e s c r i b e d .  However, i t i s b e l i e v e d  that accuracy can be best obtained by measuring the  current at  d e f i n i t e p o t e n t i a l s before and a f t e r the half-wave p o t e n t i a l . Meroury i s c o l l e c t e d a t the same p o t e n t i a l to determine while chart.  ' t ' may  be determined  Then 'm'  potential.  The  and  ' t ' are determined  recorded  a g a i n a t the half-wave  current measurements a r e then c a l c u l a t e d to  r e f e r to the v a l u e s o f The  from pen t r a v e l on the  'm*  'm'  and  ' t ' at the half-wave p o t e n t i a l .  v a r i a n c e among d u p l i c a t e determinations  with  standard z i n c s o l u t i o n s i n t h i s work i s w i t h i n the l i m i t s o f experimental  e r r o r reported by o t h e r s (p.51).  be obvious that there was  However, i t must  c o n s i d e r a b l e l a t i t u d e i n the e x e r c i s e  of control. In amalgam polarography must a l s o be c o n s i d e r e d . as described h e r e i n ,  there are o t h e r f a c t o r s which  F i r s t l y , the amalgam must be  l o other method was  formation o f a s u r f a c e f i l m and  found  stabilized  to prevent  consequent decrease  the  i n concen-  75 tration.  The amalgam r e s e r v o i r and dropping c a p i l l a r y must be  c l e a n and f r e e o f adsorbed oxygen.  Prolonged sweeping w i t h  p u r i f i e d n i t r o g e n or hydrogen appears n e c e s s a r y .  The p o s s i b i -  l i t y o f i n t e r a c t i o n o f t h e amalgam with g l a s s appears n e g l i g i b l e , although over a long p e r i o d o f time some e f f e c t may o c c u r . possibility  This  i s suggested by the f i l m y appearance o f o r i g i n a l l y  clear glass after  impure mercury has been stored f o r some time.  This f i l m i s permanent.  In p r e l i m i n a r y work, f i l m i n g was ob-  served a f t e r an amalgam had stood f o r s e v e r a l hours w i t h the stabilizing circuit  applied.  The f i l m i n g was p a r t l y removed by  i n c r e a s i n g the s t a b i l i z i n g v o l t a g e .  However, the amalgam -  g l a s s i n t e r f a c e appeared to become wetted f u r t h e r from t h e amalgam - water i n t e r f a c e w i t h i n c r e a s i n g p o t e n t i a l . be e x e r c i s e d to prevent w e t t i n g at the c a p i l l a r y .  Care must  Under 10  v o l t s s t a b i l i z i n g E.M.F. the w e t t i n g extended about 1-3 cm from the amalgam - water  interface.  wetting extended 8-10 cm.  Under 25 v o l t s E.M.F. the  The f i l m i n g observed i n t h e s e i n s t -  ances was e a s i l y removed by d i l u t e n i t r i c a c i d the f i l m i n g mentioned  - different  from  previously.  It was observed t h a t a t low p r e s s u r e s o f mercury t h e r e was no f l o w i n g from the c a p i l l a r y . mercury column the mercury and f i n a l l y began dropping.  Upon i n c r e a s i n g t h e  thread moved slowly along the bore This suggests that the amalgam T K AT-  can be made up i n apparatus resembling the=&© shown i n F i g s . The apparatus i s swept out with n i t r o g e n . maintained a t the c a p i l l a r y while a weighed i s run into the r e s e r v o i r .  IJ  Nitrogen pressure i s amount o f mercury  The approximate amount b e i n g prev-  i o u s l y determined by experiment. . The water l a y e r i s formed and  .  Applied  Pressure  I  AMALGAM RESERVOIR  Dropping  Capillary  N i t r o g e n Pressure Figure  /7  Dropping E l e c t r o d e f o r Amalgam Polarography  76. a weighed  sample o f t h e s o l u t e metal added.  While the metal i s  d i s s o l v i n g under the i n f l u e n c e o f the a p p l i e d s t a b i l i z i n g potent i a l an o c c a s i o n a l bubble o f n i t r o g e n i s forced to the  ensure a homogeneous amalgam.  i n t o the r e s e r v o i r  When ready f o r polarography  n i t r o g e n p r e s s u r e can be removed from t h e c a p i l l a r y and  p r e s s u r e a p p l i e d to f o r c e t h e amalgam through the c a p i l l a r y . The pressure can be maintained constant by means o f a manometer with due c o n s i d e r a t i o n to the v a r i a t i o n o f the mercury p r e s s u r e . Other methods f o r h a n d l i n g t h e amalgam p r e s e n t difficulties.  In the siphon method d e s c r i b e d i n t h i s work en-  trapped gas bubbles presented a d i f f i c u l t  problem.  The method  of  Handles ( 2 1 ) appears f e a s i b l e except f o r t h e u n c e r t a i n t y as  to  whether the mercury o r i g i n a l l y i n the siphon becomes homo-  geneous with the l a r g e r body o f amalgam. of  Here too the p o s s i b i l i t y  entrapping gas bubbles i n the dropping e l e c t r o d e column appears  rather  large. In order to prevent w e t t i n g by the o v e r l a y o f water o r  entrainment o f gas bubbles by the amalgam column r a t h e r apparatus appears to be r e q u i r e d .  