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

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It 3 37 I<3$I PI a DROPPING ZINC AMALGAM ELECTRODES IB POLAROGRAPHY by Wm. R. E. COGHLM A thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements for the Degree of MASTER OF ARTS in the Department of CHEMISTRY The University of B r i t i s h Columbia October, 1950. i ABSTRACT The g e n e r a l p r i n c i p l e s o f p o l a r o g r a p h y a r e mentioned b r i e f l y and t h e e q u a t i o n s f o r . t h e p o l a r o g r a p h i c d i f f u s i o n c u r r e n t a r e compared. The s e v e r a l d e r i v a t i o n s a r e t r a c e d and t h e p o i n t s o f d e p a r t u r e l e a d i n g to c o r r e c t i o n terms a r e n o t e d . I t i s known t h a t the assumptions upon which t h e d e r i v e d equa-t i o n s f o r t h e d i f f u s i o n c u r r e n t a r e based a r e not i n a c c o r d w i t h r e a l i t y . I t i s a l s o known t h a t t h e d e p a r t u r e s from i d e a l i t y tend t o oppose so t h a t , f i n a l l y , t h e b a s i c a s s u m p t i o n s , even i f i m p e r f e c t l y f u l f i l l e d , may he c o n s i d e r e d v a l i d . These f a o t o r s a r e d i s c u s s e d d u r i n g development o f t h e e q u a t i o n s . A 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 c o m p l e t e . P u b l i c a t i o n s d e a l i n g w i t h t h e s u b j e c t a r e r e p o r t e d almost i n e n t i r e t y . The p r e p a r a t i o n o f d i l u t e amalgams i s d i s c u s s e d i n t h e l i g h t o f r e s u l t s o b t a i n e d i n p r e l i m i n a r y work. The i d e a l 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 apers d e a l i n g w i t h E. M. F. measurements>. The e v i d e n c e f o r t h e i o n i -z a t i o n and p o l y m e r i z a t i o n o f z i n c m e t a l i n s o l u t i o n i n mercury i s d i s c u s s e d b r i e f l y a l o n g w i t h t h e h y p o t h e t i c a l r e a c t i o n s which e x p l a i n t h e i n s t a b i l i t y o f v e r y d i l u t e amalgams. In a d d i t i o n , i t i s noted t h a t a few w o r kers have i n v e s t i g a t e d t h e b e h a v i o u r o f d i l u t e amalgams d u r i n g passage o f d i r e c t c u r r e n t . The 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 has p r o p e r t i e s analogous to a s a l t s o l u t i o n . P a r t i c u l a r l y , t h e phenomena o f t r a n s p o r t d u r i n g passage o f t h e e l e c t r i c a l c u r r e n t has been i i r e p o r t e d . F u r t h e r i n v e s t i g a t i o n o f t h e phenomena i s suggested 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 passage o f t h e 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 t h e p o l a r o g r a p h i c t h e o r y . 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 z i n c 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 method a r e t a b u l a t e d . I t i s n o t e d t h a t 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 has not been s a t i s f a c t o r i l y e s t a b l i s h e d . 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 i m p r e s s i n g a v o l t a g e a c r o s s t h e amalgam r e s e r v o i r and a p l a t i -num e l e o t r o d e i n a water l a y e r o v e r t h e amalgam i s d e s c r i b e d . The u t i l i z a t i o n o f t h e Sargent P o l a r o g r a p h Model X X I I i n c o n j u n c t i o n w i t h a Leeds and B o r t h r u p Student Type p o t e n t i o m e t e r f o r m a n u a l l y r e c o r d i n g p o larograms i s d e s c r i b e d . P o l a r o g r a m s o f s t a n d a r d z i n c s o l u t i o n s 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 and measured under t h e same c o n d i t i o n s i n t e n d e d f o r r e c o r d i n g and measuring t h e polarograms o f z i n o amalgams. The d a t a so ob-t a i n e d agreed to w i t h i n 5$ o f t h e v a l u e s p r e v i o u s l y r e p o r t e d f o r t h 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 and to w i t h i n 2% o f t h e r e -p o r t e d h a l f - w a v e p o t e n t i a l f o r z i n c s a l t s i n G.H p o t a s s i u m 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 . I t was noted t h a t t h e v a l u e s o f t h e d i f f u s i o n o u r r e n t c o n s t a n t i n c r e a s e d w i t h d e c r e a s i n g 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 pub-l i s h e d r e p o r t s but c o n t r a r y to the f i n d i n g s o f K a l t h o f f and L i n g a n e . The d e v i a t i o n i s b e l i e v e d to be due i n p a r t t o t h e p r e s e nce o f t r a c e s o f oxygen. F u r t h e r i n v e s t i g a t i o n i s sug-g e s t e d . The behaviour o f d i l u t e z i n c amalgam a t t h e dropping e l e c t r o d e i s shown to correspond to that o f mercury except f o r an i n f l e c t i o n i n the drop time vs p o t e n t i a l curve. The i n f l e c t i o n i s found i n the range o f p o t e n t i a l over which the 'wave' f o r z i n c amalgam develops. It i s al s o shown t h a t the amalgam s t a b i l i z i n g c i r c u i t has a n e g l i g i b l e e f f e c t on the recorded polarograms. In s h o r t , accuracy o f the same order obtained i n o r d i n a r y p o l a r o g -raphy can a p p a r e n t l y be a t t a i n e d . Reproducible polarograms o f 0.000288$ z i n c amalgam have been o b t a i n e d . C a l c u l a t i o n s f a i l to r e v e a l g r o s s e r r o r . The d i f f u s i o n c u r r e n t constant c a l c u l a t e d from the o r i g i n a l I l k o v i o equation i s found to be 5.16 ±. 0.07. The mean va 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 o f z i n c i n mercury i s c a l c u l a t e d 2.4 X 10"^cm 2 s e c " l a t 25.0°C from v a l u e s reported i n the l i t e r a t u r e . For t h i s v a lue o f the d i f f u s i o n c o e f f i c i e n t the nume r i c a l constant 'B' i n the second term of the Stre h l o w - S t a c k e l b e r g e q u a t i o n , ^ has been c a l c u l a t e d 23.6 dt 2.3. This value i s w i t h i n range o f the values p r e d i c t e d f o r B, from t h e o r e t i c a l approximations. Choice of the l a r g e r v a l u e s o f the d i f f u s i o n c o e f f i c i e n t would give l a r g e r v a l u e s f o r B. here, the r e s u l t i s taken as evidence t h a t streaming a t the drop s u r f a c e i s near minimum. From the data obtained i n polarography o f standard z i n c so-l u t i o n s i t i s observed that the lingane-Lo ve r i d g e equation gave the best agreement with accepted v a l u e s . A®oordingly,the value f o r 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 meroury at 25.0°C has been c a l c u -l a t e d a c c o r d i n g to e q u a t i o n ^ A s 2.58cm 2sec -l±0.09. A v a l u e i 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 v a l u e s . C o n s i s t e n t r e s u l t s w i t h amalgams 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 i n t h e p o l a r o -g r a p h i c l i t e r a t u r e . I n t h i s work an amalgam 0.000288$ has p r o v i d e d not o n l y 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 from w h i c h remarkable agreement w i t h p u b l i s h e d d a t a has been ob-t a i n e d . T h i s i s t a k e n as e v i d e n c e t h a t t h e method i s s u i t a b l e f o r work o f t h e p r e c i s i o n and a c c u r a c y o b t a i n a b l e i n o r d i n a r y p o l a r o g r a p h y . The c o n d i t i o n s f o r work o f g r e a t e r p r e c i s i o n and a c c u r a c y a r e s e t f o r t h w i t h a b r i e f d i s c u s s i o n o f t h e d i f f i -c u l t i e s and s o u r c e s o f e r r o r i n v o l v e d . 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 p o l a r o g r a p h y a r e s u g g e s t e d . ACKNOWLEDGMENT. A g r a n t from the 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 . to t h e U n i v e r s i t y o f B r i t i s h Columbia R e s e a r c h I'und enabled p u r c h a s e o f t h e Sargent P o l a r o g r a p h used i n t h i s work. Tadanac Z i n c (99.99 + $) was a l s o s u p p l i e d by 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. The a u t h o r w i s h e s to e x p r e s s h i s a p p r e c i a t i o n f o r the d i r e o t i o n of t h i s r e s e a r c h by D r . L.W. S h e m i l t . Thanks a r e a l s o due to Mr. Wm. Pye f o r c o n s t r u c t i n g t h e a l l g l a s s d r o p p i n g e l e c t r o d e a s s e m b l i e s . Mr,G.W. Larkham gave a s s i s t a n c e w i t h photography. TABLE OF CONTENTS ABSTRACT i INTRODUCTORY NOTE v PART A INTRODUCTION 1 PART B POLAROGRAPHY. THEORY AND APPLICATIONS 1. POLAROGRAPHIC THEORY 2 2. DROPPING AMALGAM ELECTRODES 27 PART C ZINC AMALGAMS 1. METHODS OF PREPARING ZINC AMALGAM 31 2. CHEMICAL and PHYSICAL PROPERTIES o f 52 ZINC AMALGAMS PART D EXPERIMENTAL 1. MATERIALS AND SOLUTIONS 41 2. APPARATUS 45 3. METHODS 49 PART E RESULTS AND DISCUSSION 1. POLAROGRAPHY OF STANDARD ZINC SOLUTIONS 51 2. AMALGAM POLAROGRAPHY 62 3. SUMMARY OF RESULTS 78 BIBLIOGRAPHY 82 COPY 'THE USE OF DILUTE AMALGAMS IN THE DROPPING ELECTRODE 1 by HEYROVSKY AND KALOUSES 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 thesis into several parts has been found necessary to o l a r i f y presentation of the various phases involved i n the work. F i r s t l y ^ the equations for the polarographic d i f f u s i o n current are derived. Since an equa-t i o n for the d i f f u s i o n ourrent is the law required i n the fundamental theory of polarography,the several derivations have been integrated for comparison. Secondly, since the l i t e r a t u r e dealing with amalgam polarography i s limited i t was decided to gather as much as possible under one cover. T h i r d l y f i n order to have as much useful information as poss-i b l e i n one place for future investigations,a wide range of subjects i s discussed herein. These subjects are the prepara-t i o n , chemistry and physics of zinc amalgams described in the l i t e r a t u r e as well as c l o s e l y related subjects such as the transport of metal i n an amalgam during passage of the e l e o t r i c ourrent. Unfortunately, some of the information i s fragmentary due to the fact that the o r i g i n a l l i t e r a t u r e was not immediate-l y a vailable. On the other hand }there are some subjects which were not covered due to the fact that time did not permit f u r -ther l i t e r a t u r e search. Among the omissions may 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 of mercury and d i l u t e mercury amalgams. This subject ^ owever^ appears to be a f i e l d for separate investigation. Fourthly^the experimental methods and results of t h i s work are presented. Due to the considerable range of material covered some overlapping and r e p e t i t i o n i s required for continuity. In a few instances experimental evidence i s given without d e t a i l of method. In these cases, however, the r e s u l t s were unsatisfactory and d e t a i l was considered superfluous since the context explains the basis of the method. It i s regretted that time did not permit further investigations under the conditions which experience gained i n t h i s work had shown to be necessary. 1. DBOPPIIG AMALGAM ELECTRODES IS POLAROGRAPHY A—INTRODUCTION During investigation for suitable methods of analysis i n research on zinc anodes i n chrornate e l e c t r o l -y s i s the polarographic technique was considered. Lingane'sf / ) note on the dropping oadmium amalgam electrode suggested that perhaps a dropping zinc amalgam electrode i n the polarography of ohromate solutions wouia afford some useful information with respect to the electrode reactions i n v o l -ves. Further search i n the l i t e r a t u r e at that time revealed no quantitative data roopeet to the anodio d i f f u s i o n current of dropping amalgam eledtrodes. Consequently, t h i s work has been directed towards determining the characteris-t i c s of dropping zino amalgam electrodes l n polarography with respect to the f e a s i b i l i t y of t h e i r use i n investigating anode reaotions. Since time did not permit & » completion of the entire work l n mind, i t was decided that the determination of the apparent d i f f u s i o n c o e f f i c i e n t of zinc i n meroury under polarographic conditions would provide the most useful data towards further investigations. 2 B - Polarography. Theory and Applications (l)--POLAROGRAPHIO THEORY The polarographio method of chemical analysis was invented by J . Heyrovsky. The method i s based on the interpretation of the current-voltage carves that are obtained when solutions of electro-reducible or electrp-oxidizable substances are electrolyzed in a c e l l i n which one electrode consists of mercury f a l l i n g drop-wise from a fine bore c a p i l l a r y . The .solution contains a minute amount of the electro chemically reacting sub-stanoe in the presence of a r e l a t i v e l y huge amount of an in d i f f e r e n t e l e c t r o l y t e . The unique current-voltage curves obtained by the method indicate both the species and concentration of the reactive substance. On account of the smallness of the dropping mercury electrode, extreme concentration 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 of the reacting substance and the area of the mercury drop. The d i f f u s i o n current i s thus proportional to the concen-t r a t i o n of the reacting substance when a l l other factors influencing the d i f f u s i o n current are made constant. That i s The proportionality constant /< i s determined by measuring the d i f f u s i o n current A* for a solution of known concentra-t i o n C . Subsequently, an unknown concentration may be determined by using the experimentally determined value for K • However, i t i s more desirable to oaleulateK^or any reasonable variations of the faotors whioh Influence the diffusion current. An equation for the polarographic diffusion current has been derived by Ilkovic (X) and substantiated by others (3) (*/)• The general and theoretical principles of polaro-graphy have been discussed in some detail by 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 Strehlow and Staokelberg (J) have added much to the theory of the polarographic diffusion current. Before deriving the Ilkovic equations i t may be in order to present a brief summary of their development. She original Ilkovic equation reads (JL) where average current in microamperes during the l i f e of the drop. //i t number of faradays of e l e c t r i c i t y required per mole of the electrode reaction. p-z. diffusion coefficient of the reducible or oxi-dizable substance in the units Cs>n.x C " i t s concentration in mlllimoles per l i t r e . /yn-i rate of flow of mercury from capillary in ?n*n -^ c^T1 "C - drop time in seconds. Sinoe^5-^O dChas been chosen as a standard condition for polarographic work the values of the physloal oonstants at that temperature must be used. The Ilkovic diffusion current equation for the stanaara condition ZS-OO Cie given - 6>oj<n. &k C ort^ C^t (ID B y c o l l e c t i n g the variable terms —4^7-^ - <*°7^ - I ( i n ) where JL r d i f f u s i o n current constant. However, Lingane and loveridge (£} (,0) have shown t h a t j f v a r i 9 s s i g n i f i c a n t l y with ohanging values of orC^ E^ -* thus demonstrating that the o r i g i n a l Ilkovio equation, although approximately correct, i s not completely s a t i s f a c t o r y . They have also shown that the equation can be derived 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 electrode. Presumably^ tfee s i m p l i f i c a t i o n s i n intermediate mathematical operations became equivalent to a negleot of the curvature of the mer-cury drop i n the o r i g i n a l Ilkovio equation. By a simple a r t -i f i c e Lingane and Ioveridge obtained a new equation (l V). *Cjz (.07^ P ^ 6 ^ n % C I * - 3 ? * . % < 7 r r 4 t t) (IV) Strehlow and Stackelberg (*?) have derived a similar equation(y) whioh d i f f e r s only i n the value o f the numerical constant Their derivation from basic p r i n c i p l e s also gave the equation ft//) for the polarographic d i f f u s i o n ourrent of dropping amalgam eleotrodee. The problem involved i s to calculate the d i f f u s i o n of the reactant across an area which i s defined by the surface area of an expanding drop. Sinoe the d i f f u s i o n ourrent i s the product of the quantity of e l e c t r i c i t y required per mole of electrode reaction and the unit f l u x and the area of the 5. electrode an equation of the form (VII) might he expected where sCz •=- d i f f u s i o n current at the time <C • - the electrochemical equivalent^ the faraday^ 7^2 *=. the number of faradays required per mole of electrode reaction. J) - proportionality constant for d i f f u s i o n . / 9 £ : A ~ r a t e of change of concentration C with {jfT-Slz change of distance 7^ from a fixed o r i g i n % - O at a plane defined by 7^ at the time t.