However, from e x p e r i e n c e gained  i n t h i s work the simple apparatus shown i n P i g s the  requirements.  elaborate  / °7 ,  supplies  Here the mercury head must be determined so  that i t does not flow through the c a p i l l a r y i n i t i a l l y nor must i t be so low that w e t t i n g a t the;,amalgam-glass the  i n t e r f a c e extends to  capillary. As mentioned  by Heyrovsky and Kalousek ( '?) and con-  firmed i n t h i s work,the anodic c u r r e n t o f an amalgam i s much g r e a t e r than the c a t h o d i c c u r r e n t o f a metal s a l t i n s o l u t i o n by p o l a r o g r a p h i c measurement.  In t h i s work i t i s shown, but not  77 confirmed t h a t q u a n t i t a t i v e measurements are p o s s i b l e .  For  a n a l y t i c a l work with a known weight o f mercury i n t h e r e s e r v o i r a supernatant s o l u t i o n may be subjected to c o n t r o l l e d e l e c t r o l y s i s f o l l o w e d by polarography o f the amalgam. s o l u t i o n oan then be recovered and by a s i m i l a r another amalgam could be determined.  potential^?) The  procedure  The method could be u s e f u l .  f o r determining t r a c e s o f i o n s which reduce to mercury s o l u b l e metals i n the presence o f l a r g e amounts o f m a t e r i a l s which do not. The a p p l i c a t i o n o f amalgam polarography to p r a c t i c a l a n a l y s i s , however, must await establishment o f t h e teohnique and also systematic i n v e s t i g a t i o n o f the i n t e r a c t i o n s o f the mercury s o l u b l e m e t a l s .  78  I I I - Summary o f R e s u l t s Polarograms o f standard  z i n c i n 0.1U potassium  c h l o r i d e p l u s 0.0001% g e l a t i n were reoorded proposed f o r amalgam polarography. d i f f u s i o n current versus  i n t h e manner  The s t r a i g h t l i n e p l o t o f  c o n c e n t r a t i o n over the c o n c e n t r a t i o n  range 0.6187-0.1040 m i l l i m o l a r z i n c passes very c l o s e to the origin. with  The d i f f u s i o n c u r r e n t constant was found to i n c r e a s e  d ec r easing "-'e<5nc ent r a t i o n . Concentration 0.6187 m i l l i m o l a r 0.3365 " 0.2061 " 0.1040 "  The value reported  1= D i f f u s i o n ourrent 3.44 3.55 3.62 3.61  constant  i n the l i t e r a t u r e f o r l m i l l i m o l a r zinc i n  O.IK potassium c h l o r i d e p l u s 0.005% methyl red i s 3.42.  Since  the v a r i a t i o n o f I with c o n c e n t r a t i o n appears to he c o n t r o v e r s i a l the agreement i s considered  satisfactory.  When oxygen was present was decreased  although  oxygen was removed.  the d i f f u s i o n c u r r e n t f o r z i n c  the t o t a l c u r r e n t was the same a f t e r  This effect  i s explained by t h e removal o f  z i n c by p r e c i p i t a t i o n or complex formation l a y e r w i t h t h e h y d r o x y l o r peroxide electro  reduction.  i n the d i f f u s i o n  products  of the oxygen  The t o t a l c u r r e n t i s not a f f e c t e d s i n c e t h e  amount o f z i n c removed i s e l e c t r o c h e m i c a l l y e q u i v a l e n t to t h e amount o f oxygen reduced to h y d r o x y l . Since a n i t r o g e n sweep only reduces the c o n c e n t r a t i o n o f oxygen to a minimal value t h e r e could be some c o n s i d e r a b l e e f f e c t on the development o f the z i n c wave a t very low concen-  79 trations of zinc.  In t h i s work 0.0168 m i l l i m o l a r z i n c  to develop a wave form. polarograms  0.0042 m i l l i m o l a r z i n c s o l u t i o n s gave  which could not be d i s t i n g u i s h e d  obtained with 0.11  failed  from  potassium c h l o r i d e a l o n e .  polarograms  Further i n v e s t i -  g a t i o n i s r e q u i r e d at these extremely low c o n c e n t r a t i o n s . The apparent  d i f f u s i o n c o e f f i c i e n t o f zinc i n  potassium c h l o r i d e was  computed from the equations f o r the  f u s i o n c u r r e n t as g i v e n by I l k o v i c , l i n g a n e and Strehlow and  Stackelberg.  0  7.2 X l O  - 6  cm2  sec" . 1  dif-  Loveridge, and  T h e o r e t i c a l l y the v a l u e i s t h a t o f  the d i f f u s i o n c o e f f i c i e n t o f z i n c at i n f i n i t e D=  0.1N  The  dilution,  I l k o v i o equation gave v a l u e s  f o r D w i t h i n 28%, that o f Lingane and Loveridge w i t h i n 12$ and that o f Strehlow and S t a c k e l b e r g w i t h i n 17$.  The d e v i a t i o n s a r e  o f approximately the same degree as reported i n the l i t e r a t u r e . Contrary to Lingane and  Loveridge' statement a know-  ledge o f the value o f D i s not e n t i r e l y e s s e n t i a l to the use o f t h e i r new  equation.  The equation i s a simple q u a d r a t i c and  the  solution i s where A = the n u m e r i c a l constant i n the c o r r e c t i o n term.  The  v a l u e s computed from t h i s formula were 0.4$  than  - 2.5$  larger  the values computed by the method suggested by the authors mentioned. The r e s u l t s were found to agree w i t h i n 15$ o f p r e v i o u s l y recorded data reported i n the l i t e r a t u r e even when the most c o n t r o v e r s i a l p o i n t s were a l l o w e d . i n complete  agreement.  the method proposed  Some i n d i v i d u a l r e s u l t s were  The agreement i s used as evidence that  f o r amalgam polarography i s e q u a l l y  satisfactory  80  Within the limits of determination^very dilute zinc amalgams were found to behave like pure mercury i n their dropping characteristics. The amalgam stabilizing circuit i s shown to have no effect on the droptime or recording apparatus which w i l l introduce an error greater than 0.1%. Thus, the agreement with theoretical or other data should he attained as in ordinary polarography. When oxygen was present i n the solution a deviation of the drop time versus potential curve was found to occur over the same potential range as the anodic zinc wave developed on thecurrent versus potential curve. Polarograms of zinc amalgam, 0.5963 millimolar zinc or 0.000288/0 zinc by weight, dropping i n 0.1K potassium chloride plus 0.005% gelatin were recorded. The diffusion current constant,according to the Ilkovic equation i s 5.16 ±0.07 at 25°C. Assuming that the diffusion coefficient of zinc in mercury -5 2 -1 i s 2.4 X 10  cm  sec  , the values of B, the numerical constant i n the  second term of the Strehlow-Stackeiberg equation for the diffusion current of amalgam electrodes, range from 19.4 to 26.0 with an average value of 23.6. This i s taken as evidence that the streaming current in the mercury drop did not introduce serious error. Computation by the Lingane-Loveridge diffusion current equation gave the value 2.58 X 10  5  cm^sec  ±0.09 at 25°C. i n  -5 2 -1 excellent agreement with the values reported by Wogan,2.52 X 10 cm sec o -52-I at 11.5 C , and by Meyer, 2.42 X 10 cm sec at 15 C. Schwarz gives -5 2 - 1 o a value 2.00 X 10 cm sec at 25.0 G. 0  Computation by the solution of the quadratic equation from Lingane and Loveridge  j_  (/ / - 0-/2g6"  81  gave rather discordant results which, however, are of the correct degree 5 2 —1 —5 2 -»i of magnitude with a range 1.59 X 10" cm sec to 3.01 X 10 cm see . —  The most important result i s the maintenanceof the diffusion current oyer a period of several days as shown "by the relatively consistent values of the diffusion current constant. The results show that the method used for stabilizing the amalgam was successful. Such a device now enables the application of amalgam polarography to analysis. However, i t remains to completely establish the method and then to investigate the behaviour of multicompenent systems, say sodium, zinc and lead i n mercury. It would be interesting to investigate the behaviour of several solute metals together or to investigate selective amalgamation by reduction from salt solution.  £2.  BIBLIOGRAPHY (1)  J.J.Lingane, J.A.C.S., 61, 976 (1939).  (2)  D . I l k o v i c , C o l l . Czech. Chem.Commun., 6, 498 (1934).  (3)  J.J.Lingane and I.M.Kblthoff, J.A.C.S.,61,825 (1939).  (4)  J.Maas, Coll.Czech.Chem.Commun., 10, 42 (1938).  (5)  I . S . K o l t h o f f and J.J.Lingane, "Polarography", I n t e r s o i e n e e P u b l i s h e r s Inc., New York  (1946).  (6)  J.J.Lingane and I.M.Kolthoff, Chem.Rev.1-94 (1939).  (7)  OiH.Muller, "The P o l a r o g r a p h i c Method o f A n a l y s i s " , Mack P r i n t i n g Co. (1941). J.J.Lingane and B.A.Loveridge, J.A.C.S., 72, 438 (1950) H.Strehlow and M.von S t a c k e l b e r g , Z. Elektrochem.,  (8) (9)  54, 51-62 (1950). (10) J.J.Lingane and B.A.Loveridge, J.A.C.S., 68,395 (1946). (11) D.MacGillavray and E.K.Rideal,  Rec.trav.chem.,  56, 1013 (1937). (12) Ref. 5, pp. 32-37 (13) Ref. 5, p. 64. (14) M.Von S t a c k e l b e r g , Z.Elektrochem., 45, 466 (1939). (15) G.S.Smith, Mature,  163, 290 (1949).  (16) Ref. 9, p. 56. (17) M.von S t a c k e l b e r g and H.von F r e y h o l d , Z. Elektrochem., 46, 120 (1940). (18) Ref. 5, p. 148. (19) J.Heyrovsky and M.Kalousek, Co 11.Czech.Chem. Commun., 11, 464 (1939). (20) J.Heyrovsky, D i s c u s s i o n s o f the Faraday S o c i e t y , 1, 212 - 222 (1947). (21) J.E.B.Randies, i b i d , 1, 15 (1947). (22) T.Erde Gruz and E.Varga, Chem.Abs., 42, 8676g (1948). Hung. A c t a Chim., 1, 18 - 27 (1947).  