(sinee the concentration at any plane i s dependant on the time} /1^= Area of the drop at the time c7« Such an equation would give the instantaneous current at the time T~ • However, we have a drop expanding with time which counteracts the decrease of thre unit f l u x with time. Further, the concentration at y~ referred to a fixed coordinate %--=o must be changed since 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 incompressibility of l i q u i d . In view of these considerations i t i s required to r e p l a c e / J j ^ ^ and /\ c with the appropriate expressions. F i r s t l y , i t has been assumed that the reactant reaches the electrode by d i f f u s i o n alone. In the case of ordinary polarography t h i s condition i s adequately f u l f i l l e d . Although the e l e c t r i c f i e l d and the e l e c t r i c transport of the reactant are never n i l , the effect i s immeasurably small since the i n d i f f e r e n t e l e c t r o l y t e i s usually / O to 10 times the concentration of the reactant. In the oase of amalgam polarography, however, the assumption w i l l be considered questionable pending further investigations. Here the question of e l e c t r i c transport of metals dissolved i n mercury a r i s e s . Elsewhere there i s given some evidence for the phenomena* Whether or not the effeot i s measurable i n amalgam polarography cannot be stated here. In addition to e l e o t r i o a l transport, a convection ourrent could also i n t e r f e r e with true d i f f u s i o n . Actually,a convection ourrent of considerable magnitude does e x i s t . According to Strehlow and Stackslberg the mexoury ourrent issuing 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 the mercury surfaoe. This streaming, or r i n s i n g e f f e c t , i s not as strong i n ordinary polarography^where the reactant i s i n s o l u t i o n i s i t i s i n amalgam polarography. She streaming, or r i n s i n g e f f e e t , 1B shown schematically i n f i g . l . Thus ,the i n i t i a l assumption for the derivation o f the equation for the polarographic d i f f u s i o n current i s imperfectly f u l f i l l e d . For l i n e a r d i f f u s i o n the number of moles, jLfi^i. reactant d i f f u s i n g aoross a cross sectional plane of area 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 proportional to the concentration gradient at the plane i n question and i s expressible by where j),the p r o p o r t i o n a l i t y constant,is the d i f f u s i o n coef-f i c i e n t . The f l u x at a plane distanoeXfrom the o r i g i n desig-nated . ^ In order to oaloulate the t o t a l amount of material that w i l l d i ffuse across a given plane i n a f i n i t e p e r i o d ; i t i s necessary to have a knowledge of the change i n concentration with time at FIGURE 1. — Schematic representation of current due to mercury outflow and resultant streaming or r i n s i n g e f f e o t . the plane i n question. The change i n concentration with time between two planes separated by the i n f i n i t e s i m a l distance i s equal to the difference between the number of moles whioh enter across the plane at and the number whioh leave across the plane at ^  divided by the volume /4<^cnolosed between the planes; that i s Sinoe^j i s equal to unity when we speak of the f l u x we also Since from we f i n d from equation (X) that the ohange i n oonoentration with time at a given plane at a given instant i s expressed 3 "t" d tr *d y- (ziiD The problem i s to obtain an expression for the concentration gradient at any instant a t ^ r < 2 , from whioh by means of equation (EL) the f l u x , and hence the current can be computed. At the instant the EMP i s applied,(C-=©), the oonoentration at the electrode, ( i s equal to that in the body of the solution, ( C ) . After the EMJ1 i s applied, ( £ 7 0 ) , CZo i s rapidly decreased by the eleotrode reaotion. The i n i t i a l and boundary conditions are therefore, Co - C when - O Co^<- C or C 0 - 0 when t "7 O These conditions hold i n polarography since at an approp-r i a t e applied EMF the reactant i s e l e o t r o l y t i o a l l y reduced )or oxidized^as fast as i t meets the electrode surface. Under these conditions the solution of equation (XIII) i s 1 # By d i f f e r e n t i a t i n g equation (XIV) under the oondition that X - O we obtain Substituting in equation (VII) we have ^Tr = FA C fy^ (xvi) This i s the equation for the instantaneous current at any time afte r the BMP i s applied where lin e a r d i f f u s i o n to a plane electrode- i s considered. Lingane and Loverldge ( £T) derived the corrected Ilkovio equation (II) from equation(XVI) by substituting the values for A- . integrating to obtain the average current and multiplying by a numerical constant. Suoh a derivation provided a d u e to the inadequacy of the o r i g i n a l Ilkovio equation* However, the problem involves a spherical electrode. In the derivation i t i s assumed that the mercury drop i s a free sphere. Later i t w i l l be shown that t h i s i s not a c t u a l l y the case. Here we w i l l consider the reactant d i f f u s i n g to a free spherical electrode of radius Sl0 . The d i f f u s i o n f i e l d i s a spherical s h e l l surrounding the electrode at distance s\s measured from the centre of the sphere. The area of the sur-face i s LjJfsL1-. 1. See reference (iT) page 21 for a discussion of t h i s solution, equation (XIV). 9 . The number of moleB which diffuse across t h i s surfaoe i n the time<^£"is given by the expression, analogous to Pick's F i r s t Law, _ y and the f l u x at i s S i m i l a r l y ; t h e number of moles that diffuse across the surface at A.-t-e/'X i n the time d & i s Ufi^u^ = H'rrc++J^ J>(zk)«~tt^t (xix) and i^l - (^^ -i)-!-r1-*^ - (XX) The concentration gradient at /i i s related to that . and hence equation (XIX) may be written as Expanding and neglecting the terms containing i n f i n i t e s i m a l s of the second and t h i r d orders, equation (XXII) becomes Jth+J-x H i r U t + 2*(%=)J* ^ ^ y ^ ( x x i i i ) The change i n concentration i n the spherical s h e l l i n the time cl^C i s t ^ 1 6 difference between the number of moles whioh enter the s h e l l at - i * - * / - ! and the number which leave at A. divided by the volume of the s h e l l which i s ^ / T ^ 2 * T ^ L ; that i s Vc - ^ / — clN*- (xxiv) *trrst*-Therefore,the rate of ohange of oonoentration with time at given values of A and C i s i/T^ cist c{C 10, By substituting the values expressed by equations (XVII) and (XXIII) into (XX¥) we obtain „ . - i f ? - J L ^ +^(^7/ (mi) In order to oalculate the t o t a l flow through a given s h e l l of i n f i n i t e s i m a l thickness i n a f i n i t e time i t i s necessary to integrate equation (XXVI). She i n i t i a l and boundary conditions for l i n e a r d i f f u s i o n are applicable that i s : C-o - C- when C ~ O Co C or Co ~ O r' when V y O Under these conditions the solution i s 1 C t t - c(/-^t) ^ - ^ o fivm £7y*yy (xxviD and £ ^ ^ = C ( / - (xxviii) That i s with increasing time of d i f f u s i o n the concentration at any given point i n the d i f f u s i o n f i e l d gradually approaches a constant value, a steady state i s said to e x i s t . The con-stant concentration i n the steady state i s a function of and varies from zero at the electrode surface (si'-slo) to C at a large distanoe from the electrode (i>-77/7o and-^? -<?). This i s an important fundamental difference between symmetri-c a l spherioal d i f f u s i o n and lin e a r d i f f u s i o n , in which l a t t e r r case a steady state i s t h e o r e t i c a l l y unattainable. 1. See reference ( 5" ) Pages 28-29 -for a discussion of t h i s solution. 11. The current at any instant i s governed by the f l u x at the electrode surfaoe, i . e . , by the concentration gradient at^l=-^lo • By d i f f e r e n t i a t i n g equation (XXVII) the concen-t r a t i o n gradient at the electrode surfaoe at any time C i s given by , The instantaneous value of the r e s u l t i n g current i s , therefore, - c r A M O - - ^ ^ ^ ( i ^-^=. ) (xxx) In the case o f the dropping mercury electrode the area of the d i f f u s i o n f i e l d ohanges continuously during the l i f e of a drop and d i f f u s i o n takes plaoe i n a medium that i s moving with respect to the centre of the drop, i n a d i r e c t i o n opposite to the di r e c t i o n of d i f f u s i o n . Due to the inoompres-s i b i l i t y of a l i q u i d a d i f f u s i o n spherical s h e l l remains the same distance from the electrode surfaoe but the surface area increases continuously with time during the l i f e of each drop. Therefore }the equations that describe d i f f u s i o n to the dropping electrode d i f f e r from those for stationary spherical d i f f u s i o n by terms whioh describe the increase i n the area of the d i f -fusion f i e l d with time. It i s assumed that the mercury drops are free spheres. A c t u a l l y a small part 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 are deformed by g r a v i t a t i o n and beoome tear shaped,thus oreating a larger ./surface area thanr> i s possessed by a true sphere of equal v o l -ume. Thus ,the screening e f f e c t and deformation oppose each other with respect to the deviation of the surface area. 18. It i s assumed that a t C - s O t h e drops have an a r e a ^ . In r e a l i t y an area i s always maintained. It i s also assumed that the rate of flow of mercury i s constant; Actually^at the beginning of drop formation a very considerable counter pressure due to the ourvature o f the drop prevails,although i t i s very quickly removed. Thus, at the beginning of the drop time the rate o f increase i n surface area i s considerably decreased for a b r i e f i n t e r v a l . This compensates to some extent the maintenance of an area a t T ~ o . It i s assumed that the thickness of the d i f f u s i o n layer i s small compared to the radius of the 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 further on. further discussion i s based on at least three dif f e r e n t l i n e s of development. F i r s t l y the derivation i s based on that shown by Kolthoff and Lingane ( f r o m a d i s -oussion by MacGillavray and Rideal { H ). Secondly, Lingane and Loveridges iff) derivation w i l l be traced. Thirdly, the more rigorous derivation given by Strehlow and Stackelberg ( ^ ) w i l l be introduced. We have seen that the fundamental d i f f e r e n t i a l equation for symmetrical spherical d i f f u s i o n i s i n which s t ^ i a r a d i a l distanoe measured on a fixed coordinate system whose o r i g i n i s at the oentre of the spherical electrode. In order to apply t h i s equation to d i f f u s i o n at the dropping electrode the fixed ooordinate/*"must be replaoed by a moving coordinate,^), to take into account the increase i n area of the 13. d i f f u s i o n f i e l d during the growth of the mercury drops. The moving coordinate,/ 3 i s defined as the radius of a hypothetical sphere whose volume i s the same as the volume enclosed between the surface of the growing mercury drop and a spherioal sur-faoe of radius s l i g h t l y larger than the radius of the drop. 3 * (XXXI) or - y)'* — /to (XXXII) where A* i s the r a d i a l distance from a point i n the solution to the centre of the drop, and / ) 9 i s the radius of the drop at any instant • If we assume that the mercury drop i s t r u l y spherical, then i t s volume at any time 'C measured from the beginning o f i t s formation i s V * $ W = ^ = e t c - m i > where vn - weight of mercury flowing from c a p i l l a r y per second. <^ •= the density of mercury. cpi -z p r o p o r t i o n a l i t y constant r volume of mercury flowing from the c a p i l l a r y . p e r second. For a given c a p i l l a r y and a constant pressure <m~ and ad are v i r t u a l l y constant and independent of the i n t e r f a o i a l tension at the mercury-solution interface (/? )• However, during the formation of a single drop there i s a very considerable ohange i n pressure. Assuming/>rvconstant then the volume of the drop i s d i r e c t l y proportional to i t s age, but i t s radius increases with the oube root of i t s age; that i s irr 14. / I n view of these r e l a t i o n s , ana equation (xxxii) can be expressed as a function of the age of the drop by /O* - ^1^- (ft (xxxv) The f l u x of the d i f f u s i n g substance at a given instant and given value of su i s From equation (XXXV) for a given value of tr 1 ^ - ' (XXXVII) and henoe equation (XXXVI) becomes where/4^ , i s the area of the d i f f u s i o n f i e l d atsv- at any instant, and^ His the number of moles that diffuse through i n the time e/t~. D i f f e r e n t i a t i n g equation (XXXVIII) low i n terms of f l u x of the d i f f u s i n g substance equation (XXVI) may be written By substituting the foregoing r e l a t i o n s for and "^^-v into t h i s equation and simplifying This 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 electrode. We are interested i n the region very close to the surfaoe of the dropping electrode and since i n t h i s region Sis i s only s l i g h t l y larger t h a n ^ o i t follows that ^ ^ i s very much smaller than ^ ' C . W h e n } f t we have -~i ana ^ a (yt) 3 Therefore, for t h i s region very near to the surfaoe of the 15. dropping electro f e ' ei-aat'idfi" VX&l) beoomes In order to obtain a solution of t h i s equation i t i s convenient to perform a substitution of variables to simplify the algebra. Let ^ y -Then = 3 / ° ^ < 2 r ^ - 4 ^ ana <s£y . 3 - r- % In terms of these new variables * y ^Tr ~ 3 <- 3 5 y (XLIII) - (XLIV) Substituting the rel a t i o n s expressed by equations (XLIII) (XLIV) ana (XLV) into (XLII) leads to where ^ -A solution of equation (XLVI) i s ^ - A T - 5 -j/fr Jo^y If <?( y (xivn) where ^Kis an integration v a r i a b l e , ana £3 are constants ana the value of the i n t e g r a l aepenas only on the value of the upper l i m i t . !• The i n i t i a l ana boundary conditions Co - C- when XT - -O i CQ C or Co ~ O when "C ^ where (C, i s the concentration in. the body of the solution, and (CQ the oonoentration at the surfaoe o f the meroury drops. When t ? 0 } ^ - O and sinoe X ' / ^ t 7 ^ i s a l s o s^ 1 1*! *° 1. See reference (S~) page 35 16. Hence ;when^ "70 the upper l i m i t of 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 equal to zero. Since Co i s also equal to zero when tzpoit follows that K must be equal to zero. On the other hand,when C - O since ^ '• P the upper l i m i t of the i n t e g r a l beoomes i n f i n i t y and the value of the i n t e g r a l becomes • Since C a — C-when C7 ~ ° i t follows that the constant J3l& equal simply to C. Henoe , equation (XLVII) becomes Co - j ^ ^ l ^ »l f (XLVIII) Sinoe ¥• - /O^ and y - C % and - ^ 2 / ~= J? and hence equation (XLVIII) may be written Co~- ^ T f t f o * ^ ~ r ^ r 111 The resultant ourrent at any instant during the l i f e of a drop i s governed by the fLux of the d i f f u s i n g substance at the sur-face of the drop (^-.o), and i s given by From equation (XXXVIII) j<y. • D£ By d i f f e r e n t i a t i n g equation (L) with respect to so t we obtain or i n view of equation (XLIX) C - ^ y ^ ) t ^ d m ) i : * T>/O - -^th ( 3 w x ( 1 I V ) 17. Hence from equation ( U V ) , the fl u x at the surface of the drops i s given by (IV) given  a r / J Z — ) and the expression for the current i n equation (LI) becomes Since — 3 ^ - ^ 3 ^ ^ 7 (LVII) equation (LVI) becomes ^ r - £>• 732L ^ F ~ < r n % C"^ (LVIII) where 0.732 i s simply a combination of the numerical constants 1. This 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 current i n micro-amperes, the concentration i n millimoles per l i t e r and m as milligrams/second and on t h i s basis when the numerical value of F 2 i s introduced into equation (LVIII) we have The average current during the l i f e of a drop i s defined as the hypothetical constant current which, flowing for a length of time equal to the drop time, would produce the same quantity of e l e c t r i c i t y as the quantity actually associated with each drop. Mathematically the average current, »,is defined by where C ^ ^ i s the drop time. In view of equation (LIX) yoc^ p^c^^jW- ^ f ^ / r (Lxi) By performing the'^ntegration we f i n a l l y obtain 1. The value for d i s taken here as 13.6 g/om3. 2. The value for F i s taken here as 96500 coulombs. When the density of mercury at 25.0°C i s taken as 13.53 gm.cm"3 the equation becomes1 ^ T - £>o7^ D z 6 ^ ^ r i : ( L X I I D Lingane and Loveridge ( % ) substituted the r e l a t i o n for the area of a spherical meroury drop into equation (XVI) and a f t e r integrating found that the equation for the d i f f u s i o n current was J ~ 3 ^ 7 ^ V^- C % ZTT (LXIV) If the constant 397 i s multiplied by |/J"the "Ilkovio Constant" 607 i s obtained. In the Ilkovic derivation the factor represents the fact that the expansion of the mercury drops counteracts the decay of the concentration gradient at the electrode surface andjhence,the factor has t h e o r e t i c a l s i g n i -ficance. Therefore^this factor was substituted i n the equation for the instantaneous d i f f u s i o n current at a stationary spheri-c a l electrode ^ r r - ^ F D C A C^i TrSr) ( x x x ) Substitution and integration gave the equation for the d i f f u s i o n current From equation (LXV) the true d i f f u s i o n current constant,lo, i s Strehlow and Stackelberg have also derived a new equation for the polarographic d i f f u s i o n current. Their equation i s similar to that obtained by Lingane and Loveridge's somewhat 1. The publication dealing with t h i s correction has not b een located so f a r . 19. a r b i t r a r y procedure. In the derivation shown by Kelthoff and Lingane we have and However,the r e l a t i o n from equation (XXXV) /O2*i" %t ~ was not substituted for the term r 4 i n equation (XLI). Strehlow and Staokelberg have made t h i s substitution and obtain J>((^rO*f£^ +- zL«>*-rr> | % 7 { m i I , with the conditions for C^z ^ CD^ = C /*»o Cv^0 o ~ ® Equation (LXVII) i s expanded to ,3 i s the proportion of d i f f u s i o n volume to drop volume and,under polarographic c o n d i t i o n s j S m a l l compared to 1. Then, indicating the middle value of the d i f f u s i o n layer by'd' so that and Sl--^o + ol s£=^U* , (djLtf^2i^ 3 ^ - § M L X I X ) f t rv rr d-t Since the d i f f u s i o n layer d i s proportional jjD'C and SIo i s proportional to ( L ) 3then i s proportional tol/' 2'^7? The value of ^rCTis about 0.15 and therefore not to be disregar-ded-1. Hence,both terms l i n e a r i n -TT^are kept, the higher terms are neglected. The approximation i s then 1. See reference ( *f ) page 56. 20. This equation i s not exactly solvable. For an approximate solution assume that ^.j- i s small compared to 1 and i s always po s i t i v e , and during the drop time at every point has a constant average value . As grows with £~M;he average deviation from the central value i s small. Set and / -t Then equation (LXX) reads ' ^ -frf - - ^ s = C 2)^ ^~ 7)^J (LXXI) Equation (LXXI) can be transformed to an equation of the type yy ' ?