S3 (23)  F . L . E n g l i s h , A n a l . Ohem., 20, 889  (1948).  (24)  J.W.Mellor, "A Comprehensive T r e a t i s e on Inorganic ana T h e o r e t i c a l Chemistry", Vol.IV,ppl037 - 1048 langmans Green, London (1923).  (25)  H u l e t t and DeLury,  (26)  H u l e t t and Crenshaw, J . Phys.Chem., 14, 175 (Hot a v a i l a b l e i n U.B.C.Library)  (27)  T.W.Richards and G.S.Forbes,  J.A.C.S., 30, 1805  l o . 56 (1906) (Q G 156 R  (1908). (1910)  Pub. Carnegie I n s t . , 52)  (28)  J.H.Hildebrand, J.A.C.S., 35 501  (1913).  (29)  P i e r c e and Eversole,J.Phys.Chem.,  (30)  J.L.Crenshaw, J.Phys.Chem., 34, 863  (31)  H . A . l i e b h a f s k y , J.A.O.S., 57,2657 (1935).  (32)  W.G.Horsch, i b i d , 41, 1791  (33)  H.A.liebhafsky, i b i d ,  (34)  Scatchard and T e f t , i b i d ,  (35)  Getman, J . Phys. Chem. 35, 2755 (1931).  (36)  Shrowder, Gowperthwaite and LeMer, J.A.C.S., 56,  32, 209-220 (1928). (1930).  (1919).  59, 452  (1937).  52, 2280 (1930).  2348 (1934). (37)  Cohen, Z. Physik Chem., 34, 612  (38)  P u s c h i n , Z. anorg.Chem., 63, 230  (39)  C l a y t o n and Vosburgh, J.A.C.S., 58, 2093 (1936). (see a l s o Garner,Gran and Yost,ibid,57,2056 (1935)  (40)  J.H.Hildebrand, Trans.Electrochem.Soc., 22, 335  (41)  Lewis, J.A.C.S., 37, 2656 (1915).  (42)  G.Mayr, Chem. Abs., 14, 2578 (1920). Huova oimento 19, 116 (1918). F.Skaupy, Chem.Abs., 15, 978-3 (1921). Physik Z., 21, 597 (1920). K.Schwarz, Chem.Abs., 27, 3382-9 (1933) Z. Elektrochem., 39, 550 (1933). C.Wagner, Chem.Abs., 26, 2097 (1932) Z. p h y s i k . Chem., B 15, 347 (1932).  (43) (44) (45)  (1900). (1903).  (1913)  (46)  K.Schwarz, Z.physik.Chem.Abt.,A 156,227 (1931).  (47)  G.Bianchi, Chem.Abs., 41, 2631a, 7281c (1947) A t t i accad. n a z l . L i n c e i C l a s s e s c i . f i s . mat.e n a t . , 1, 786 (1946). 2, 58 (1947). 2, 627 (1947).  (48)  G. Meyer, Chem. Abs., 6, 446 (1912) B e r . p h y s i k Geo., 793 (1911 (see P h y s i k Z. 12, 975 - Q C p.51).  (49)  I n t e r n a t i o n a l C r i t i c a l T a b l e s . I I , 591, Mc'Graw H i l l , New York (1933)  (50)  Landolt B a r n s t e i n p. 136  (51)  G.Meyer Ann. Phys. Chem., 61, 225-34 (1897).  (52)  Smithsonian P h y s i c a l Tables 6th Ed. p.140 Smithsonian I n s t i t u t i o n , Washington  (53)  Samarin and Shvartsman, Chem.Abs., 42, 7593a (1948) I s v e s t . Akad. Hack S . S i S i R i O d t e l Tekh.Nank,1947,1649  (54)  S q u i r e s ' Companion to the B r i t i s h Pharmacopoeia, XIX Ed., 702, J . & A. C h u r c h i l l , L o n d o n  (1916)  (55)  J . J . Lingane, Anal.Chem., 21, 47 (1949)  (56)  L. Meites and T. M e i t e s , Ana1.Chem., 20, 984 (1948)  (57)  Ref.5, Table 8 p. 64, Table 11 p. 72.  (58)  Ref.5, p.307.  (59)  Ref.5, Table 13 p. 76.  (60)  Ref.5, p. 487.  (61)  Ref.5, p.79.  (62)  Ref.5, p.60, Table 6 p.59.  (63)  Ref.9, p. 60.  (64)  J . Heyrovsky,  Chem.Abs. 44, 1834a (1950)  Chem.Listy., 36, 267-71  (1942).  (65)  Ref.5, Table 8* p.64.  (66) (67)  Ref.9, Table 4, p.59. J.J.Lingane, D i s c u s s i o n s o f the Paraday 203-212 (1947).  S o c i e t y , 1,  I POLAROGRAPHIC STUDIES WITH THE DROPPING MERCURY ELECTRODE. - PART XI. - THE USE OP DILUTE AMALGAMS IN THE DROPPING ELECTRODE.o by J . Heyrovsky  and M.  Ealousek.  THEORETICAL. The dropping mercury e l e c t r o d e a o q u i r e s i n a mixture o f a r e d u c i n g agent (denoted  (denoted  "red") and an o x i d i z i n g  agent  "oxy") a p o t e n t i a l , TV , which i s t h a t o f a r e v e r s i b l e  "redox" e l e c t r o d e and  i s thus g i v e n as  Aooording to the nature o f the r e d u c i n g or o x i d i z i n g agent and the phase i n which they are p l a c e d , we may  distinguish  three t y p i c a l c a s e s . 0  1. the agent "oxy" ( i . e . t h e h i g h e r stage o f o x i d a t i o n ) c o n s i s t s o f k a t i o n s i n the s o l u t i o n around the dropping mercury kathode, which on t h e i r e l e c t r o - d e p o s i t i o n form an amalgam f u r n i shing thus the agent " r e d " ( i . e . t h e lower stage o f o x i d a t i o n ) . 2. the agent "oxy" i s a compound o f o x i d i z i n g propert i e s ( l i k e a t i t a n i c s a l t or quinone), which i s p l a c e d i n the s o l u t i o n around t h e dropping mercury kathode and gets reduced t h e r e to a r e d u c i n g agent ( i . e . t h e t i t a n o u s s a l t or hydroquinone), y i e l d i n g thus the agent " r e d " . The same p o t e n t i a l i s reached, however, when the reducing agent (e.g.a t i t a n o u s s a l t or hydroquinone) i s o x i d i z e d a t the dropping mercury anode to the o x i d i z i n g agent ( i . e . t h e t i t a n i o s a l t or quinone). 3. S i m i l a r l y as i n the l a t t e r case also the r e d u c i n g agent o f case 1. may be o x i d i z e d , i f i n the dropping e l e o t r o d e an amalgam i s used i n s t e a d o f pure mercury and the e l e o t r o d e i s made the anode, sending the i o n s o f the base metal d i s s o l v e d i n mercury into the s o l u t i o n . These i o n s then f u r n i s h the substanoe "oxy".  °)  A communication p u b l i s h e d i n "Chemicke L i s t y " 35,p.47-50 (1940), to the o c c a s i o n o f the 60th b i r t h d a y o f P r o f e s s o r J . Milbauer.  II. She  redox system 1, i s r e a l i z e d  i n the  electrodepo-  sI1;ion o f k a t i o n s at the dropping mercury kathode, about which many s t u d i e s a r e p u b l i s h e d *  To the redox system 2.  be-  long the r e v e r s i b l e p o l a r g r a p h i o r e d u c t i o n s and o x i d a t i o n s i n the s o l u t i o n , such as a r e d e s c r i b e d by H.O.Muller and  J.P.  B a u m b e r g e r , ) ) E. Kodicek and K.Wenig, ) R . S t r u b l , ) 1  2  3  M.Spalenka ) and K.Schwarz, ). 5  6  4  The case 3.has not yet been  t r e a t e d f u l l y : an account  o f i t has been g i v e n ) by one  the present a u t h o r s )  a note was  and  7  i n 1939.  The  started i n  of  0  p u b l i s h e d by  J.J.lingane ) 8  experimental work here described was,  however,  1937.  Before going  i n t o the experimental  d e t a i l s and  the  d i s c u s s i o n o f the r e s u l t s , l e t us deduce an equation o f the o u r r e n t - v o l t a g e curve obtained with the dropping  eleotrode i n  oase 3, vi:z. when using i n s t e a d o f pure mercury an amalgam. T h i s oase i s c l o s e l y a l l i e d w i t h c a s e . L a s of  case 3. i s the reversed one  the anodic  to t h a t i n case 1. so t h a t a  g e n e r a l s o l u t i o n would express the procedure i n e i t h e r t i o n o f the r e v e r s i b l e prooess  prooess  direc-  i n v o l v e d , i . e . the anodic  dis-  s o l u t i o n of the metal d i s s o l v e d i n mercury as w e l l as the k a t h o d i c formation o f the amalgam. Let  us denote the c o n c e n t r a t i o n of k a t i o n s i n the  s o l u t i o n surrounding  the dropping  e l e c t r o d e by C*and the con-  c e n t r a t i o n of the metal i n the amalgam by c i of  the dropping  The  potential  e l e c t r o d e i s g i v e n by the c o n c e n t r a t i o n pre-  v a i l i n g c l o s e l y a t the e l e c t r o d e i n t e r f a c e : there the conoen0  )  In a p u b l i c l e c t u r e o f J.Heyrovsky at the F a c u l t y o f S c i e n c e , Masaryk U n i v e r s i t y , Brno, A p r i l 26th,1938: compare a l s o the D i s s e r t a t i o n o f M.Kalousek i n 1939.  Ill t r a t i o n o f k a t i o n s i s CQ and metal i n mercury c£.  We  the c o n c e n t r a t i o n o f the  assume the presence o f an  baser  indifferent  e l e c t r o l y t e i n the s o l u t i o n i n a c o n c e n t r a t i o n s u f f i c i e n t to f u r n i s h the t o t a l t r a n s f e r e n c e o f the c u r r e n t j so that the k a t i o n s o f the d i s s o l v e d metal p r a o t i o a l l y do not take p a r t i n the  migration. We  take the view, used i n the p r e v i o u s  o f the mathematical equations v o l t a g e curves  due  deductions ) 9  f o r the p o l a r o g r a p h i c  to r e v e r s i b l e processes,  ence o f the c u r r e n t a c r o s s the e l e o t r o d e  t h a t the t r a n s f e r -  i s given s t r i c t l y  d i f f u s i o n o f the d e p o s i t i n g or d i s s o l v i n g p a r t i c l e s . anodic  current-  by  The  c u r r e n t thus depends on the d i f f u s i o n rate o f the  m e t a l l i c atoms from the i n t e r i o r o f the amalgam drop to i t s surfaoe and on the d i f f u s i o n rate o f the m e t a l l i o i o n s from the e l e c t r o d e s u r f a c e i n t o the s o l u t i o n *  These two  diffusion  r a t e s must be e q u a l during the formation o f eaoh drop o f the amalgam otherwise  an accumulation  or i n s u f f i c i e n c y o f p a r t i c l e s  would grow at the e l e c t r o d e i n t e r f a c e and p o t e n t i a l , as i t depends on l o g C Q / O Q .  would change the  Experiments, however,  show that during the formation o f the mercury drop i t s e l e c trode p o t e n t i a l i n r e v e r s i b l e e l e c t r o d e processes  remains  constant, which i s o n l y p o s s i b l e , i f GQ as w e l l as C Q are constant  (at a c e r t a i n a p p l i e d  E.M.F.).  