>y^- (LXXII) with coordinates ufa —\\ y., so"**-, y ^ r * ^ 0 I f one neglects the terms that multiply with (a-rl) and are therefore small compared to the rest then The boundary conditions are given as before. The solution of (LXXIII) i s then (LXXIV) I with e current i s given Dy r^, 7)cTl Ft* 2^T o 3 ^ c _ C J ± _ _ — ^^7^<LXXVI) Substituting i n equation (LXXVI) flow _ J - ' >. ~~zJ~^0 "^"3""^) (LXXVIII) 21. If a l l powers of e except the f i r s t are neglected one obtains from (LXXVII) . , " i / , \ When 1 y' i s expressed 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 the constants and integrating From equation (LXIX) ^ ^ ^ % T 4 - ^ n ~ 3 (LXXXI) and upon substituting i n equation (LXXX) From t h i s i s shown that the d i f f u s i o n constant A =• ITT--^  whioh was found not to be a constant p r a c t i c a l l y {/o ) i s also not a constant t h e o r e t i c a l l y . In order to caloulate the constant A we make use of the derivation of the Ilkovio equation as given by M.van Stackelberg (W). Here two d i f f u s i o n layers were defined % ~ -^ V^ =r ) ( i x x x i n ) and / S > f (^-C0) (LXXXIV) The current density i s now ^ ° - E - r - . ( i x x x v ) looo % where q i s the drop area /\ i s proportional to the decreasing parts By combining these equations then 22. For l i n e a r diffusion,the d i f f u s i o n laws y i e l d 1 & ~ ^jf % (LXXXIX) Substituting i n equation (UXXVII) ^^-^ j0 ^''o/t The solution i s 2  £ = \J ^ TTDr ( z o ) By a combination of equations (LXXXV) (LXXXVIII) and (XC) and converting to the units proposed by Kalthoff and Lingane one obtains the Ilkovic equation ( I I ) . The s i m p l i f i c a t i o n i n these derivations l i e s i n the assumption that d i f f u s i o n to a plane surfaoe takes place. These si m p l i f i c a t i o n s are equivalent to the assumption that the d i f -fusion layer i s very small oompared to the radius of the mercury drop. The r e l a t i o n ""^ must also be calculated f or d i f f u s i o n to a spherical surfaoe. The place and time dependanoe for d i f -fusion to a sphere i s given by Co--c^c--cO-1f)+^ l^^'^Y ( x x v i i ) That i s S\ — //<> ^ y~ i s according to d e f i n i t i o n (XCI) Setting (XXVII) i n (XCI) ^ . _ 7 J" ^.-r^lfr >o ^ (XCII) r 'Heifer 5 + W 'Z^o^djyi Integra" This i a l would solve i n an approximate manner by putting the logarithmic terms i n series ^ (<si° - ^ s i o — ^ 'J^-^rXr 1. See equation (XCV). Wa.en.yto becomes i n f i n i t e , l i n e a r d i f -fusion e x i s t s . 2. See equation (XCVIII) 23. If X i s very small compared to SI* then the sum of the f i r s t two terms only applies 4 ^ f ^ f b X C^^' "^y)-^ V <?/?-2< ^ i s according to d e f i n i t i o n £ - "T§^) (LXXXIII) (XOIV) By ins e r t i n g G from (XXVII) from (XOIII) and (XCIY) , ,J^r-. Substituting (XOV) i n (LXXXVII) one obtains the i n t e g r a l equation v. Assuming that the term Vj^Jjf^l as the smallest correction term i n the time O to ZT , a constant average value JZ' i s assumed. Equation (XOVI) becomes A solution i s ^ f * * " Substituting Z / ^ / ^ ' X ^ - ^ j ^ £ - / - 2 - — T O Since the expression on the l e f t i s a constant then -^77 — and i t follows -A - £ -For i from equations (LXXXV) (LXXXVIII) and (XCVIII) 24. I Y f i T i r . was l ^ - ^ a n d for a growing drop Z^QTZT) 3 Then w _ \Tiny£^- - 3 V- / 3 Substituting for the constant A i n equation (LXXXII) jjzco^ u^cm^zrz (i+ n p ^ ^ i ' ^ c±) <iv) The constant A may also be derived from the geometry of the mercury drop and the d i f f u s i o n layer as shown i n F i g i 2 . A i s the mercury drop, B i s the 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 the derivation of the Ilkovio equation. However the reactant diffuses to the curved surface ab through the region C ( i n cross s e c t i o n a l view - wedge shaped). Instead of equation ( i i ) may also be considered -CJ r 6o7— D ^ C ^ 3 ^ ~C± C l + ~ > ) ( 0 ) . Where X i s the r e l a t i o n of volume C to the volume B. r s radius of mercury drop d ? thickness of the d i f f u s i o n layer. Volume B (for the whole drop) Volume B*0 - 3 TT/h ~ 0 3-<7 The correction factor ) + X i s given by y Sinoe d under polarographic conditions i s small compared to r the term -^-z-can be disregarded.« as d i f f u s i o n layer i s pro-portional to I/DV% r as drop radius i s proportional to (syr\ cL Therefore the correction term - ^ T . can be giv«n FIG. Z. Schematic Diagram of Mercury Drop and the Di f f u s i o n Layer i s given by %  7 7 ^ ~ ^ T S T T ^ 1 • 25. From these simple ways equation (LXXXII) i s obtained. To calculate the value of A approximately we assume a l i n e a r decrease of the concentration and set c/~ % - f~y TT^C^ I 3 5 " 3 0 Therefore 3/- . , , . Though the closer to the surfaoe extends the solution so that more i s contributed to the current density i t must s t i l l be averaged over d. For A by li n e a r decrease of concentration A -^-^ - iv- % This value i n view o f the omissions i n the Ilkovic derivation i s s a t i s f a c t o r y . From the previous derivation A » 17 which i s in better agreement with experiment and jtherefore^ s h a l l be assumed v a l i d . For a reaotant with 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 correction term i s Hi/To lO 3^~3 =. 0.OS^^C^ Since the q u a n t i t i e s ^ ! ^r^with commonly used c a p i l l a r i e s varies perhaps about 0.5 to 1.2 the correction term amounts to 2.7$ to 6.5$ and i s by no means to be neglected. It may be mentioned that the Lingane and Loveridge value of A = 39 amounts to a correction factor of 6.2$ to 15$ which appears to be somewhat larger than the 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 very small outflow, m, and very large drop times are used the Ilkovic equation i s no longer applicable sinoe then becomes comparable to 1 or larger. The improved Ilkovic equation may then be written - K on % r - f e C 1 -h^^-'i +- aJ^ ^ n ' H r i ) 1. The value 13530 i s taken as the density of mercury i n milligrams per cm^ at 25° C. 26. I f ^7? ' then the f i r s t two terms become small compared to the t h i r d . For very long drop times the current density should be . i proportional to C^as G.S.Smith ( I S ) found experimentally. However, with thick d i f f u s i o n layers there i s greater r i s k of convection and the assumption of l i n e a r d i f f u s i o n i s no longer admissable. The dissolution of a base metal from an amalgam at the dropping electrode as anode gives a current density whioh i s likewise expressed by the Ilkovic equation. However the expression used i n the previous derivations must be repla-oed by-/3. This change of sign merely results i n a negative sign i n the correction term. By an approximation Strehlow and STACK £/. Schlcoinger ( have evaluated the value of the correction faotor B i n the term / — S J)~7-<^n ~C to be 1.5 to 2 times the value of A i n the term / -f- A D ' T - - T v t - " 5 Since A has been accepted as 17 then B would l i e in the range of values 2 5 - 3 5 . A second effect causes the value of B to be larger than A i n that the ratio i s no longer very small. In view of the conclusions drawn with respect to the transport of metals dissolved i n mercury t h e n ^ =• / i s not inadmissable. In r e a l i t y } t h e streaming effeot caused by the outflow current from the c a p i l l a r y complicates the problem considerably. Strehlow and Stackelberg have determined the value of B as 28.5 when a cadmium amalgam i s used as the dropping electrode. 27 (2)~DROPPING AMALGAM ELECTRODES In 1939,J.J.Lingane ( / ) published a note reporting the q u a l i t a t i v e behaviour of a dropping cadmium amalgam elec-trode In polarography of cadmium sulfate solution. Using 0.01$ cadmium amalgam dropping i n a i r free O.IW potassium chloride solution containing 0.04 M cadmium sulfate ;he ob-tained cathodic and anodic d i f f u s i o n currents for the reduc-t i o n of the cadmium ion i n solution and for the oxidation of the cadmium metal i n the amalgam respectively. The two branohes formed a single polarographic wave. The anodic d i f f u s i o n current showed a •maxima' which was eliminated by the addition of 0.1 ml. of 0.1$ methyl red. He stated that t h i s i s evidence that the polarographic 'maxima' i s a pheno-mena of the solution side of the solution metal in t e r f a c e . In 1940 ;M.v.Staokelberg and H.v.Freyhold ( l~T) included a paragraph on the dropping zinc amalgam eleotrode i n th e i r paper on the determination of the coordination number of metal ions i n complex formation by the s h i f t of the polarogra-phic 'half-wave' p o t e n t i a l . Using 0.005$ zinc amalgam dropping i n 0.01M zinc s a l t solutions with potassium chloride or potas-sium n i t r a t e as supporting e l e c t r o l y t e ; t h e y obtained a single wave for the anodic and cathodic branches of the d i f f u s i o n currents. The single wave indicated almost complete r e v e r s i b i -l i t y of the eleotrode reactions. However, with IN potassium hydroxide the anodic wave and the cathodic wave were separated thus indicating an i r r e v e r s i b l e electrode reaction. 38. Although no quantitative data was presented i n the above papers, Kolthoff and lingane (If?) state that the anodic d i f f u s i o n currents obtained with the dropping amalgams were of the order of magnitude expected on the basis of the assump-t i o n that the Ilkovic equation held good. Late i n 1940, J.Heyrovsky and M.Kalousek ( )°J) published an account of the i r work with very d i l u t e amalgams of copper, cadmium, lead and zi n c . This work had been announ-ced i n 1938 thus cre d i t i n g these workers with the i n i t i a l investigations of 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 included with t h i s work). However, they added nothing to the quantitative data with respect to the anodic d i f f u s i o n current. Heyrovsky's (2.0) oontinued investigations have led to an os c i l l o g r a p h i c techni-que for recording current-voltage curves at dropping or streaming mercury electrodes. Electrodepositions involving single electron transfers and some few E-electron transfers show the anodic and cathodic depolarization wave at the same po t e n t i a l . However, for most electrodepositions involving £-electron transfers the po t e n t i a l of the anodic wave i s different from the po t e n t i a l of the cathodic wave. It may be noted that the cathodic wave i s due to the reduction of the ion i n solution to form a d i l u t e amalgam. The reversal of the pot e n t i a l sweep i s so rapid that the amalgam formed by the cathodic sweep i s discharged on the anodic sweep even when a streaming mercury electrode i s used. Prom the results obtained so far^Heyrovsky has deduced that a 2-electron transfer i s a two step process. One electron i s accepted: i n an e l e c t r o l y t i c 29. process: ^ ^ + +~ ^ — ^ ^ + The other electron i s acquired by dismutation: Unfortunately ,t he r e s u l t s are reported more or les s q u a l i t a -t i v e l y and the si g n i f i c a n c e of Heyrovsky's deduction cannot presently be appreciated. Comparisons of the behaviour of amalgam electrodes i n the polarographic and os c i l l o g r a p h i c techniques should be useful. In 1947, J.E.B.Randies ( A / ) used a form of the polarographic c a p i l l a r y electrode i n his study of the k i n e t i c s of electrode reactions with alternating current. Dropping amalgam electrodes (copper, cadmium, thallium and zinc) were -used where an a u x i l i a r y direct current c i r c u i t was maintained across the amalgam reservoir. The c a p i l l a r y was attached to a siphon from the reservoir. The purpose of the a u x i l i a r y c i r c u i t i s to s t a b i l i z e the d i l u t e amalgams. A similar technique has been used i n this work and i l l u s t r a t i o n s are shown elsewhere. Also i n 1947, T.Erde Graz and E.Varga (XX) reported the effect of non el e c t r o l y t e s on the electrode potentials of amalgams. The potentials of resting and dropping amalgams of bismuth, copper, thallium, lead and zinc were dsetermined i n solutions of various isoamyl alcohol, benzyl alcohol, o - t o l u i -dine, o-oresol, p - c r e s o l r b u t y r i c aoid and v a l e r i c a c i d i To make the solutions e l e c t r i c a l conductors^ sodium sulfate was added and the solutions and apparatus were c a r e f u l l y freed of oxygen. When the amalgam concentrations were above 10~ 5 to 10-4 gram atoms per l i t e r ^ t h e electrode potentials were reproducible to m i l l i v o l t s . The potentials are determined 30. p a r t l y by 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 s i d e o f t h e s o l u t i o n - m e t a l i n t e r f a c e , p a r t l y 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 on t h e amalgam s i d e o f t h e double l a y e r . The adsorbed m e t a l i o n s form t h e p o s i t i v e p a r t o f the double l a y e r c r e a t e d w i t h i n t h e amalgam. The n e g a t i v e p a r t c o n s i s t s o f d i f f u s e l y d i s t r i b u t e d e l e c t r o n s . (Experimen-t a l t e c h n i q u e and data i s not a v a i l a b l e s i n c e o n l y the a b s t r a c t 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) r e p o r t e d t h e drop time c h a r a c t e r i s t i c s o f co p p e r , g o l d , s i l v e r , t i n and z i n c amalgams a t p o l a r o g r a p h i c e l e c t r o d e s . Z i n c m e t a l was d i s s o l v e d i n mer-cury and the amalgam a f t e r f i l t e r i n g t h r o u g h chamois was washed w i t h methanol and acetone to remove g r e a s e and o i l . 0.01$ and 0.0001$ z i n c amalgams gave t h e u s u a l t y p e o f drop t i m e v e r s u s v o l t a g e c u r v e i n t h e n e g a t i v e v o l t a g e r a n g e . However, s i m i l a r to p u r e mercury, i n t h e v o l t a g e range - 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 among re p e a t e d d e t e r m i n a t i o n s was found. I n t h e p o s i t i v e v o l t a g e range the pen o s c i l l a t i o n s per drop were e x c e e d i n g l y i r r e g u l a r i n both shape and a m p l i t u d e . The e l e o t r o l y t e s used i n t h i s work were 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 o f m e t h y l r e d or g e l a t i n . A f t e r t h i s work had s t a r t e d a paper by S t r e h l o w and S t a c k e l b e r g (9) r e p o r t e d t h e d i f f u s i o n c u r r e n t f o r d r o p p i n g cadmium amalgam e l e o t r o d e s . A manual c i r o u i t was employed f o r a c c u r a c y . A l l measurements 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 the 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 measured to 0.1° and t h e 30a d i f f u s i o n current corrected by c a l c u l a t i o n to 25.0°. The values for ' i ' and ' t ' were determined in the solution at the same time the d i f f u s i o n current was measured. A cadmium amalgam 13.92 millirnolar was used with di f f e r e n t dropping c a p i l l a r i e s where the pressure was varied from 37 cm - 110 cm -r ^ of mercury. The d i f f u s i o n current constant J. = ^ r^zr_z so deter-mined varies up to 2% for duplicate determinations. However, I i s found to vary considerably with changing values of 'm' and ' t ' . For dif f e r e n t c a p i l l a r i e s the values of were plotted versus y, where 3 c <- . The ourves beoame asymptotic to a straight l i n e for the larger values of 'm* and ' t ' . From the d i f f u s i o n current equation f o r amalgam anodes (Equation V/) can be obtained Therefore,a plot of I versus y would y e i l d the value of 607 n Dg- from the intercept and the value o f BD-J from the slope. Since the curves were asymptotic to a straight l i n e , Strehlow and Stackelberg used the values of i t s intercept and slope for the 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 the value of the numerical constant B. Their experimental value f o r the d i f f u s i o n c o e f f i c i e n t at 25.0°G 1.52 X 10~5 cm2 sec-1 i s in excellent agreement with the value reported i n the l i t e r a t u r e 1.520 X 10*5 cm 2sec-l at 20.0°G. The value of B i s determined as 28.5. When the value of B i s calculated from the given data i t i s found that the values vary considerably. For those points which l i e close to the straight l i n e B varies from 24 to 29. As the deviation increases the value for B becomes more negative and a value -90.'9 has been calculated. It 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 the 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 source o f e r r o r ^ t h e n as t h e o u t f l o w c u r r e n t d e c r e a s e s t h e e l e c t r i c a l c u r r e n t becomes more t r u l y r e l a t e d to a d i f f u s i o n p r o c e s s a l o n e and t h e v a l u e o f B approaches a l i m i t i n g v a l u e . The l i m i t i n g v a l u e l i e s w i t h i n t h e range 25-35 a c c o r d i n g to t h e o r e t i c a l app-r o x i m a t i o n s . A c t u a l l y , a range 21-35 i s o b t a i n e d i f one c o n s i d e r s a l l t h e t h e o r e t i c a l a p p r o x i m a t i o n s g i v e n by S t r e h l o w and S t a c k e l b e r g . I n our own work i t w i l l be c o n s i d e r e d t h a t t h e l a r g e r v a l u e s f o r B i n d i c a t e 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 drop s u r f a c e . I t s h o u l d be mentioned t h a t S t r e h l o w and S t a c k e l b e r g do not des-c r i b e 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 they mention any t e c h n i q u e f o r overcoming 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 (64) 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 between the maximum on 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 and t h e maximum e x i s t i n g on the c a t h o d i c waves. An attempt I s made to e x p l a i n t h e ev i d e n c e i n t h e l i g h t o f I l k o v i c ' s t h e o r y o f t h e p o l a r o g r a p h i c maxima. T h i s t h e o r y i s based on t h e i d e a o f an inhomogeneous e l e c t r i c f i e l d due to t h e c h a r g i n g o f t h e d r o p p i n g mercury. S i n c e cadmium i s reduced a t a p o t e n t i a l c o r r e s p o n d i n g to t h e e l e c t r o c a p i l l a r y z e r o ^ t h e maximum cannot e x i s t a c c o r d i n g to t h e t h e o r y . 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 -c a p i l l a r y zero i s s h i f t e d by t h e anions^whereas t h e r e d u c t i o n o r o x i d a t i o n p o t e n t i a l o f cadmium remains unchanged and t h e r e f o r e the o b s e r v e d maximum. 31 C - ZING AMALGAMS (1)—METHODS OF PREPARING ZINC AMALGAM The l i t e r a t u r e (24) reports many variations of three basic methods used i n the preparation of zinc amalgams. These methods may be enumerated: 1. Simple contaot of zinc metal and mercury. 2. E l e c t r o l y t i c reduction of zinc s a l t s at the mercury cathode. 3. Chemical reduction of zino s a l t s by a l k a l i metal amalgams. In addition, there i s the method of Hulett and De Lury (25)(26) where zinc metal i s i n contact with the mercury cathode under a layer of d i s t i l l e d water which contains the platinum anode. Dissolution of the zinc metal proceeds rapidly when ten v o l t s direct ourrent are impressed. Preliminary experiments, reported elsewhere, showed that the method of Hulett and De Lury i s by far the best for preparing standard zino amalgams. 32. C (8)—CHEMICAL AID PHYSICAL PROPERTIES OP 2IIC AMALGAMS The s o l u b i l i t y of zinc i n mercury has been reported as 2.2199 grams of zino i n 100 grams of mercury at 25°C. Ho evidence of intermetallio compounds i s shown by the freezing point diagram. The non existence of such oompounds i s c o n f i r -med by observations on the s o l u b i l i t y , e l e c t r i c a l resistance, s p e c i f i c volume, vapour pressure and various observations on the eleotromotive force of zinc amalgams ( 2 V ) . Richards and Forbes (2.7) suggested that the deviation of the electromotive force values from the values calculated by the l e r n s t equation could be explained by polymerization of the zinc atoms. Hulett and Crenshaw {2-L) report that i n the range 0.006IU - Q. 000003 S^WJ, where I = mole f r a c t i o n the pot e n t i a l difference between any two amalgams conforms to the laws of a perfect solution. However, the values reported by Richards and Forbes did not agree with the values reported by Hulett and Crenshaw. Addi-t i o n a l l y , no f a u l t could be found i n the methods used by the two groups of c a r e f u l workers. Hildebrand (2.^) measured the vapour pressure of zino amalgam and found that the data of Richards and Forbes conformed to the laws of i d e a l solutions when the presence of a diatomic molecule,Zn2,was postulated. Pierce and Eversole (Z°f ) repeated the eleotromotive force measurements and found good agreement with the data of Richards and Forbes. Crenshaw (3<5) then showed that the data of the three papers could be made to agree by consideration of a single a r b i t r a r y constant. Liebhafsky (31 ) reported that the data of 33. a l l the papers were i n agreement when the measurements were referred to the p o t e n t i a l of the two phase zinc amalgam* Furthermore, he showed that the amalgams conform to i d e a l i t y over the entire range of composition studied when i t was postulated that zinc metal i n solution was present as mono-atomic, diatomic and triatomic zinc. He proposed that the concentrations of extremely d i l u t e amalgams could he oaloulated accurately by means of the Nernst equation from the values of E.M.F. measurements. This proposal may find some further application i n determining the concentration of the amalgams used i n polarography. However, from the foregoing i t has been shown that d i l u t e zinc amalgams are unique i n that they conform to the laws for i d e a l solutions. A l l of the above quoted papers as well as several others {/^ ) U4) (3x) (33) report on the i n s t a b i l i t y of d i l u t e zinc amalgams. W.G.Horsoh (32.) gave up the study of the app-arently anomalous behaviour of d i l u t e zinc amalgams. He reported that between two samples of the same amalgam the E.M.F. varied i n an e r r a t i c manner,falling and r i s i n g r a p i d l y . In our own work i t was impossible to find evidence of zinc from polarograms of amalgams whioh had been exposed to a i r over-night . (Although the l i m i t s of detection have not been reaohed at 0.1 ppm there i s reason to believe that i t w i l l be found of the order 0.001 ppm. This l a t t e r figure being estimated from the waveheight shown by a very dilute amalgam and the s e n s i t i -v i t y settings of the recording apparatus.) Richards and Forbes (2-7) found that when oxygen was removed from t h e i r solutions the E.M.F. values for the very d i l u t e amalgams f i t t e d i n with I 34. the data obtained with more concentrated amalgams. Although this i s evidence that oxygen plays some part i n the reactions leading to i n s t a b i l i t y ^ liebhafsky (33 ) states that even i n the absence of oxygen the amalgams tend increasingly to lose zinc as they become more d i l u t e . It i s also known that hydrogen gas i s not readily evolved from d i l u t e zinc amalgams immersed i n acid solutions UH ). According to liebhafskyjthe absolute rate of oxidation increases only s l i g h t l y with increasing con-centration of z i n c . He has postulated the following reaotions to explain the experimental evidence obtained with d i l u t e zinc amalgams i n s u l f u r i c acid solutions. A rapid equilibrium exists between the amalgam and amalgam surfaoe: Amalgam y Amalgam surface ~h electrons The rate determining step: 0 2 -h 2 electrons J- 2H~^ ^ HgOg A rapid follow reaction: Amalgam surface 1 ) = Amalgam surfaoe -/-The electron density at the amalgam surface is regarded as a constant depending on space and charge f a c t o r s . Thus^in clean-ing mercury the removal of zinc becomes progressively easier as the concentration of zinc decreases. In view of this i n s t a b i -l i t y i t i s not surprising that few papers report investigations of d i l u t e amalgams at the concentrations required i n the polarographic technique. There i s some considerable l i t e r a t u r e which deals with subjects pertaining to or applicable to th i s work. The normal electrode p o t e n t i a l of zinc has been determined by several workers as shown i n Table 1. 35. TABLE 1. THE NORMAL ELECTRODE POTENTIAL OP ZINC INVESTIGATOR E.M.F.Volts REP. Hor8Ch 0.758 TETT Scatchard and Teft 0.7610(corr.) (3V) Getman 0.7613 (3b~) Shrowder.Cowperthwaite and LeMer 0.7614(corr.) (34): The corrections noted i n Table 1 refer to the correction for the E.M.P. between zinc metal and the two phase zinc amalgam in zinc s a l t solutions. The values determined by various workers are shown i n Table 2. TABLE 2i THE ELECTROMOTIVE FORCE OF ZINC-ZINC AMALGAM INVESTIGATOR E.M.F.MILLIVOLTS REF. Cohen 0.570 (37 ) Puschin -2.0 ( 3S") Clayton and Vosburgh 0.0 ( 39 ) For the value of the pot e n t i a l difference between zinc amalgams Hulett and Crenshaw found that i n the range 0.006IN-0.00000307N, where N - mole f r a o t i o n , the simple equation held true E : E t l n Ci n F % where E electromotive force R 5 the gas constant T = absolute temperature n = electro equivalents per mole F = Faraday In « natural loganthm C s a concentrations of respective amalgams. 35(a) Richards and Forbes (27) have published a table showing the electromotive force between zinc amalgam and amalgamated zinc i n zinc s u l f a t e solution as determined by e a r l i e r workers. The only reference they give i s "Lindeck 1888". The values are shown i n Table 3. TABLE 3. EMF Zinc Amalgam vs. Amalgamated Zino in Zinc Sulfate Solution. % Zinc E.M.F. 1.860 0.003 volt 0.467 0.022 n 0.064 0.047 0.028 0.057 " 0.0014 0.096 " 0.0010 0.11 0.00038 0.13 " 0.00027 0.14 " 0.00020 0.15 0.00015 0.16 36. Hildebrand ^O) from h i s findings on the vapor pressure of zino amalgams plus the data published by Richards and Forbes^ gives the folldwing equation for the eleotromotive force between zino amalgams, 2.• ^Q'L -Z F L 0 A/, r 2- / T v ^ T / / where N subscript - mole percent zinc of respective amalgam the remaining symbols having the previously given meaning. Pierce and Eversole (2*?) give the following r e l a t i o n E = RT In A2 nF a2 where Ag, ag = a c t i v i t y of zino i n the respective amalgam. These workers have given tabled values for the a c t i v i t y of zinc and of mercury i n zino amalgams as w e l l as for f r e e energy, entropy and temperature c o e f f i c i e n t s . Liebhafsky (SlJ^by r e c a l c u l a t i n g previously publis-hed data^has established the r e l a t i o n E s 0.09922 T l o g ^ Z m ^ z*2 where isLZn sub - terms for equilibrium oonstants and concentration of zinc i n the respec-t i v e amalgams. The log terms are based on the assumption of a rapid e q u i l i b r i a between monoatomic, diatomic and triatomic zinc i n the amalgam. 2n Zn 2 2n3 The best values of the equilibrium constants required for a solution of the equation are given i n Liebhafsky's paper. Although the electromotive force of zinc amalgam 37. electrodes appears to be well established,there are few reports on the behaviour of zino amalgams during conduction of e l e c t r i -c i t y . Lewis and h i s co-workers C-U ) found that a l k a l i metals in d i l u t e amalgams apparently migrate to the anode during the passage of e l e c t r i c a l current. G.Mayr {NZ) reported a similar behaviour for a l l base metals. F.Skaupy ( £ / 3 ) ( ) concluded that since the addition of zinc increases the conductivity of mercury considerable i o n i z a t i o n occurs. He postulated that the solvent metal and solute metal are i n equilibrium with a common ion, the electron. He explains that the change of electron concentration during the passage of current induces the p o s i t i -vely charged metal ions to migrate. The po s i t i v e ions apparently drag along neutral atoms* He gives an expression f o r transport i n amalgams, t = U/V (1 + Z) (_C_ ) (100 ) u = mobility of mercury cation V r " " electron Z - number of neutral mercury moles for each cation G - concentration of a l k a l i metal amalgam According to K.Sohwarz (VH) and G.Wagner . during the passage of e l e o t r i o i t y mercury i s almost completely dissociated into Eg1"h ions but Hgg^11" ions cannot be excluded. Zinc i s dissolved i n mercury as ions. Schwarz (yC>) states that the ion with the greater charge density migrates to the cathode. Prom the transference number he has determined the d i f f u s i o n constant of zinc i n mercury at 25°C and 35°G as shown i n Table 3. More recently,G.Bianchi (^7) has presented h i s findings on the dissolution of metal electrodes i n di l u t e amalgam solutions. The results he obtained indicate some s i m i l a r i t y to the d i s s o l u -t i o n of metal electrodes i n s a l t solutions. Anomalies are 38. evident - for instance at temperatures over 150°C the anode corrodes faster than the cathode, at lower temperatures the oathode corrodes f a s t e r . This r e s u l t was obtained for the passage of direct current through copper electrodes i n mercury. He has also found that the s o l u b i l i t y of copper i n mercury i s greatly reduced when zinc i s present in the meroury. According to Meyer (^ £Q the dis s o l u t i o n of zino i n meroury lowers the surface tensioni^of mercury as some s a l t s i n water lowers i t s surfaoe tension. The ava i l a b l e data i s given in 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 published values for the d i f f u s i o n constant of zinc i n mercury are somewhat confusing with respect to the units employed. The data has been recalculated for expression i n the unit8 cm2 sec-1 for Table 5. 39. TABLE 5. DIFFUSION CONSTANT OF ZINC IN MERCURY INVESTIGATOR TEMPERATURE DIFFUSION CONSTANT REF. G.Meyer 150 C 2.42 x: io-Pom'3 eeo""1 Wogan 11*5°C 2.52 x 10" 5 rf (so) n 99.2°C 3.36 X 10" 5 tf (so ) Sohwarz 25° C 2.00 X 10" 5 t» ( ^ k ) n 35° C 2.13 X 10 r • 5 it ( tJL>) Guthrie 15° C 1.15 X 10" 5 Tl ( S i ) Some considerable v a r i a t i o n i s shown between the values reported. For t h i s r eason ;it i s somewhat doubtful that the value of the d i f f u s i o n oonstant at 25°C has been established. Further, Samarin and Shvartsman (53) have calculated the coef-f i c i e n t of d i f f u s i o n of several 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. - - — — — — - — - - For the a l k a l i and a l k a l i n e earth metals the c a l c u l a -ted and experimental values were i n agreement to 10%. However, for gold, lead, thallium and zinc the discrepancies were up to 50$. This discrepancy i s explained i f zinc atoms i n mercury solution polymerize to form diatomic and triatomic molecules. From the foregoing } i t i s apparent that a solution of zinc i n mercury may be considered i n some ways similar to a solution of s a l t i n water. It i s an i n t e r e s t i n g analogy which, perhaps, could bear further investigation. So far as t h i s work i s concerned the e l e c t r i c a l transport of the solute metal i s most important,sinoe polarographic theory demands a d i f f u s i o n process alone. Provided that e l e c t r i c a l transport may be considered n e g l i g i b l e then the determination of the d i f f u s i o n 40. c o e f f i c i e n t would be s t i l l complicated by the polymerization of zinc i n amalgam as postulated by several workers. In th i s oase the d i f f u s i o n c o e f f i c i e n t would become a function of the concentration. Such a r e l a t i o n would explain the v a r i a t i o n i n the experimental values for the d i f f u s i o n c o e f f i c i e n t as w e l l as the deviation of the value calculated by the Stokes-Einstein Law. 41. J> ~ EXPERIMENTAL I - Materials and Solutions Mercury The mercury used i n t h i s work was o r i g i n -a l l y very d i r t y . The mercury was f i l t e r e d at a o a p i l l a r y funnel and then aerated under 5$ n i t r i c acid for several days. The supernatant l i q u i d being siphoned o f f and renewed three or four times for each batch. Following aeration ^ the mercury was passed i n a fine spray through four scrubbing columns containing 5% n i t r i c a c id, 5$ sodium hydroxide, 2.5$ n i t r i c acid and d i s t i l l e d water i n that order. The mercury was then vacuum d i s t i l l e d at least three times. After each d i s t i l l a t i o n the mercury s t i l l was cleaned with n i t r i c aoid v. flushed with tap water, rinsed with d i s t i l l e d water and f i n a l l y dried in a r stream of dry a i r . Polarograms recorded with the f i n a l product showed no unexpected curves. The D.S.Pharmaooepia test for mercury purity ( 5^ )was applied. In this work the meroury remained b r i g h t l y metallic one minute and ten seconds to one minute and twenty-five seconds a f t e r the appearance of b o i l i n g at the surfaoe of the sol u t i o n . Zinc — Tadanao zinc (99.99 +• $) was fractured and the loosened c r y s t a l s were pried o f f with horn-tipped tweezers and weighed immediately. The weight was taken to be that of pure zino. Potassium chloride — Reagent grade potassium chloride was r e o r y s t a l l i z e d three times from doubly d i s t i l l e d water and f i n a l l y dried overnight at 110°C. 42. O.IN Potassium chloride — 14.822 gm. of r e c r y s t a l l i z e d potassium chloride was dissolved i n d i s t i l l e d water and made up to 2000 ml. Calculated 0.0994 I KGL Standard zinc solutions r— Zinc c r y s t a l s were dissolved i n 5 ml. Hichol's Hydrochloric Acid ,0.P., i n a covered 250 ml. beaker. Very l i t t l e , i f any, spraying was observed. The solu-t i o n was evaporated just to dryness on a hot plate at 1 low heat. The zinc chloride c r y s t a l s were washed into a 2000 ml, volumetric fl a s k containing 14.822 gm,of potassium chloride and made up to the mark with d i s t i l l e d water. Aliguats were made up to the mark with O.IH potassium chloride solution. The zinc standards are reoorded i n Table 6. TABLE 6. Standard Zinc Solutions. l o . MAKE UP Molarity m i l l i m o l e s / l i t e r 1 0.0809 gm.Zn i n 2000 ml. 0.6187 2 0.0440 " " " " 0.3365 3 0.02695 " " " " 0.2061 4 0.0136 n " " " 0.1040 5 25.0 ml #2 to 500 ml. 0.0168 6 25.0 ml #2 to 1000 ml. 0.0084 7 10.0 ml #3 to 500 ml. 0.0041 Zinc Amalgam — In preliminary work d i l u t e zinc amalgams prepared by simple contact of the metals 'proved unsatisfactory. Whether prepared i n a i r , in nitrogen atmos-phere, in vacuum or under zinc sulfate solution a surface f i l m was evident. In a i ^ a black f i l m of zinc suboxide appeared on the surface of the mercury. In nitrogen or i n vacuum a c r y s t a l l i n e metallic f i l m appeared. The existence of these films prevents the preparation of amalgams of known concentra-43. t i o n by simply weighing the two metals before amalgamation. Amalgams prepared under zino sulfate solution were covered by considerable amounts of a white flocculent p r e c i p i t a t e which i s presumed to be a mixture of basio zinc s a l t s and zino hydroxide. Upon exposure to a i r the amalgam was covered with a black f i l m almost immediately. A l l of these amalgams showed a marked tendency to adhere to g l a s s . When a small globule was r o l l e d around on a clean watch glass streaks of amalgam would be l e f t s t i c k i n g to the glass. On the whole, amalgams prepared by these methods were not suitable for use i n glass apparatus nor did the method allow quantitative preparations. Amalgams prepared by the method of Hulett and DeLury closely resembled pure mercury so long as they were not exposed to a i r for more than a few seconds. However, i t i s advisable that oxygen does not come i n contact with the amalgam at any time. Unfortunately, Hulett' s (z (*) paper on the preparation of zinc amalgam i s not immediately a v a i l a b l e . However, Hulett and DeLury have shown that cadmium metal dissolves quantitatively i n mercury under the same conditions. In t h i s work polarography of the water layer af t e r amalgamation gave polarograms (Fig. STC ) which could not be distinguished from polarograms of d i s t i l l e d water. It has been found that 0.008 millimolar zinc solutions can be distinguished from d i s t i l l e d water by polarographic methods. Thus i t can be said that the water layer a f t e r amal-gamation contains less than 0.5 / per m i l l i l i t e r . For an amalgam made up with 30 milligrams of zinc metal with a water layer of 25 cm^ i n volume an error of the order of O.lfo i n concentration may be possible. The method o f f e r s the most 44. sat i s f a c t o r y results for preparation o f the amalgams used i n polarography. The method for making up a standard zinc amalgam i s described in the section dealing with the amalgam c e l l . Calomel Electrode Paste — Mercurous chloride, CP., was mixed with p u r i f i e d mercury to form a powdery paste. Gelatin — 0.2 gm.of Knox Sparkling Gelatin was dropped into 10 ml.O.II potassium chloride and heated just to b o i l i n g or u n t i l the g e l a t i n dissolved. Immediately a f t e r dissolution 20 ml.of 0. IN potassium chloride was run i n . This make up i s approximately 0.6% g e l a t i n i n 0.1! potassium chloride. 