Then the i n t e n s i t y o f c u r r e n t , i , i s g i v e n by r a t e w i t h which the m e t a l l i o atoms are f u r n i s h e d to t h e  the surfaoe  IV of  the amalgam drops; t h i s i s expressed by the equation  The same i n t e n s i t y , however, i s also determined by the r a t e with which t h e m e t a l l i o i o n s , formed by the anodio d i s s o l u t i o n o f the metal, d i f f u s e from the s u r f a c e o f the anode; hence a l s o From these equations we o b t a i n f o r whioh s u b s t i t u t e d  into the o r i g i n a l formula f o r the r e v e r s i b l e  "redox" e l e o t r o d e p o t e n t i a l , lead to  ^  ^  T h i s may be a l s o w r i t t e n  The i n t e n s i t y o f the anodio c u r r e n t w i l l reach i t s l i m i t , when the surfaoe o f the amalgam drops w i l l beoome exhausted  from the metal d i s s o l v e d , i . e . when CQ= 0; hereby the  anodic l i m i t i n g c u r r e n t , ^Cal -to/,  "  i s g i v e n as .  ^  S i m i l a r l y the k a t h o d i c l i m i t i n g c u r r e n t ,  is  reached, when the s o l u t i o n surrounding t h e dropping e l e o t r o d e becomes exhausted  o f the k a t i o n s o f the e l e c t r o - d e p o s i t e d metal.  This c o n d i t i o n i s t h a t  Substituting for k ^ a n d  ~0)  %  or  kgC^values  and —-  we o b t a i n  the f i n a l equation o f the c u r r e n t - v o l t a g e curve, which expresses the course o f e l e c t r o l y s i s i n o l u d i n g anodic and kathodio p o l a r -  The  curve  the p o l a r i z a t i o n , Jf  ( f i g . l ) r e p r e s e n t i n g t h i s equation, , v a r i e s and the o u r r e n t ,  i n which  , accordingly  changes, has the form o f a t y p i c a l " p o l a r o g r a p h i c wave"; the o n l y d i f f e r e n c e from the curves h i t h e r t o deduced i s t h a t i s an anodic as w e l l as a kathodio  l i m i t i n g current.  there  The " h a l f -  wave" o f t h i s curve occurs when  and hence the p o t e n t i a l ,  JTJ- , a t whioh t h e c u r r e n t reaches the ~2-  "half-wave" value i s  rr - rr-<*>  TTJ.-  or  ^  Ho  ^  ^  ^  z  — EX  -2.  A No  The  1  F i g . 1. shape o f the continuous wave. The  tial"  VIC-  l a t t e r formula  polarographic  anodio-kathodio  shows t h a t t h i s "half-wave poten-  i s a c h a r a c t e r i s t i c constant,  independent o f t h e concen-  t r a t i o n s o f the agents "red" o r "oxy", and g i v e n o n l y by t h e type o f the r e d u c t i o n and o x i d a t i o n prooess,  T h i s value i s  VI very near to the "normal redox p o t e n t i a l " ,  IT.  , a t whioh red oxy  , d i f f e r i n g from i t o n l y by t h e r a t i o o f t h e d i f f u s i o n  constants o f t h e e l e c t r EXPERIMENTAL ode process. An o l d e r type o f polarograph, was  used.  made by D r . V . I e j e d l y ,  The c o n t a c t s l e a d i n g to t h e p o t e n t i o m e t r i c wire were  f u r n i s h e d w i t h mercury j o i n t s , as described by J . V . N o v a k ) . 10  The  continuous  anodic was  change o f t h e e x t e r n a l E.M.F. e f f e c t i n g t h e  and the kathodic p o l a r i z a t i o n of the dropping  produced by t h e adjustment o f J . H o e k s t r a ) . 1 1  purpose a l s o a simpler arrangement has been found  electrode  For t h e same convenient  v i z . t h a t shown i n F i g . 2 . ; i n t h i s one o f the e l e c t r o d e s ( e . g . the u n p o l a r i z a b l e ) i s j o i n e d to the middle t e r m i n a l o f a p a i r o f accumulators w h i l s t the other e l e c t r o d e ( i . e . the dropping one)  i s connected to t h e s l i d i n g contact on t h e p o t e n t i o m e t r i c  wire. The  l a t t e r arrangement was used only f o r approximat-  i v e measurements, as the two accumulators have r a r e l y an i d e n t i c a l E.M.F. so t h a t the s l i d i n g contact a t the middle p o i n t o f the p o t e n t i o m e t r i c wire does not e x a c t l y branch o f f zero  f/G-ZThe scheme o f connections f o r continuous polarization;  voltage.  anodic-kathodic  VII One o f the above schemes has to be a p p l i e d , when the amalgam i s used both i n the dropping e l e c t r o d e as w e l l as i n the l a r g e u n p o l a r i z a b l e e l e c t r o d e at the bottom o f an o r d i n a r y conical electrolytic vessel. anodic  to the kathodic  However, the change from the  p o l a r i z a t i o n can a l s o be e f f e c t e d , i f  i n s t e a d o f the l a y e r o f the amalgam a separate trode  standard  i s used f o r the u n p o l a r i z a b l e e l e o t r o d e .  o f t h i s standard  eleo-  The p o t e n t i a l  e l e c t r o d e has to be c o n s i d e r a b l y more p o s i t i v e  than that o f t h e amalgam i n order that the a p p l i e d E.M.F. may be i n c r e a s e d from zero  i n one d i r e c t i o n o n l y  ( i . e . making the  p o t e n t i a l o f t h e dropping e l e c t r o d e more n e g a t i v e ) , f o r which the o r d i n a r y p o l a r o g r a p h i c  connection  suffices.  