1 ml. diluted to 125 ml.is approximately 0.005% g e l a t i n . II Potassium chloride — 75 grams reagent grade potassium chloride was made up to 1 l i t e r . Saturated potassium ohloride — Reagent grade potas-sium chloride was added to d i s t i l l e d water u n t i l an excess remained after standing several days. Saturated potassium chloride zinc chloride App-roximately 100 grams of zinc chloride was added to 100 ml,of saturated 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 u n t i l an excess remained undissolved on standing several hours. Approximately 150 grams of zinc n i t r a t e were added to the saturated potassium n i t r a t e . A l l chemicals used were reagent grade as supplied by the University of B r i t i s h Columbia, Chemicals Storeroom. Doubly d i s t i l l e d water was used throughout the experi-mental procedures. 45 II - Apparatus , A Sargent Model XXII Polarograph was used to record the polarograms. A manual method was also devised which employed the recording polarograph to measure the current at constant applied E.M.F. A Leeds and lorthrup Student Type Potentiometer measured the p o t e n t i a l across the dropping electrode and the O.HJ oalomel electrode. The c i r c u i t diagram i s shown i n Pig. 3 . Opening and closing the s t a b i l i z i n g c i r c u i t did not cause any deflection of the potentiometer galvanometer thus indicating that the p o s s i b i l i t y of error from t h i s source i s n e g l i g i b l e . The effect of switching on the current recorder could not be determined. The error involved here depends on the magnitude of the current and the shunt resistances selected by the s e n s i t i v i t y settings. Por a current of 6 microamperes and a s e n s i t i v i t y setting of 0.04 mioroamps/mm an error of the order of 0.0015 vo l t can be expected. Such an error i s n e g l i -g i b l e in most polarographic work. The method appears to o f f e r the same degree of accuracy as the simple manual c i r c u i t des-cribed by Lingane (5^5"). The amalgam c e l l — The amalgam c e l l i s shown i n Pig. H . The container was weighed f i l l e d with mercury and weighed again to determine the weight of mercury. The four hole rubber stopper contains a contact electrode , C, which extends to the bottom of the c e l l , a platinum wire c o i l electrode, B, which is positioned about 1 cm. above the mer-cury surface, a siphon tube, A, which extends to within 1-2 mm Sketch of 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 - Amalgam P - Platinum c o i l electrode E - Mercury contact electrodes W ' - Water layer B - Reference eleotrode S - E l e c t r o l y t e B - Anode pool DE - Dropping electrode Figure 4 The Amalgam C e l l A. Siphon tube B. Platinum o o i l electrode C. Contact electrode to bottom of mercury D. Pressure tube TO POTENT F i g u r e 5. P o l a r o g r a p h i c C e l l A. Reference E l e c t r o d e B. Platinum c o i l e l e c t r o d e i n water l a y e r C. P o l a r o g r a p h i c c e l l showing anode p o o l c o n t a i n e r T. Thermometer M. N i t r o g e n gas l i n e R. Amalgam r e s e r v o i r 46. of the bottom of the c e l l and a short tube, D, which i s used to exert pressure for s t a r t i n g the siphon. After positioning the stopper,a weighed zinc c r y s t a l was dropped through the hole for the pressure tube, D. D i s t i l l e d water was added t i l l the c o i l electrode was covered. The pressure tube was replaced. F i n a l l y , 10 v o l t s were impressed across the c e l l making the c o i l electrode the anode and the mercury the cathode. The c e l l was agitated so as to rotate the mercury at i n t e r v a l s . After sev-e r a l days e l e c t r o l y s i s the amalgam was siphoned into the drop-ping electrode assembly. Although no r e a l evidence has been obtained i n t h i s work j i t i s believed that the zinc amalgam i s ready for use i n the dropping electrode shortly af t e r the metallic zino d i s -appear S i -The Polarographic (Cell Assembly — The polarographic c e l l i s shown i n F i g , S • The c i r c u i t connections are shown i n F i g . 3 • A 250 ml. beaker was used as the e l e c t r o l y s i s vessel. A large rubber stopper was bored so that the dropping c a p i l l a r y , the contact electrode, the nitrogen l i n e , the thermometer and the calomel electrode, A, could be inserted i n the e l e c t r o l y t e i The contact electrode dipped into a mercury pool contained i n a glass dish, C, positioned so that the f a l l i n g drops did not f a l l into the pool. The 0.IN calomel electrode was made up with O.IN potassium ohloride, calomel paste and mercury. It was always placed i n the el e c t r o l y t e so that the solution flowed from the c e l l towards the calomel eleotrode before coming to the common l e v e l . The thermometer i s graduated 0.1°C per scale d i v i s i o n . The nitrogen l i n e was a piece of 4mm, glass tubing drawn to a 47. fi 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 tubing. Dropping Electrode Assemblies The soft glass capi-l l a r y tubing, S - 29350, supplied with the Sargent Polarograph was cut to lengths 7.0 - 7.5 cm and joined to 8 mm soft glass tubing. F i g . <o shows the regular dropping electrode assembly for mercury alone. The mercury reservoir A, i s connected to the c a p i l l a r y and column, B, by neoprene rubber tubing. The tubing was cleaned by passing steam through i t for two hours followed by drying i n a stream of a i r . Before c o n n e c t i n g ^ small quantity of mercury was allowed to flow through i t to carry out any loose material remaining. The contact eleotrode, C, dips into the mercury reservoir through a rubber stopper. A i r entered the reservoir and the c a p i l l a r y column through the attached drying tubes, D. The mercury l e v e l was controlled to 1 mm,by a sl o t in the marker E. The dropping eleotrode assemblies for use i n amal-gam polarography are shown i n Figs. 7 t B~. The c a p i l l a r y i s connected to the reservoirs by 8 mm.soft glass tubing. The reservoirs have a capacity of about 100 ml. The t o t a l height of the assemblies i s about 45 om^thus allowing an amalgam column of about 35 cm. A platinum contact electrode i s set into the 8 mm.glass tubing about 1 cm^below the res e r v o i r s . The assembly shown by i t s e l f had a second contact electrode about 1 cm.above the c a p i l l a r y . The platinum c o i l eleotrode i s held i n the rubber stopper shown at the top of the reser-v o i r s . Before the mercury was siphoned into the amalgam reservoirs they were swept out for two or three hours with F i g u r e 6 Dropping E l e c t r o d e Assembly A . Mercury r e s e r v o i r B. Mercury column connected to r e s e r v o i r by neoprene t u b i n g . C. Contact e l e c t r o d e D. D r y i n g tubes E. Marker f o r mercury l e v e l . r F i g u r e 7 A l l g l a s s dropping e l e c t r o d e assembly f o r amalgam polarography. C. C a p i l l a r y E. Contact e l e c t r o d e s P. Platinum c o i l e l e c t r o d e (Dips into water l a y e r i n amalgam r e s e r v o i r . ) * 48. nitrogen. A 4 mm.glass tube was lowered t i l l i t was r e s t i n g on the upper part of the c a p i l l a r y so as to sweep out a i r by the nitrogen stream. The nitrogen stream was maintained as long as possible while the mercury was siphoned i n . As the t h i n glass tube was withdrawn i t was manipulated so as to remove entrapped gas bubbles. As quickly as possible^ d is t i l l e d water was layered on the amalgam surface and the c o i l electrode i n -serted to close the s t a b i l i z i n g c i r c u i t . Nitrogen p u r i f i c a t i o n Tank nitrogen used to sweep out dissolved oxygen was p u r i f i e d i n a vanadous sulfate t r a i n a f t e r the method described by Meites (SO. The p u r i f i c a t i o n t r a i n consisted of four scrubbing bottles containing O.IN vanadous sulfate solution and a f i n a l bottle containing O.IN potassium chloride made basic by the addition of one or two p e l l e t s of potassium hydroxide to which 1-3 grams of sodium s u l f i t e were added. 4 9 . III-METHODS t The mass of mercury flowing from the 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 the mercury drops were caught on a tared watch glass. As a drop f e l l the stop watch was started and the next drop was caught. The stop watch was stopped as the l a s t drop f e l l into the watch glass. In 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 glass l a d l e . The collected mercury was washed with a stream of d i s t i l l e d water. The excess water was decanted and the spoon and mercury dipped into acetone and swirled around. This process was repeated with fresh acetone* The excess acetone was decanted and the mercury globule tipped into a weighed watch glass. After the acetone had evaporated,the watch glass and mercury was weighed and the weight of mercury determined by difference. For polarographic work the room was warmed to 23°C-27°G by means of a hot plate. The temperature being determined by means of thermometers distributed about the room. The mercury was f i l t e r e d at a c a p i l l a r y funnel into the anode con-tainer and about 125 ml,of standard solution added. The re-quired amount of g e l a t i n was then added. After setting up the dropping electrode assembly,the solution was swept out with nitrogen. The temperature of the e l e c t r o l y t e was brought to 25.0°G by holding the sides of the beaker by hand or rubbing with dry i c e . The temperature was found to hold within 0.1°C during the run. When ready f o r the run the nitrogen tube was withdrawn so that i t would maintain a blanket over the solution. 50 Usually the drop time was determined from the record-ing. In some cases the drop time was determined by timing with a stop watch graduated to 0.1 second. It was found that the drop times could only be reproduced in the absence of v i b r a t i o n . Even movements i n other parts of the building seemed to have some effeet. For t h i s reason polarographic runs were made at such times outside interference was at a minimum. In amalgam polarography the d i a l settings and electrode connections were set so that the potential of the dropping elec-trode became more p o s i t i v e . The d i a l settings for the amalgam runs are as follows: RANGE 1.500 Volts, SPAN 1.500 Volts OPPOSED, DME 0 , DAMPING 1, SENSITIVITY 0.06>^amp. fo RANGE was set 10.0 and zero current set at 40 mm. chart reading. The apparatus was calibrated (see manual of instructions) during zero current check. The recorder was run at E.M.E.CONSTANT u n t i l the pen reached the l i n e chosen for the start of 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 potential across the c e l l varied by setting % RANGE. When the chart showed steady current the recorder was switched o f f (the applied E.M.F. i s maintained) and the p o t e n t i a l of the drop-ping electrode determined vs. O.IN calomel reference electrode by the potentiometer. The potentiometer was frequently calibrated against a Weston Standard C e l l . The potentiometer reading i s that setting for which the galvanometer (Leeds and Northrup CAT. NO. Z. 330-D period ^/sec. s e n s i t i v i t y 0.3 s ^ ^ J ) i s deflected equally from zero. 51 E - Results and Discussion I - Polarography of Standard Zinc Solutions. Determinations of the c a p i l l a r y constant 'm' for the regular dropping mercury eleotrode are recorded i n Table 7. The mean value 2.595 mgm/sec. TABLE 7. The Rate of Meroury Flowing from C a p i l l a r y into A i r . Room Temperature 21°C ±. 3° Date Mass of % Outflow Time *m' Feb*13 3201.2 mgm 1231 seo 2.601 mgm/sec Apr.16 442.0 " 170.7 sec 2.589 " " 16 476.5 " 183.9 " 2.591 " 25 823.7 " 316.7 " 2.601 " Mean Value 2*595 " has been used i n c a l c u l a t i o n s . The use of t h i s value for 'm* i s not s t r i c t l y v a l i d since 'm' varies with the p o t e n t i a l of the dropping electrode. From rather meager data shown by Kolthoff and Lingane (.57) an error of the order of Zfo i s expeoted. The removal of dissolved oxygen by p u r i f i e d tank nitrogen was tested with the regular polarographic apparatus. The results are shown i n Table 8. TABLE 8. Removal of Dissolved Oxygen by l i t r o g e n Sweep Ele c t r o l y t e IK KCL EMF applied 1 v o l t . Time of HgSweep S e n s i t i v i t y Damping ' Current Pen Travel 0 min 0.04^amp/mm #1 5.8>^amp 21mm 5 n " " 0.64 " 2 . 0 m n v ]_Q ti «t n ii 0 2 7 " M >N t h*t* ^K^s. O 15 " tt n n o!24 " 20 " n II n Q # 2 5 rt »• " " " " none 0.25 n 2.25mm " ,f 0.01 " #1 0.245 " 0.25 " " " n it n o n e 0.245 " 6.0 " " " 0.003 " #1 0.255 " 0.25 " " " " none 0.255 " 14.0 " 25 " 0.04 " #1 0.25 " M » N I ^ M - ? C lgm la2 S0 3added " " " 0.18 " 1.0 mm 52. It i s seen that a f i f t e e n minute nitrogen sweep i s s u f f i c i e n t for p r a o t i c a l purposes. However, traces of oxygen remain d i s -solved i n the solution. After a nitrogen sweep of one hour a small 'wave' appeared on the polarograms at approximately -1.10 vol t versus O.IH calomel electrode when maximum s e n s i t i -v i t y of the recording instrument was used. It i s believed that t h i s 'wave' i s due to dissolved oxygen. Oxygen i s reduced stepwise at the dropping electrodei The f i r s t wave i s due to the reduction of oxygen to hydrogen peroxide, equation 1. The h a l f wave po t e n t i a l i n O.IK 0) 0 2^2H 20 + 2e > HgOg i- 20H" E i - O.lv potassium ohloride i s given versus S.C.E. The second wave corresponds to the reduction of the hydrogen peroxide (5~Sf) • (2.) HgOg +- 2e > 20H" E i - 0.9v. It i s seen that i n the presence of dissolved oxygen i n a neu-t r a l solution,the d i f f u s i o n layer about the mercury drop becomes a basic solution containing hydrogen peroxide* The small wave noticed at - 1.1 volt versus O.I! calomel eleotrode i n t h i s work i s presumably due to the reduction of hydrogen peroxide. The wave heights varied somewhat between 0.03^amps to 0.09/^amps. Results of a test for r e p r o d u c i b i l i t y of the i n s t r u -ment settings are shown i n Table 9A. After each reading the d i a l s were thrown o f f and reset before taking the potentiometer reading. 53 TABLE 9A Reproducibility of Instrument Settings Dropping mercury electrode i n standard zinc solution D i a l Settings Calculated Potentiometer Span I n i t i a l % Range Voltage Reading 1.5 v o l t s add 0.1 volt 49$ 0.8350 K ^ - * - 0.8346 I / « * T n n II ti .. • 0.8344 it it n ?n .. 0.8349 " " " " " " 0.8343 " " " " •• 0.8345 •• n " n II 0.8350 •• Since one scale 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 of the potentiometer readings 0.0006 v o l t s represents 4$ of one scale d i v i s i o n . It i s evident that the instrument settings can be duplicated accurately. It was found, however, that the pen position on the chart varied by as much as 0.2 chart d i v i s i o n . That i s the chart voltage reading varied from the d i a l setting value. This v a r i a t i o n i s due to backlash i n the chart drive mechanism. Fortunately }the discrepancy i s noticeable as the instrument operates and consequently the error can be estimated when the instrument i s stopped. For an error of 0.1 chart d i v i s i o n at a span setting of 1.500 v o l t s an error i n the measure ment of the half-wave p o t e n t i a l of 0.0015 volts r e s u l t s . When the polarograph was used i n conjunction with the potentiometer for point by point readings the applied p o t e n t i a l was calculated from the d i a l settings and checked against the potentiometer reading. The res u l t s are shown i n Table 9B. 54 TABLE 9B Polarograph vs. Potentiometer Readings. Polarograph Setting Potentiometer Reading Deviation 1.350 vo l t 1.347 volt -0.003 volt 1.005 " 1.003 " -0.002 " 0.900 " 0.900 " 0.000 " 0.750 " 0.753 " 0.003 " 0w525 " 0.531 " 0.006 " 0.300 w 0.309 " 0.009 ,T 0.015 " 0.021 " 0.006 n It i s seen that the potentiometer readings become increasingly higher than the instrument s e t t i n g with decreasing applied pot e n t i a l by an amount outside the l i m i t of error determined from Table 9A. It i s assumed that the deviation i s en t i r e l y due to inherent error of the potentiometer* Consequently, a similar degree of error i s expeoted i n the determination of the potential of the dropping electrode for point by point polaro-grams. In order to obtain information with respect to the 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 of the method used, polarograms of standard zinc i n O.IN potassium chloride with added g e l a t i n were recorded. The data i s given i n Table 10. Typical polarograms are shown i n Pigs* A } 10A^ 55. TABLE 10 Polarographic Characteristics of Zinc Solutions (1) Recorded with Sargent Polarograph. Standard Zino i n O.IN KCL with 0.0001$ g e l a t i n . Temperature 25.2°C 0.2° Mo Concentration id(a) 4 .44X< t . E i ( b ) 1 0 . 6 1 8 7 m molar(c) amp. 2 . 8 4 sec 1 . 1 0 5 v o l t 2 n " (o) 4 . 5 1 it 2 . 7 0 i i 1 . 0 9 8 Tl 3 IT II 4 . 8 9 IT 2 . 8 9 it 1 . 0 9 3 tt 4 n n 4 . 7 1 11 2 . 7 0 i t 1 . 0 9 5 It. 5 ti t i 4 . 8 3 n 2 . 9 1 n 1 . 0 9 5 11 6 tt i i 4 . 8 3 it 3 . 0 4 i t 1 .084 It 7 tt tt 4 . 7 4 i t 2 . 9 8 i t 1 . 0 9 0 It 8 0 . 3 3 6 5 it 2 . 6 8 i i 2 . 6 2 IT 1 .092 11 9 tt t i 2 . 6 2 t i 2 . 5 8 ti 1 . 0 9 0 It 10 n rt 2 . 6 3 i t 2 . 4 9 i t 1 .098 IT 11 it i t 2 . 6 2 i i 2 . 4 9 i t 1 .095 tl 12 0 . 2 0 6 1 it 1 .67 tt 2 . 9 5 i t 1 .098 It 13 i i i f it 2 . 9 2 i t 1 . 0 9 3 tt 14 i i tt 1.66 i t 2 . 7 0 tt 1 . 1 0 1 IT 15 0 . 1 0 4 0 it 0 . 8 2 8 i t 2 . 5 2 n 1 .107 If 16 n Tl 0 . 8 3 7 i t 2 . 7 0 ti 1 . 1 0 5 11 17 0 . 0 1 6 8 tt n i l i t 2 . 7 0 Tt n i l 18 0 . 0 0 8 4 i i it i i 2 . 7 0 it i t 19 0 . 0 0 4 1 " (d) 0 . 0 3 5 ti 2 . 7 0 ti 1 .113 II (a) Corrected to 25.0°C (b ) Applied voltage reading (c) Oxygen present (d) Identical wave found i n O.IN KCL alone. Standard Zinc in O.IN KCL with 0.0001$ g e l a t i n , plus 0.1 gm Na£ SOg per 100 ml. Temperature 25.1°C 0.2° No. Concentration id t . Ei(a) TTa~) 0 . 6 1 8 7 mmolar 2 . 9 5 sec 0 . 8 9 5 volt 1 ( h ) 11 tt 2 . 6 4 •• 2 . 8 9 IT 0 . 8 7 7 n 2(a) 0 . 2 0 6 1 11 0 . 6 7 •• 2 . 9 1 11 0 * 8 5 8 " 2 ( h ) it tt 0 . 6 1 •• 2 . 9 5 It 0 . 8 9 1 " 3(a) 0 . 1 0 4 0 11 0 . 5 1 2 . 7 3 It 0 . 9 3 0 " 3 ( h ) n tt 0 . 4 4 " 2 . 7 9 II 0 . 9 1 8 " (a) Applied voltage reading. 56. (2) Manually Beoorded Standard Zinc i n O.IH KGI with 0.0001$ Gelatin. Temperature 25.0°C. Concentration id t E i (a) 0.2061 mmolar 1.40/^amp (b) 3.15 sec. ~1.095volt (a) E i vs. O.IN calomel electrode. (b) oxygen indicated. Standard Zinc i n O.IH KCL with 0.0001$ g e l a t i n plus 0.1 gm Hag SOg per 100 ml. Temperature 25.2°C 0.2° Concentration i d t =Ej (a) 0.6187 mmolar 2.6lXamp 3.04 sec -1.095 volt 0.2061 " 0.65 " 2.70 n -1.098 " (a) E i vs. O.IH calomel electrode. The d i f f u s i o n current and drop time were measured by the method described i n the Sargent Manual of Instructions for the Polarograph. The temperature c o e f f i c i e n t 2.0$ per degree ( S^f ) w a s used to correct the measured value to the value at 25.0°C where necessary. In most cases the correction term i s n e g l i g i b l e . The maximum correction i s shown i n the following c a l c u l a t i o n . id measured at 25.3°C = 4.74>^/amp. id corrected = 4.74^amps. - 0.3 X:2 Z 4.74^amps 100 = 4.71 " at 25.00C. The h a l f wave pot e n t i a l f o r zinc i n O.U potassium chloride i s determined as - 1.095 volt versus O.IN calomel electrode. The value given in the l i t e r a t u r e i s - 1.084 volt ( CO). It i s seen that the h a l f wave potentials determined from the instrument settings agree with the value determined 57. within the l i m i t of error. On the other hand in the presence of s u l f i t e the Ei values calculated from the instrumental set-tings do not correspond to the determined values — 1.095 v o l t and 1.098 v o l t versus O.U. calomel electrode. The runs made with s u l f i t e present were duplicates, that i s run b was made immediately following run a. There i s a considerable degree of discordance among the r e s u l t s . The only consistency i s that the current decreased further during run b. The decrease of the d i f f u s i o n current upon the addition of s u l f i t e i s not s a t i s f a c t o r i l y explained. It was noted that the presence of oxygen also de-creased the d i f f u s i o n current for zinc. F i g . shows polaro-grams of 0.6187 mmolar zinc i n O.II potassium chloride with 0.0001$ g e l a t i n . F i g . ^ (a) was obtained with oxygen present. The pen t r a v e l before the zinc wave indicates the presence of a reducible substance. F i g . ^ ( b ) shows that the oxygen has been removed to i t s minimal concentration. Its presence i s not detectable. According to the electrode reaction of dissolved oxygen the d i f f u s i o n layer becomes basic and contains hydrogen peroxide. The conditions therefore favor the formation of zincate or zinc peroxide, most l i k e l y the former. The zinc complex i s not reducible except at a more negative p o t e n t i a l and, therefore, does not contribute to the d i f f u s i o n current at--1*095 volt half-wave p o t e n t i a l . It may be noticed that the t o t a l current i s approximately the same. Such behaviour could be expected on the basis that the amount of zinc removed by complex formation i s proportional to the concentration of oxygen. The disappearance of the zinc wave at a concentration FT 5 0 -CL-iJHum T/!«r.s O* O 1 / ^ A M P / A I M — 6 0 - - 1 5 0 d i -e t I C M R i j r ^ r . in. Q-1*131-* MOLAR : HEr^ATtD AFTER. 4. CURRENT 2 H » O U R l l f l i r -5, F i g u r e 8 P o l a r o g r a m s o f 0.6187 m i l l i m o l a r z i n o i n 0.1U p o t a s s i u m c h l o r i d e p l u s 0.0001% g e l a t i n . S e n s i t i v i t y 0.04/^amp/mm. Dr o p t i m e s (8a) E.84 s e c , (8b) 2.89 s e c . In F i g u r e 8a t h e p r e s e n c e o f d i s s o l v e d o x y g e n i s shown by pen t r a v e l p r e c e d i n g t h e c u r r e n t i n c r e a s e due t o t h e r e d u c t i o n o f z i n c . 8a 8b R e s i d u a l c u r r e n t p l u s o x y g e n o u r r e n t a t E§- 0.92/"amp 0.36/^amp Z i n c c u r r e n t a t E4- 4.44 " 4.88 " T o t a l o u r r e n t a t Bj. 5.36 " 5.24 " Figure 8C Polarogram of supernatant water layer from amalgam o e l l with added potassium chloride, A , compared with polarogram of O.lil potassium chloride,B, Both solutions swept out with nitrogen. S e n s i t i v i t y 0.003y^amp/mm without damping. Both polarograms are similar to polarograms of 0.0041 millimolar zinc i n 0.1U potassium chloride plus 0.0001$ g e l a t i n swept out with nitrogen. Voltage - 1.15 volt versus O.M calomel electrode read from instrument s e t t i n g s . 58. 0.0168 mmolar zinc i s believed due to the fac t that the oxygen remaining i n solution t i e d up most of the zinc i n complex formation. The polarograms of 0.0084 mmolar zinc resembled those of 0.0168 mmolar zinc i n that a reducible substance was indicated to be present by the pen t r a v e l during drop forma-t i o n . However, polarograms of 0.0041 mmolar zinc could not be distinguished from polarograms of O.IS potassium chloride alone. These l a t t e r were found to correspond to the polaro-grams of the supernatant water from the amalgam c e l l a f t e r a small amount of potassium chloride had been added for the polarographic a n a l y s i s . Thus i t i s evident that the super-natant water contained less than 0.0084 mmolar z i n c A plot of d i f f u s i o n current vs. concentration i s line a r i n the range of concentration 0.1040-0.6187 mmolar zi n c . The straight l i n e passes extremely close to the o r i g i n upon extrapolation, f i g . v*5 The d i f f u s i o n current constant and the apparent polarographic d i f f u s i o n c o e f f i c i e n t of zinc i n O.IS potassium chloride have been calculated by the Ilkovic equation Xj - L>oy^K D^- c /*n?z C - c ( i n ) The value so determined for 3 i has been substituted i n the second terms of the equations proposed by Lingane and loveridge, and Strehlow and Stackelberg and the value for D# i n the f i r s t term redetermined. The r e s u l t s are shown i n Table 11. Theoretically the 'D' values should corcespond to the value of the d i f f u s i o n c o e f f i c i e n t o f zinc at i n f i n i t e d i l u t i o n , 7.2 1 l'O"6 cm2 s e c " 1 (C /), 58(a) The calculations have been performed i n the manner suggested by lingane and Loveridge (8). These authors state that a knowledge of J) i s necessary for the p r a c t i o a l use of th e i r new equation. Late in t h i s work i t was realized that the equation i s a simple quadratic 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 fact i n t h e i r paper. The solution of the equation of Lingane and Loveridge i s , 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 following values calculated from these formulae may be compared with those shown i n Table 11. Ho. 3 4 5 6 7 Average 7.03 cm^ s e c - 1 6.78 6.85 6.75 6.57 6.79 n Tt tt ft J?s X 10 c 7.71 cma sec--*-7.32 7.51 7.40 7.26 7.44 n tt it tt it The values of J?t_ here are about 0.10 cm** se c " 1 higher than those shown i n Table 11. The values P$ are about 0.03 om2seo-l higher. It should have been stated that the general solution i s V/) 2 A >3 t 'L F i g u r e 9A Polarograms o f z i n c i n 0.1H 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 showing wave-h e i g h t versus c o n c e n t r a t i o n . S e n s i t i v i t y 0.04X'amp/mm. Compare polarogram o f 0.0168 m i l l i m o l a r z i n c with F i g u r e 8a. The presence o f oxygen i s not i n d i c a t e d here by pen t r a v e l as i n F i g u r e 8a. O-Ooo O./oo o.*-oo O.soo OMOO O'SOO a. coo 0 . 7 0 0 C O N C EN TRA T I O N A 7 / U t / M OJ-AR. r [•( 1 t.| [ I I i +j-r i | j | \\ \\ | i l l tttmf IOA A Figure IOA Polarogram o f 0.1040 millimolar zinc i n O.lfl potassium chloride plus 0.0001$ g e l a t i n swept out with nitrogen. S e n s i t i v i t y 0.006/^amp/mm. Dif f u s i o n current 0.83 , y amp. ff: ijiiilsi, /0B Figure 10B Polarogram run immediately aft e r that shown i n Figure IOA afte r addition of sodium s u l f i t e . Concentration 0.1040 millimolar zinc i n 0.1U potassium chloride plus 0.0001$ g e l a t i n plus 0.1 gm sodium s u l f i t e /lOO oc. S e n s i t i v i t y 0.006^" amp/mm. Diff 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 Coefficient of Zino in 0.113 Potassium Chloride No. Concentration I D X 106 3 0.6187 mmolar 3.51 8.34cm£ 4 n II 3.42 7.92 " 5 it n 3.46 8*12 " 6 n it 3.43 8.00 " 7 n it 3.38 7.76 " 8 0.3365 it 3.59 8.75 " 9 it 3.52 8.41 n 10 it 3.56 8.57 " 11 II it 3.54 8.51 " 12 0.2061 it 3.58 8.71 " 13 n it 3.68 9.16 n 14 tt n 3.61 8.87 " 15 0.1040 it 3.61 8.90 " 16 ii tt 3.61 8*86 " DiXlO 6 <aJ 1 D SX 106 (b) 6.92 'see - 1 7.68 cm ^ sec~ 6.61 tt 7.31 it 6.75 ft 7.48 tt 6.66 , n 7.37 n 6.47 rt 7.16 tt 7.25 tt 8.05 it 7.00 it 7.75 tt 7.13 tt 7.90 it 7.08 it 7.80 ft 7.19 ft 8*00 7.54 it 8.40 tt 7.33 it 8.14 tt 7.34 tt 8.15 it 7.32 n 8.13 n Average Values Concentration I D X 10 6 DiX 10 6(a) DsX 10 6lb) 0.6187 mmolar 3.44 8.03 cm 2see-l 6.68 cm^sec-1 7.40 cm £sec-l 0.3365 n 3.55 8.56 " 7.11 " 7.91 n 0.2061 " 3.62 8.91 " 7.35 " 8.18 " 0.1040 " 3.61 8.88 " 7.33 " 8.14 " (c)1.00 " 3.41 7.91 " (a) D-i from equation by Lingane and Loveridge (b) D g " n " Strehlow and Stackelberg (o) Values reported i n l i t e r a t u r e The values f o r D are seen to increase with decreasing concentration of zinc. Kolthoff and Lingane (£Z) mention that similar deviations have been reported for other metals. They themselves found no such behaviour when the work was repeated. However, t h e i r published data for lead i n O.IN potassium chloride shows some evidence of t h i s deviation. Suoh a deviation can be eas i l y explained, i n fact^such a deviation i s expected when the current i n the mercury drop i s considered; According to Strehlow and Stackelberg (Cj>), Antweiler has shown evidenoe of the current 60 . and resultant streaming of the drop surface when a dye and water are used at a dropping c a p i l l a r y . Consequently,,: such behaviour i s presumed to he ch a r a c t e r i s t i c of the dropping mercury. Under polarographic conditions i t may also be presumed that the current along the axis of the c a p i l l a r y i s constant for a given set of conditions of temperature, mercury head and back pressure. However, surface streaming would be governed by the surfaoe conditions. One of these conditions would be the concentration of the amalgam formed by reduction to a mercury soluble metal. Assuming that the surface streaming i s reduced by increasing ia concentration of amalgam then the ratio t?cF or the values for D would increase with inorease i n rate of streaming, that i s with decrease i n concentration of the reducible ion. Such id behaviour has been denied apparently because the ratio ~~C" has again decreased at very low concentrations. The nature of thiss decrease at very low concentrations could be explained by the effeot of the minimal oxygen concentration. The foregoing explanation appears v a l i d f o r the rather limited number of papers studied so f a r . On the other hand fthe phenomena i s d i r e c t l y related to the occurrence of current maxima which are s t i l l the subject of controversial papers ( ^ V ) * Further review of reported data should a s s i s t i n the esta b l i s h -ment of an adequate explanation. I f , as reported by Kolthoff and Lingane, the r e l a t i o n id (T~ i s s t r i c t l y l inear then t h i s work agrees with published data id to within 15$. I f the r a t i o 0 a c t u a l l y increases with decreas-ing concentration of zinc the agreement i s within 5$. The maximum deviation i s considered i n both cases. 61. It i s evident that the method does not produce gross deviations and for t h i s reason i t is assumed that the same order of accuracy can he obtained i n amalgam polarography. Provided, of course, that i t can be shown that a dropping amalgam has the same dropping c h a r a c t e r i s t i c s as pure mercury. According to English the properties mentioned do agree over the range of p o t e n t i a l necessary f o r polarographic measurements. 62. II - Amalgam Polarography. A few tests were made to show that the d i l u t e amalgam behaved s i m i l a r l y to mercury at the dropping c a p i l l a r y and that the s t a b i l i z i n g c i r c u i t had no effeot on the recorded polarograms. The data from these tests i s given i n Tables 12 - 14. TABLE 12 The Rate of Amalgam Plowing from the Cap i l l a r y into Various Media Amalgam: 0.0148 gm Zn i n 791.9 gm Hg S t a b i l i z i n g c i r c u i t closed. Uo. Media Time Amalgam Collected 'm' 1 A i r 162.2 seo 287.7 mgm 1.774 mgm/sec 2 n 161.1 n 284.9 rt 1.768 n 3 Water 113.2 rt 200.9 it 1.775 rt 4 tt 113.2 rt 201.1 tl 1.777 it 5 Sat KCL 107.7 tt 191.4 tl 1.777 rt 6 n tt 107.5 n 190.6 n 1.773 it 7 A i r 174.0 it 306.8 rt 1.763 rt 8 166.2 rt 290.8 it 1.750 it 9 Sat KCL Zn 01o 108.9 it 191.2 rt 1.756 rt 10 n n tt C 128.4 tt 224.8 it 1.751 it 11 Sat KH0*Zn(]S0,z)p(a) 124.3 n 216.0 n 1.738 tt 12 119.0 ti 207.5 it 1.744 it 13 A i r 68.4 it 12022 it 1.757 tt 14 ti 159.0 rt 275.4 tt 1.732 it (a) Swept out with I 2 for 15 minutes. The successive values for 'm' determined for a i r show the effect of the decreasing amalgam head - about 2 mm during the t e s t . Comparison with a similar table for the rate of mercury flow( ^) i s strong evidence that the rate of amalgam flow i s independant of the media i n which the drops form. The determination of 'm' at the c a p i l l a r y electrode i s shown i n Table 13. 63. TABLE 13 The Bate of Amalgam Flowing from the C a p i l l a r y Electrode Amalgam 0.0042 gm Zn in 1457.7 gm Hg. S t a b i l i z i n g c i r c u i t closed Group Media Applied Voltage Time Amalgam Air 173.5sec 175.2 * 301.6 i f 303.1 IT O.U KCL -0.45 v 176.8 " 297.4 If n IT n 178.7 299.6 2 A i r n i l 179.8 ri 306.3 i t it 178.4 " 303.9 IT O.Iin KCL -0.22 179.3 " 301.9 11 If IT i t 179.4 '* 304.1 IT ff IT -0.60 177.2 " 301.9 IT ff It it 177.0 " 301.5 lgm 1.738mgm /se ^ 1.730 " 1.682 " 1.677 " 1.704 " it 1.704 n 1.684 " 1.695 " 1.704 it 1.703 " Here the data i s not extensive enough to warrant any conclusions with respect to the v a r i a t i o n of 'm' with the p o t e n t i a l of the dropping electrode. However, i t i s seen that the value for 'm1 determined i n a i r may be used i n the c a l c u l a t i o n s since the v a r i a t i o n appears to be about -t 3%, The value of 'm' should be determined i n the e l e c t r o l y t e at the appropriate potential of the dropping electrode. In the case of amalgam the d i s s o l -ution o f the amalgam i t s e l f i s an a d d i t i o n a l complication to the v a r i a t i o n of 'm' with p o t e n t i a l . The effect of the s t a b i l i z i n g c i r c u i t was tested by determining the drop time with the c i r c u i t open and closed. The drop time i s a function of surface tension which i n turn i s a function of 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 . If the s t a b i l i -zing c i r c u i t had any effect there should be some deviation of the drop times on open and closed c i r c u i t . The data i s recorded i n Table 14. 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 Closed. Amalgam 0.0148 gm 2n in 791.9 gm Hg.Electrolyte IE KCL. S t a b i l i z i n g c i r c u i t 10 vo l t s applied. Drop Time Dropping Electrode S t a b i l i z i n g C i r c u i t S t a b i l i z i n g C i r c u i t P o tential (a) Open Closed  0.00 v o l t s 5.98 seo 5.98 sec " " 5.98 " " n 5.99 " 6.01 *' " " 5.99 " -0.40 " 6.08 " 6.08 " -1.60 n 4.84 " 4.21 n n ti 4 > 2 2 r, " " 4.25 " 4.24 " " " 4.24 n (a) Applied p o t e n t i a l reading across dropping electrode and external S.C.E. The drop times on open and closed c i r c u i t are seen to coincide within the l i m i t of determination. A more extended range of poten t i a l vs drop time deter-minations i s shown i n Pig. /I . In the po s i t i v e voltage range and at potentials more negative - 1.80 volt s vs. S.C.E.the drop time was highly e r r a t i c . A polarogram obtained manually i s also shown i n P i g . / / . It i s seen that the i n f l e c t i o n i n the drop time versus potential curve coincides with the i n f l e c t i o n i n the current-voltage curve. In both cases oxygen was present i n the s o l u t i o n . By breaking and closing the s t a b i l i z i n g c i r c u i t during a polarographic run i t was found that the effeot 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 setting 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 quantity compared to a total d i f f u s i o n current of r mm H i : 1 1 Figure 12 Recordings of d i f f u s i o n current of 0.000288$ zinc amalgam at constant E . f l l.f, values. The s t a b i l i z i n g o i r c u i t was opened and closed to determine effeot on instrument reading. S e n s i t i v i t y 0.06>^amp/mm. At 0.600 volt applied E.M.F. the current i s deoreased 0.06yVamps when the s t a b i l i z i n g c i r c u i t i s closed. Total current 6.45/^amps. This i s the maximum deviation shown by several t e s t s . In most cases the deviation was indeterminate. 