The v e s s e l , which has t h e separate  standard  electrode  a f f i x e d to the v e s s e l with t h e dropping e l e c t r o d e , i s shown i n F i g . 3. The  s o l u t i o n c o n t a i n i n g t h e k a t i o n s o f the metal used  i n the amalgam i s plaoed l l a r y electrode  i n t h e v e s s e l B, i n t o which t h e c a p i -  (C) i s introduced  through a rubber  stopper.  The  s i d e tubes o f t h i s v e s s e l serve f o r p a s s i n g an i n d i f f e r e n t  gas  ( i n t h i s case n i t r o g e n ) through the s o l u t i o n i n order to  f r e e i t from atmospheric oxygen.  The amalgam accumulated by  dropping i s l e t out from time to time through t h e tap E. unpolarizable keeps—in The  e l e c t r o d e i s plaoed  The  i n t h e v e s s e l A, where i t  the form o f a mercury l a y e r — i t s  standard p o t e n t i a l .  c u r r e n t passes to t h i s e l e c t r o d e through a platinum  wire  sealed to a s i d e c o n t a c t , which i s f i l l e d with mercury. During the polarographio D i s kept open, so as to o f f e r l e a s t  i n v e s t i g a t i o n the broad tap electrolytic  resistance  VIII between the v e s s e l s A and B.  The tap F serves f o r the ex-  change o f the e l e c t r o d e s o l u t i o n .  Fi^.'S  E l e c t r o l y s i s v e s s e l f o r amalgam polarography. The e l e c t r o l y t e i n t h e standard e l e c t r o d e was  O.ln potassium potassium  either  s u l f a t e s a t u r a t e d with mercurous s u l f a t e o r i n  c h l o r i d e s a t u r a t e d w i t h calomel to matoh the anion  o f the e l e c t r o l y t e surrounding the dropping e l e c t r o d e ; The amalgams a p p l i e d were those o f copper,  cadmium,  lead and z i n c i n c o n c e n t r a t i o n s not exceeding 0.005$.  More  concentrated amalgams were found to adhere to t h e w a l l s o f t h e glass c a p i l l a r y . The C-V curves obtained, were a l l o f the type t h e o r e t i c a l l y deduced.  F i g . 4 r e p r e s e n t s the curves p o l a r o g r a p h i c a l l y  recorded w i t h lead, amalgam used i n t h e dropping e l e c t r o d e . S i m i l a r curves were obtained a l s o with o t h e r amalgams.  )NKCL  12 The s t r a i g h t l i n e p a s s i n g through the middle o f the polarogram  denotes the 0 p o s i t i o n o f the galvanometer, i . e .  the zero o u r r e n t .  At the beginning o f t h e curves i n t h e i r  lower branch the dropping amalgam e l e c t r o d e i s the anode, i . e . Pb atoms a r e t r a n s f e r r e d to the s o l u t i o n as Pb  ions*  The upper branch o f the curve above the zero l i n e shows where the dropping amalgam e l e o t r o d e a c t s as eathode, Pb*^  from the s o l u t i o n . Curve 1 has been o b t a i n e d w i t h amalgam  dropping i n t o a s o l u t i o n f r e e from Pb the anodic c u r r e n t shown. zero  i . e . deposits  hence, t h e r e i s o n l y  The c a t h o d i c one b e i n g p r a c t i c a l l y  (the s m a l l ourrent above t h e zero l i n e i s due to t r a c e s  o f oxygen i n t h e s o l u t i o n ) .  Curve 2 has been obtained w i t h  a more d i l u t e lead amalgam i n a s o l u t i o n 1 m i l l i m o l e s i n Pb"*" . +  T h i s curve shows t h e anodio branch due to the e l e c t r o l y t i c d i s s o l u t i o n o f Pb from t h e amalgam as w e l l as t h e oathodio branch caused by t h e e l e c t r o d e p o s i t i o n o f Pb i s simply due to t h e e l e o t r o d e p o s i t i o n o f Pb p i n g mercury e l e c t r o d e .  I t i s remarkable  ^" . Curve 3 a t the drop-  that #e o f a l l  t h r e e wafes c o i n c i d e c l o s e l y (corresponding to - 0.46 V  from  the p o t e n t i a l o f t h e r e f e r e n c e e l e c t r o d e H.C.E.).. The curves obtained w i t h the same amalgams but a t v a r i o u s times were not c o i n c i d i n g as f a r as the h e i g h t o f t h e l i m i t i n g anodic c u r r e n t i s concerned.  This i s explainable  by the i n s t a b i l i t y o f the amalgams whioh a r e e a s i l y o x i d i z e d and thus lower t h e i r content o f t h e d i s s o l v e d metal*  After  shaking the amalgam a c o n s i d e r a b l e decrease o f t h e anodic c u r r e n t was  produced.  I n t e r e s t i n g i s t h e s h i f t o f the  o f the anodic  X wave observed when the e l e c t r o l y t i c d i s s o l u t i o n o f the amalgam takes plaoe i n a s o l u t i o n i n whioh the m e t a l l i c i o n forms A c c o r d i n g to t h e g e n e r a l t h e o r y t h e E i should  complexes.  s h i f t to more n e g a t i v e p o t e n t i a l v a l u e s i f the r e s p e c t i v e i o n enters i n a complex.  