65. the order of even O.iy^amp. In the working range of s e n s i t i v i t y settings with damping no deviation of the d i f f u s i o n current 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. (Pig. )Z~). The breaking of the c i r c u i t , however, does cause an immediate defl e c t i o n of the recording pen which then d r i f t s back to the o r i g i n a l value. To sum up, the data so far indicates that dropping amalgam eleotrodes behave s i m i l a r l y to dropping mercury elec-trodes 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 appreciable effect on the recording c i r c u i t nor on the ca p i l l a r y c h a r a c t e r i s t i c s . In short, the conditions are such that accuracy of the same order obtained i n ordinary polarography could be expected i n amalgam polarography. By adding increments of g e l a t i n solution and compar-ing the polarograms i t was found that a concentration of about 0.005% was optimum for amalgam polarography. For d i f f e r e n t amalgam concentrations and di f f e r e n t c a p i l l a r y c h a r a c t e r i s t i c s i t i s possible that the optimum g e l a t i n concentration may vary. Polarograms of 0.0003% zinc amalgam are shown i n Pigs. /3 , A f . Pig. 12> i s a polarogram obtained before the addition of g e l a t i n . The maxima i s seen to be very considerable. Pig. Jljls a polarogram a f t e r the addition of g e l a t i n . The data obtained for t h i s amalgam i s recorded 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 potassium c h l o r i d e swept out wit h n i t r o g e n . S e n s i t i v i t y 0.06/^/amp/mm. D i f f u s i o n c u r r e n t 11.Stamps. The r a p i d decrease i n ourrent s t a r t i n g a t 50% span, may he due to a ohange i n drop time. The dropping e l e c t r o d e was almost streaming from 70% span to end o f run. For t h i s reason i t i s d i f f i c u l t to determine whether o r not a maxima e x i s t s . w r A 1 Art* 8. - to % -y» *PAH -tob-J Figure 14 Polarogram of 0.000288$ zino amalgam i n 0.1N potassium chloride plus 0.005$ g e l a t i n swept out with nitrogen. S e n s i t i v i t y 0.06^amp/mm Dif f u s i o n current 5.5>7amp. The addition of g e l a t i n has a marked effeot on the ourrent oompare with Figure '-^  r y iinin.i. . ••.•TTTT till: -4 F i g u r e 15 P o l a r o g r a m o f 0.000288% z i n c amalgam i n 0.1H p o t a s s i u m c h l o r i d e p l u s 0.005% g e l a t i n w i t h o x y g e n p r e s e n t i n s o l u t i o n . T h e r e i s no c l e a r d i s t i n c t i o n b e t w e e n t h e o u r r e n t due t o r e d u c t i o n o f o x y g e n o r h y d r o g e n p e r o x i d e and t h e c u r r e n t due t o o x i d a t i o n o f t h e z i n c i n amalgam, 5 M M , L I N E S A C C E N T E D , C M . L I N E S H E A V Y H A D E I N C A N A D A 66. TABLE 15 Polarographic Characteristics of Zinc Amalgam (1) Recorded with Sargent Polarograph Amalgam: 0.0042 gm Zn i n 1457.7 gm Hg a E l e c t r o l y t e : O.IN KCL 0.005$ g e l a t i n . Date Ho. Di f f u s i o n Current Droptime Meroury Outflow June 5 1 5.37^/amp 2.64 sec. 1.750 mgm/sec. " 6 2 5.55 n 4.12 " 1.734 " 6 3 5.64 " 4.12 " 1.734 " 7 4 4.88 ** 2.03 " 1.703 " " 7 5 4.98 " 2.42 " 1.703 " (a) The concentration of zinc i s calculated from the molecular weight of zinc, 65.38, and the density of mercury at 25.00°C, 13.53 gm/cm3, to he 0.5963 millimolar on the assumption that the zinc lost i n making up the amalgam was n e g l i g i b l e . Polaro-grams of the supernatant water layer could not be distinguished from polarograms of d i s t i l l e d water ( F i g . ^ c ). TABLE 15 * v i (2) Manually Recorded. Date Ho. D i f f u s i o n Current Droptime Mercury Outflow June 7 6 5.23>famp 2.75 5 £ " ^ 1.703 mgm/seo " 7 5.27 " 2.75 " 1.703 Due to d i s t o r t i o n of the wave where the current i n -creases rapidly the measurement of the d i f f u s i o n current was not made i n the same manner as i n ordinary polarography. Instead the v e r t i c a l distance between the average current-at a point before and following the current increase was taken as a measure of the d i f f u s i o n current. Provided the same r e l a t i v e points are chosen on dif f e r e n t polarograms the values are as consistent as those determined at the half-wave p o t e n t i a l . The resultant values, however, are s l i g h t l y larger than those taken at the half-wave p o t e n t i a l . The difference i n values i s less than 5% i f the v a r i a t i o n of 'm' and ' t 1 i s neglected. A comparison may be made with the values shown i n Table 15 which gives the data obtained by the method used i n ordinary polarography. These re-sul t s were obtained from polarograms where d i s t o r t i o n of the -wave form did not interfere with an accurate determination of the half-wave p o t e n t i a l . It i s seen that the two methods of measurement give r e s u l t s which vary by zfo-5%. However, when 'm' and ' t ' are also measured at the p o t e n t i a l of the current measurements, the re s u l t s by either method should agree within 2%. TABLE 16 Polarographic Characteristics of Zinc Amalgam Mo. D i f f u s i o n Current(a)Ej Droptime Mercury Outflow 2 5.46-^amp 1.070 volt 4.12 sec 1*750 mgm/sec 6 5.13 " (b) 1.072 " 2.75 " 1.703 " 7 5.06 " (b) 1*068 " 2.75 n 1.703 " (a) measured by method described i n "Sargent Manual o f Instruc-tions for the Polarograph". (b) note order of difference from Table 14. It i s noted that the order of difference for the d i f -fusion currents of No.6 and 7 i s opposite i n Table 16. This result has been shown to i l l u s t r a t e that the measurement i t s e l f may be somewhat i n error. Unless the polarogram has an id e a l form there i s a ce r t a i n amount of choice i n the extrapolation of the average current as determined from the midpoint of the pen t r a v e l during the formation of each drop. Since i t has been shown that the drop time varies considerably (Pig. I' ) over short p o t e n t i a l ranges there i s l i t t l e l i k e l i h o o d of obtaining an ideal polarogram. This fact i s evidence that the method for 68 measuring the d i f f u s i o n currents as given i n the book of instruc-t s T tions has-been chosen for s t r i c t accuracy. Actually, measuring the current at potentials preceding and following the wave as well as 'm' and ' t ' at the same potentials and cal c u l a t i n g the value of the residual current by the Ilkovic equation appears to o f f e r a more accurate method for the determination of the d i f f u s i o n current. Before using the values shown i n Table 15 for calcula-tions i t should be shown that the conditions under which the d i f f u s i o n current equations can be applied have not been violated to a degree greater than expected. F i r s t l y , a rough approxima-d t i o n of the order of r, where d i s the d i f f u s i o n layer and r i s the radius of the amalgam drop, may be obtained. From Table 14, Ho. 1, id = 5.37^amp, t = 2.64 s e c , m = 1.750mgm sec"-1- where the amalgam i s 0.5963 millimolar zinc. From t h i s data i s ob-tained the number of moles reacting i n a f i n i t e period, 5.37Xamp. X 2.64 sec =  2 equivalents/mole X 96500 coulombs/equivalent = 7.52 X 10" 1 1 moles. and the number of moles of zinc contained i n the drop* 1.750 mgm/seo X 2.64 sec x _ i Y 0.5953 13530 mgm/cms 1000 cm5/ * 1000 molar = 20.4 X 1 0 - H moles. That i s approximately one t h i r d of the amalgam i n each drop reacts electro chemically. Thus i t i s shown that there i s no gross discrepancy. Assume that the reacting zinc i s contained i n a layer d 0 at the outer surface of the drop from whioh - } — \J - O • / 3 The volume of the drop can be calculated from the value of 'm' and thus the value of 'd ' may be found d 0 = 0.13 \ 3/ 3 , 1 . 7 5 0 mgm/sec X 2.64 sec V 4 rf 13.53 mgm/mm3 — 0.055 mm and r = 0*43 mm This value for d Q agrees with the value for the thickness of the d i f f u s i o n layer around the mercury drop i n ordinary i i polarography. It i s not shown that the ra t i o . r does not equal 1. The d i f f u s i o n current constant ' I ' has been calcu-lated to show the order of pr e c i s i o n . The values of I are shown i n Table 17. TABLE 17 The D i f f u s i o n Current Constant for Zinc Amalgam id  Ho. I = cm 2 t 1 3 6 1 5.28 2 5.09 3 5.17 4 5.10 5 5.06 6 5.20 7 5.24 Average value 5.16 ±- O.OjJ The v a r i a t i o n between extreme values i s less than bfo which is s l i g h t l y greater than the v a r i a t i o n between the extreme values for I for the 0.6187 millimolar zinc solution where the extremes 1. See Ref.5, p.144 70. vary by less than 4$. In order to show the accuracy of the method i t is necessary to know the value of the d i f f u s i o n c o e f f i c i e n t of zinc i n mercury. However, the values reported i n the l i t e r a -ture (see Table 5) show considerable v a r i a t i o n . From Wogan's and Schwarz values temperature increments 0.0096 em^  s e c - 1 deg." 1 and 0.013 cm2 s e c " l degT 1 are calculated. The tem-perature increments are such that a temperature c o e f f i c i e n t 0.01 would not introduce any gross error i n determining the value of the d i f f u s i o n c o e f f i c i e n t at 25.00°C from the tabled values. The resultant values are shown i n Table 18 TABLE 18 The Diffu s i o n Coefficient of Zinc i n Mercury at 25.00°C Investigator Reported Value Value Calculated for 25.0QQC 0. Meyer 150C-2.42 Z 10-bcm«sec--L 2.52 X 10-°cm«sec-l Wogan 11.50C-2.52Z 10-5 « 2.65 X 10-5 » Schwarz 25OC-2.00 X 10" 5 " 2.00 Z 10-5 » Mean Value 2.39 Z 10-5 « According to the findings of Strehlow and Stackelberg streaming at the amalgam surface results i n large deviations from calculated values for d i f f e r e n t values of 'm' and ' t 1 . However, they found that a plot of I vs. y, where produced curves which were asymptotic to a straight l i n e . From the intercept of the l i n e they determined the value of the d i f -fusion c o e f f i c i e n t of oadmium in mercury since From the slope of the l i n e they calculated the value of B to be 28.5. This value is i n agreement with the t h e o r e t i c a l approximation that the value of 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 of zinc i n mercury i s 3.4 X 10"^ cm 2sec - 1 the value of the numerical constant 'B' may be calculated d i r e c t l y . The values are shown i n Table 19 TABLE 19 Approximation o f the numerical Constant 'B' in the Strehlow-Stackelberg Equation for the Diffusio n Current of a Dropping Amalgam Electrode Ho. B 1 19.4 2 83.1 3 80.9 4 85.4 5 26.0 6 26.0 7 24.7 Average 23.6 Since the values for B l i e within the range of t h e o r e t i c a l approximation i t is assumed that the surface streaming o f the amalgam drop was no more serious than that at the mercury drop i n regular polarography. According to the calculations shown i n Table 11 the di f f u s i o n current equation aft e r Lingane and Loveridge gave values of 'D' best i n agreement with D 0, the d i f f u s i o n c o e f f i c i e n t of zinc at i n f i n i t e d i l u t i o n . For amalgam polaro-graphy the equation merely requires a change of sign i n the second term thus f / The value for D may be determined i n the manner used previously. The r e s u l t s are shown i n Table 80 71(a) After completion of t h i s work i t was r e a l i z e d that the new equations for the d i f f u s i o n current were simple quadratics with D"§" as the unknown quantity. Prom the lingane-Ioveridge equation \f~f)~ - / — ]f~^ ~ O • }Z it^ru The values of D computed by t h i s formula are given i n Table 21. TABLE 21. The Apparent Polarographic Diffusion Coefficient of Zinc i n Mercury at 25°C. Ho . D X 10-5 1 3.01 cma s e c " 1 2 1.59 " 3 1.65 n 4 2.69 " 5 2.68 " 6 2.93 " 7 2.99 " There i s considerably more discordance among these values than x among those shown i n Table 20. Here the term t L occurs i n the denominator only and consequently has a larger influence. However, the value of 'm' was not determined i n the solution as i t should be. Actually t and m should be determined simultan-eously for accuracy. The solution of the quadratic i s the most acceptable method for determining the value of the d i f f u s i o n c o e f f i c i e n t . The method also provides a better indication of the precision obtained. In view of the discordance among the values shown i n Table 21 i t i s evident that further work under c a r e f u l l y con-t r o l l e d conditions i s necessary to establish h the technique used in t h i s work. 72 TABLE 20 The Apparent Polarographic D i f f u s i o n Coefficient of Zinc i n Mercury at 25°C. lo _ I _ D X 10 5 V% X 10 5(a) 1 5.28 1.89 cm 2seo - i 2.70 om^sec 2 5.09 1.76 " 2.56 " 3 5.17 1.81 " 2.66 n 4 5.10 1.77 " 2.47 " 5 5.06 1.74 " 2.45 6 5.20 1.83 " 2.63 " 7 5.24 1.86 " 2.68 Average 5.16 1.81 " 2.58 (a) D^ from lingane-Ioveridge equation, n Do The mean value i s agreement with the values reported by Wogan and Meyer rather than the value reported by Schwarz. It i s d i f f i c u l t to draw any conclusions with respect to the accuracy of these results since the avail a b l e values reported i n the l i t e r a t u r e vary by an amount greater than the experimental error involved. Further, i t i s only assumed that the experimental error i n amalgam polarography i s of the same order as that found i n ordinary polarography. Unfortunately, time did not allow further experimentation under the conditions required to establish the techniques It has been shown that a d i l u t e amalgam can be s t a b i l i z e d for polarographic measurements. The amalgam used to obtain the data shown i n Tables 14 and 15 was used from June 4-7, 1950, or over a period of 85 hours. Polarograms obtained i n the f i r s t hour were approximately duplicated in the l a s t hour. Due to a decrease i n the height of the mercury column small differences were observed. The differences, however, were of the same order as the variations shown i n Table 14. This amalgam was made up 0.000288$ Zn. Heyrovsky and Kalousek (f0)) found that amalgams less than 0.005$ were too unstable for use. Strehlow and Stackelberg have obtained measurements which are i n better agreement for duplicate deter-minations than have been obtained in t h i s work. They used 13.93 millimolar cadmium amalgam or 0.01157$ Cd. Their method of preparing the amalgam has not been given and presumably i t was not protected from the atmosphere since no special technique i s mentioned. Unfortunately, th e i r tabled results (L C) do not show the time that each measurement or each group of measurements was made. That i s they have not shown that the concentration of the amalgam remained constant. Therefore the deviation of I vs y could be due i n part to a decrease i n concentration. Early i n th i s work an amalgam 0.000127$ Zn gave more or less consistent results at the beginning and end of a 120 hour period.March 4-9, 1950. At that time, however, con-siderable trouble was experienced with the c a p i l l a r y becoming clogged thus causing highly e r r a t i c drop times which varied from a drop time of 14 seconds to constant streaming under the same conditions at d i f f e r e n t times. This clogging has since been presumed due to the presence of zinc oxide which resulted from the int e r a c t i o n of zinc i n amalgam with oxygen which re-mained adsorbed on the glass walls of the electrode assembly. According to the manufacturers, the Sargent Polaro-graph Model XXII i s accurate to 0.1$ when the temperature i s controlled 25.00°C£0.05° at the polarographic c e l l and room temperature i s 25°C±10. It i s suggested that temperature control be extended to include the entire apparatus, recorder, dropping electrode assembly, polarographic c e l l and potentiometer. 74. The meroury column should he controlled to ±. 0.5 mm by a convenient marker and a screw device to raise or lower the mercury reservoir. It i s e s s e n t i a l that the mercury column i s not subject to v i b r a t i o n . In order to control the mercury c o l -umn 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 consistent results the external electrode appears to be better than the int e r n a l anode pool. 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 free. There i s no doubt that traces of oxygen seriously i n t e r f e r e with the determination of the d i f f u s i o n current at low concentrations. The measurement of the d i f f u s i o n current i s perhaps more convenient by the method described. However, i t is believed that accuracy can be best obtained by measuring the current at d e f i n i t e potentials before and a f t e r the half-wave p o t e n t i a l . Meroury i s collected at the same poten t i a l to determine 'm* while ' t ' may be determined from pen t r a v e l on the recorded chart. Then 'm' and ' t ' are determined again at the half-wave p o t e n t i a l . The current measurements are then calculated to refer to the values of 'm' and ' t ' at the half-wave p o t e n t i a l . The variance among duplicate determinations with standard zinc solutions i n t h i s work i s within the l i m i t s of experimental error reported by others (p.51). However, i t must be obvious that there was considerable l a t i t u d e i n the exercise of control. In amalgam polarography there are other factors which must also be considered. F i r s t l y , the amalgam must be s t a b i l i z e d as described herein, lo other method was found to prevent the formation of a surface f i l m and consequent decrease i n concen-75 t r a t i o n . The amalgam reservoir and dropping c a p i l l a r y must be clean and free of adsorbed oxygen. Prolonged sweeping with p u r i f i e d nitrogen or hydrogen appears necessary. The po s s i b i -l i t y of interaction of the amalgam with glass appears n e g l i g i b l e , although over a long period of time some effect may occur. This p o s s i b i l i t y i s suggested by the filmy appearance of o r i g i n a l l y clear glass a f t e r impure mercury has been stored for some time. This f i l m i s permanent. In preliminary work, filming was ob-served aft e r an amalgam had stood for several hours with the s t a b i l i z i n g c i r c u i t applied. The filming was p a r t l y removed by increasing the s t a b i l i z i n g voltage. However, the amalgam -glass interface appeared to become wetted further from the amalgam - water interface with increasing p o t e n t i a l . Care must be exercised to prevent wetting at the c a p i l l a r y . Under 10 vo l t s s t a b i l i z i n g E.M.F. the wetting extended about 1-3 cm from the amalgam - water interface. Under 25 vol t s E.M.F. the wetting extended 8-10 cm. The filming observed in these i n s t -ances was easily removed by dilute n i t r i c acid - dif f e r e n t from the filming mentioned previously. It was observed that at low pressures of mercury there was no flowing from the c a p i l l a r y . Upon increasing the mercury column the mercury thread moved slowly along the bore and f i n a l l y began dropping. This suggests that the amalgam T K AT-can be made up i n apparatus resembling the=&© shown i n Fi g s . IJ . The apparatus i s swept out with nitrogen. Nitrogen pressure i s maintained at the c a p i l l a r y while a weighed amount of mercury is run into the reservoir. The approximate amount being prev-iously determined by experiment. . The water layer i s formed and Applied Pressure I AMALGAM RESERVOIR Dropping Ca p i l l a r y Nitrogen Pressure Figure / 7 Dropping Electrode for Amalgam Polarography 76. a weighed sample of the solute metal added. While the metal i s dissolving under the influence of the applied s t a b i l i z i n g poten-t i a l an occasional bubble of nitrogen i s forced into the reservoir to ensure a homogeneous amalgam. When ready for polarography the nitrogen pressure can be removed from the c a p i l l a r y and pressure applied to force the amalgam through the c a p i l l a r y . The pressure can be maintained constant by means of a manometer with due consideration to the v a r i a t i o n of the mercury pressure. Other methods for handling the amalgam present d i f f i c u l t i e s . In the siphon method described 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 (21) appears f e a s i b l e except for the uncertainty as to whether the mercury o r i g i n a l l y i n the siphon becomes homo-geneous with the larger body of amalgam. Here too the p o s s i b i l i t y of entrapping gas bubbles i n the dropping electrode column appears rather large. In order to prevent wetting by the overlay of water or entrainment of gas bubbles by the amalgam column rather elaborate apparatus appears to be required. However, from experience gained in t h i s work the simple apparatus shown i n Pigs / °7 , supplies the requirements. 