The same must o f course hold a l s o  i n the  case o f t h e anodic wave. To i n v e s t i g a t e t h i s r e l a t i o n s h i p the dropping  lead  amalgam e l e o t r o d e was surrounded  by s o l u t i o n s o f e l e c t r o l y t e s  w i t h which P b ^ ^ f o r m complexes.  E i g . 5 shows the i n f l u e n o e  o f t h e formation o f complexes on the value o f E i . lead amalgam with f r e e  Curve 1.  Pb^T 2  /  -  f\Gr. S l l l l  x-t-± IN  3-  IN  KCL  +-  C IT KATE  S^o  1—  O-OOIN  PbCl^  •«  i<  Curve 2, obtained w i t h t h e same amalgam i n a l k a l i n e plumbite. Curve 3, e f f e o t o f c i t r a t e .  A l l three curves r e f e r r e d to  U.C.E. and t h e d i s t a n c e between two a b s o i s s a l - 0 . 2 / . values o f E i are therefore,(l)-0.46^.  The  (2)-0.72K. (3)-0.53^  .  These E i p o t e n t i a l s c o i n c i d e w i t h those measured i n the cathod i c e l e c t r o d e p o s i t i o n o f Pb (2) a l k a l i n e plumbite  from  (4) lead s a l t  (1) Free i n excess  Pb  r 7  ^ions  oitrate.  Less r e g u l a r a r e curves obtained when amalgam drops  21 i n a s o l u t i o n i n which the a n o d i o a l l y formed o a t i o n s a r e p r e c i p i t a t e d , e.g. i f the dropping amalgam e l e c t r o d e (Pb) i s surrounded ammonia.  by d i l u t e a l k a l i or cadmium amalgam by  dilute  However, these i r r e g u l a r i t i e s are removed i f the  c o n c e n t r a t i o n s o f the p r e c i p i t a t i n g agents a r e inoreased so as to r e d i s s o l v e the p r e c i p i t a t e d hydroxides a l k a l i added, Gd concentrated ammonia a d d e d )  (Pb $  concentrated  The  values  a r e hereby a g a i n s h i f t e d to more negative v a l u e s . The p o l a r o g r a p h i c i n v e s t i g a t i o n o f the anodio  dis-  s o l u t i o n o f d i l u t e amalgam i s l i k e l y to lead to p r a c t i c a l a p p l i c a t i o n s as f a r as q u a l i t a t i v e and  quantitative analysis  o f t r a o e metals contained i n mercury i s concerned* imagine  We  may  even a p o s s i b i l i t y o f an a n a l y s i s o f a l l o y s i n whioh  the a l l o y would not be d i s s o l v e d d i r e c t l y i n mercury and  i n an aqueaus s o l u t i o n but  the amalgam would be p o l a r o g r a p h i c a l l y  i n v e s t i g a t e d w i t h the dropping anode.  The m e t a l l i c components  would be i n d i c a t e d by corresponding anodic waves o f the G curve.  -V  Here an advantage over the o r d i n a r y p o l a r o g r a p h i c  a n a l y s i s o f m e t a l l i c c o n s t i t u e n t s i n s o l u t i o n even p r e s e n t s i t s e l f s i n c e i n the anodic d i s s o l u t i o n t r a o e s o f baser ( A l k a l i metals or z i n c ) may  be shown with g r e a t  a l s o i n the excess o f the n o b l e r metals  metals  sensitivity  (Cd,Pb,Bi,Cu,Au,Ag,Hg)  whereas i n the kathodic p o l a r o g r a p h i c i n v e s t i g a t i o n - j u s t to the c o n t r a r y - as a r u l e o n l y the n o b l e r c o n s t i t u e n t s a r e more precisely  estimated. How  used  f a r amalgams may  be prepared and  successfully  f o r such an a n a l y s i s w i t h the dropping mercury anode  remains to be s p e c i a l l y i n v e s t i g a t e d .  Here we mean j u s t to  XII h i n t to an i n t e r e s t i n g  counterpart  to the a n a l y s i s  of  solutions  with the dropping mercury cathode, v i z . to the p o l a r o g r a p h i c analysis  o f amalgams by means o f the dropping mercury anode, SUMMARY I f the s o l u t i o n  i n the amalgam, the o -  c o n t a i n s ions o f the metal present curve has an anodic and  cathodic  branch and the equation o f the curve i s  where, i d ^ i s the anodic and  idg i s the c a t h o d i c l i m i t i n g  o u r r e n t , k^ = d i f f u s i o n c o e f f i c i e n t o f metal atoms i n meroury and k g = d i f f u s i o n c o e f f i c i e n t o f m e t a l l i c  ions i n s o l u t i o n .  XIII LITERATURE. H.O.Mailer and J.P.Baumberger, Trans* Electroohem. Soc. 71,169-194 (1937) H.O.Muller, Ohem. Rev. 24, 95-124 (1939) E. Eodieek and X. Wenig, n a t u r e , 142, 35 (1938) R . S t r u b l , G o l l . Czech. Ghem. Gommun, 10, 475 (1938) M. Spalenka, i b i d K. Schwarz,  , 11, 146 (1939)  Z. a n a l . ehem., 115, 161-174 (1939)  J . Heyrovsky i n B o t t g e r s P h y s i k a l i s c h e Methoden der a n a l y t Chemio, Bd. I l l , p.428, L e i p z i g (1939) J.J.Lingane, J.A.C.S., 61, 976-977 (1939) Heyrovsky and I l k o v i o , Co 11. Czech. Ghem. Commun., 7, 198 (1935) J . Novak, i b i d ,  9, 207-235  (1937)  J . Hoekstra, Rec. Trav. Chem. Pays Bas, 50, 339-432 (1933)  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062301/manifest

Comment

Related Items