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 wetting at the;,amalgam-glass interface extends to the c a p i l l a r y . As mentioned by Heyrovsky and Kalousek ( '?) and con-firmed i n th i s work,the anodic current of an amalgam i s much greater than the cathodic current of a metal s a l t i n solution by polarographic measurement. In t h i s work i t i s shown, but not 77 confirmed that quantitative measurements are possible. For a n a l y t i c a l work with a known weight of mercury in the reservoir a supernatant solution may be subjected to controlled p o t e n t i a l ^ ? ) e l e c t r o l y s i s followed by polarography of the amalgam. The solution oan then be recovered and by a similar procedure another amalgam could be determined. The method could be useful . for determining traces of ions which reduce to mercury soluble metals i n the presence of large amounts of materials which do not. The application of amalgam polarography to p r a c t i c a l analysis, however, must await establishment of the teohnique and also systematic investigation of the interactions of the mercury soluble metals. 78 III - Summary of Results Polarograms of standard zinc i n 0.1U potassium chloride plus 0.0001% g e l a t i n were reoorded i n the manner proposed for amalgam polarography. The straight l i n e plot of d i f f u s i o n current versus concentration over the concentration range 0.6187-0.1040 millimolar zinc passes very close to the o r i g i n . The d i f f u s i o n current constant was found to increase with d ec r easing "-'e<5nc ent rat ion. Concentration 1= D i f f u s i o n ourrent constant 0.6187 millimolar 3.44 0.3365 " 3.55 0.2061 " 3.62 0.1040 " 3.61 The value reported in the l i t e r a t u r e for l m i l l i m o l a r zinc i n O.IK potassium chloride plus 0.005% methyl red i s 3.42. Since the v a r i a t i o n of I with concentration appears to he controversial the agreement i s considered s a t i s f a c t o r y . When oxygen was present the d i f f u s i o n current for zinc was decreased although the t o t a l current was the same af t e r oxygen was removed. This effect is explained by the removal of zinc by p r e c i p i t a t i o n or complex formation i n the d i f f u s i o n layer with the hydroxyl or peroxide products of the oxygen electro reduction. The t o t a l current i s not affected since the amount of zinc removed i s electrochemically equivalent to the amount of oxygen reduced to hydroxyl. Since a nitrogen sweep only reduces the concentration of oxygen to a minimal value there could be some considerable effect on the development of the zinc wave at very low concen-79 trations of zinc. In t h i s work 0.0168 millimolar zinc f a i l e d to develop a wave form. 0.0042 millimolar zinc solutions gave polarograms which could not be distinguished from polarograms obtained with 0.11 potassium chloride alone. Further i n v e s t i -gation i s required at these extremely low concentrations. potassium chloride was computed from the equations for the d i f -fusion current as given by Ilkovic, lingane and Loveridge, and Strehlow and Stackelberg. Theoretically the value i s that of the d i f f u s i o n c o e f f i c i e n t of zinc at i n f i n i t e d i l u t i o n , D0= 7.2 X l O - 6 cm2 s e c " 1 . The Ilkovio equation gave values for D within 28%, that of Lingane and Loveridge within 12$ and that of Strehlow and Stackelberg within 17$. The deviations are of approximately the same degree as reported i n the l i t e r a t u r e . ledge of the value of D i s not e n t i r e l y essential to the use of the i r new equation. The equation i s a simple quadratic and the where A = the numerical constant i n the correction term. The values computed from t h i s formula were 0.4$ - 2.5$ larger than the values computed by the method suggested by the authors mentioned. recorded data reported i n the l i t e r a t u r e even when the most controversial points were allowed. Some in d i v i d u a l results were in complete agreement. The agreement i s used as evidence that the method proposed for amalgam polarography i s equally s a t i s f a c t o r y The apparent d i f f u s i o n c o e f f i c i e n t of zinc in 0.1N Contrary to Lingane and Loveridge' statement a know-solution i s The results were found to agree within 15$ of previously 80 Within the limits of determination^very dilute zinc amalgams were found to behave like pure mercury in their dropping characteristics. The amalgam stabilizing circuit is shown to have no effect on the droptime or recording apparatus which will 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 in 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 in 0.1K potassium chloride plus 0.005% gelatin were recorded. The diffusion current constant,according to the Ilkovic equation is 5.16 ±0.07 at 25°C. Assuming that the diffusion coefficient of zinc in mercury -5 2 -1 is 2.4 X 10 cm sec , the values of B, the numerical constant in 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 is 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. in -5 2 -1 excellent agreement with the values reported by Wogan,2.52 X 10 cm sec o - 5 2 - I 0 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. 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 is 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 in 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.Ilkovic, 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.Kolthoff and J.J.Lingane, "Polarography", Intersoienee Publishers Inc., New York (1946). (6) J.J.Lingane and I.M.Kolthoff, Chem.Rev.1-94 (1939). (7) OiH.Muller, "The Polarographic Method of Analysis", Mack Pr i n t i n g Co. (1941). (8) J.J.Lingane and B.A.Loveridge, J.A.C.S., 72, 438 (1950) (9) H.Strehlow and M.von Stackelberg, Z. Elektrochem., 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 Stackelberg, Z.Elektrochem., 45, 466 (1939). (15) G.S.Smith, Mature, 163, 290 (1949). (16) Ref. 9, p. 56. (17) M.von Stackelberg and H.von Freyhold, 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, Discussions of the Faraday Society, 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. Acta Chim., 1, 18 - 27 (1947). S3 (23) F.L.English, Anal. Ohem., 20, 889 (1948). (24) J.W.Mellor, "A Comprehensive Treatise on Inorganic ana Theoretical Chemistry", Vol.IV,ppl037 - 1048 langmans Green, London (1923). (25) Hulett and DeLury, J.A.C.S., 30, 1805 (1908). (26) Hulett and Crenshaw, J . Phys.Chem., 14, 175 (1910) (Hot available i n U.B.C.Library) (27) T.W.Richards and G.S.Forbes, Pub. Carnegie Inst., l o . 56 (1906) (Q G 156 R 52) (28) J.H.Hildebrand, J.A.C.S., 35 501 (1913). (29) Pierce and Eversole,J.Phys.Chem., 32, 209-220 (1928). (30) J.L.Crenshaw, J.Phys.Chem., 34, 863 (1930). (31) H.A.liebhafsky, J.A.O.S., 57,2657 (1935). (32) W.G.Horsch, i b i d , 41, 1791 (1919). (33) H.A.liebhafsky, i b i d , 59, 452 (1937). (34) Scatchard and Teft, i b i d , 52, 2280 (1930). (35) Getman, J. Phys. Chem. 35, 2755 (1931). (36) Shrowder, Gowperthwaite and LeMer, J.A.C.S., 56, 2348 (1934). (37) Cohen, Z. Physik Chem., 34, 612 (1900). (38) Puschin, Z. anorg.Chem., 63, 230 (1903). (39) Clayton and Vosburgh, J.A.C.S., 58, 2093 (1936). (see also Garner,Gran and Yost,ibid,57,2056 (1935) (40) J.H.Hildebrand, Trans.Electrochem.Soc., 22, 335 (1913) (41) Lewis, J.A.C.S., 37, 2656 (1915). (42) G.Mayr, Chem. Abs., 14, 2578 (1920). Huova oimento 19, 116 (1918). (43) F.Skaupy, Chem.Abs., 15, 978-3 (1921). Physik Z., 21, 597 (1920). (44) K.Schwarz, Chem.Abs., 27, 3382-9 (1933) Z. Elektrochem., 39, 550 (1933). (45) C.Wagner, Chem.Abs., 26, 2097 (1932) Z. physik. Chem., B 15, 347 (1932). (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 . Lincei Classe s c i . f i s . mat.e nat., 1, 786 (1946). 2, 58 (1947). 2, 627 (1947). (48) G. Meyer, Chem. Abs., 6, 446 (1912) Ber. physik Geo., 793 (1911 (see Physik Z. 12, 975 - Q C p.51). (49) International C r i t i c a l Tables. I I , 591, Mc'Graw H i l l , New York (1933) (50) Landolt Barnstein p. 136 (51) G.Meyer Ann. Phys. Chem., 61, 225-34 (1897). (52) Smithsonian Physical 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) Isvest. Akad. Hack S.SiSiRi Odtel Tekh.Nank,1947,1649 (54) Squires' Companion to the B r i t i s h Pharmacopoeia, XIX Ed., 702, J . & A. Churchill,London (1916) (55) J . J . Lingane, Anal.Chem., 21, 47 (1949) (56) L. Meites and T. Meites, 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) Ref.9, Table 4, p.59. (67) J.J.Lingane, Discussions of the Paraday Society, 1, 203-212 (1947). 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 electrode aoquires i n a mixture of a reducing agent (denoted "red") and an oxidizing agent (denoted "oxy") a p o t e n t i a l , TV , which i s that o f a reversible "redox" electrode and i s thus given as Aooording to the nature of the reducing or ox i d i z i n g agent and the phase i n which they are placed, we may distinguish three t y p i c a l cases 0. 1. the agent "oxy" (i.e.the higher stage of oxidation) consists of kations i n the solution around the dropping mercury kathode, which on th e i r electro-deposition form an amalgam f u r n i -shing thus the agent "red" (i.e.the lower stage of oxidation). 2. the agent "oxy" i s a compound of oxidizing proper-t i e s ( l i k e a t i t a n i c s a l t or quinone), which i s placed i n the solution around the dropping mercury kathode and gets reduced there to a reducing agent (i.e.the titanous s a l t or hydroquinone), y i e l d i n g thus the agent "red". The same po t e n t i a l i s reached, however, when the reduc-ing agent (e.g.a titanous s a l t or hydroquinone) i s oxidized at the dropping mercury anode to the oxidizing agent (i.e.the 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 reducing agent of case 1. may be oxidized, i f i n the dropping eleotrode an amalgam i s used instead of pure mercury and the eleotrode i s made the anode, sending the ions of the base metal dissolved i n mercury into the solution. These ions then furnish the sub-stanoe "oxy". °) A communication published i n "Chemicke L i s t y " 35,p.47-50 (1940), to the occasion of the 60th birthday of Professor J . Milbauer. I I . She redox system 1, i s realized i n the electrodepo-sI1;ion of kations at the dropping mercury kathode, about which many studies are published* To the redox system 2. be-long the reversible polargraphio reductions and oxidations i n the solution, such as are described by H.O.Muller and J.P. Baumberger, 1) 2) E. Kodicek and K.Wenig,3) R.Strubl, 4) M.Spalenka 5) and K.Schwarz, 6). The case 3.has not yet been treated f u l l y : an account of i t has been given 0) by one of the present authors 7) and a note was published by J.J.lingane 8) i n 1939. The experimental work here described was, however, started i n 1937. Before going into the experimental d e t a i l s and the discussion of the r e s u l t s , l e t us deduce an equation of the ourrent-voltage curve obtained with the dropping eleotrode i n oase 3, vi:z. when using instead of pure mercury an amalgam. This oase i s closely a l l i e d with case.Las the anodic prooess of case 3. i s the reversed one to that in case 1. so that a general solution would express the procedure i n either d i r e c -t i o n of the reversible prooess involved, i . e . the anodic d i s -solution of the metal dissolved i n mercury as well as the kathodic formation of the amalgam. Let us denote the concentration of kations i n the solution surrounding the dropping electrode by C*and the con-centration of the metal i n the amalgam by c i The p o t e n t i a l of the dropping electrode i s given by the concentration pre-v a i l i n g closely at the electrode interface: there the conoen-0 ) In a public lecture of J.Heyrovsky at the Faculty of Science, Masaryk University, Brno, A p r i l 26th,1938: compare also the Dissertation of M.Kalousek i n 1939. I l l t r a t i o n of kations i s CQ and the concentration of the baser metal i n mercury c£. We assume the presence of an i n d i f f e r e n t e l e c t r o l y t e i n the solution in a concentration s u f f i c i e n t to furnish the t o t a l transference of the currentj so that the kations of the dissolved metal p r a o t i o a l l y do not take part i n the migration. We take the view, used i n the previous deductions 9) of the mathematical equations for the polarographic current-voltage curves due to reversible processes, that the t r a n s f e r -ence of the current across the eleotrode i s given s t r i c t l y by d i f f u s i o n of the depositing or dissolving p a r t i c l e s . The anodic current thus depends on the d i f f u s i o n rate of the metallic atoms from the i n t e r i o r of the amalgam drop to i t s surfaoe and on the d i f f u s i o n rate of the metallio ions from the electrode surface into the solution* These two d i f f u s i o n rates must be equal during the formation o f eaoh drop of the amalgam otherwise an accumulation or i n s u f f i c i e n c y of p a r t i c l e s would grow at the electrode interface and would change the p o t e n t i a l , as i t depends on log C Q / O Q . Experiments, however, show that during the formation of the mercury drop i t s elec-trode p o t e n t i a l i n reversible electrode processes remains constant, which i s only possible, i f GQ as well as C Q are constant (at a certain applied E . M . F . ) . Then the intensity of current, i , i s given by the rate with which the metallio atoms are furnished to 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 rate with which the metallio ions, formed by the anodio dissolution of the metal, di f f u s e from the surface of the anode; hence also From these equations we obtain for whioh substituted into the o r i g i n a l formula for the reversible "redox" eleotrode p o t e n t i a l , lead to ^ ^ This may be also written The intensity of the anodio current w i l l reach i t s l i m i t , when the surfaoe of the amalgam drops w i l l beoome ex-hausted from the metal dissolved, i . e . when CQ= 0; hereby the anodic l i m i t i n g current, ^Cal i s given as -to/, " . ^ S i m i l a r l y the kathodic l i m i t i n g current, i s reached, when the solution surrounding the dropping eleotrode becomes exhausted of the kations of the electro-deposited metal. This condition i s that ~0)% or Substituting for k ^ a n d kgC^values and —- we obtain the f i n a l equation of the current-voltage curve, which expresses the course of e l e c t r o l y s i s inoluding anodic and kathodio polar-The curve ( f i g . l ) representing t h i s equation, i n which the p o l a r i z a t i o n , Jf , varies and the ourrent, , accordingly changes, has the form of a t y p i c a l "polarographic wave"; the only difference from the curves hitherto deduced i s that there i s an anodic as well as a kathodio l i m i t i n g current. The "half-wave" of t h i s curve occurs when and hence the p o t e n t i a l , JTJ- , at whioh the current reaches the ~2-"half-wave" value i s rr - rr-<*> ^ ^ ^ ^ z or TTJ. - 2 . - Ho — EX A No V I C - 1 F i g . 1. The shape of the continuous polarographic anodio-kathodio wave. The l a t t e r formula shows that t h i s "half-wave poten-t i a l " i s a c h a r a c t e r i s t i c constant, independent of the concen-trat i o n s of the agents "red" or "oxy", and given only by the type of the reduction and oxidation prooess, This value i s VI very near to the "normal redox p o t e n t i a l " , IT. , at whioh red -oxy , d i f f e r i n g from i t only by the ra t i o of the d i f f u s i o n constants of the electrode process. EXPERIMENTAL An older type of polarograph, made by Dr.V.Iejedly, was used. The contacts leading to the potentiometric wire were furnished with mercury j o i n t s , as described by J.V.Novak 1 0). The continuous change of the external E.M.F. ef f e c t i n g the anodic and the kathodic p o l a r i z a t i o n of the dropping electrode was produced by the adjustment of J . Hoe k s t r a 1 1 ) . For the same purpose also a simpler arrangement has been found convenient v i z . that shown i n Fig . 2 . ; i n t h i s one of the electrodes (e.g. the unpolarizable) i s joined to the middle terminal of a pair of accumulators whilst the other electrode ( i . e . the dropping one) i s connected to the s l i d i n g contact on the potentiometric wire. The l a t t e r arrangement was used only for approximat-ive measurements, as the two accumulators have ra r e l y an iden-t i c a l E.M.F. so that the s l i d i n g contact at the middle point of the potentiometric wire does not exactly branch o f f zero voltage. f/G-ZThe scheme of connections for continuous anodic-kathodic p o l a r i z a t i o n ; VII One of the above schemes has to be applied, when the amalgam i s used both i n the dropping electrode as well as i n the large unpolarizable electrode at the bottom of an ordinary conical e l e c t r o l y t i c vessel. However, the change from the anodic to the kathodic p o l a r i z a t i o n can also be effected, i f instead of the layer of the amalgam a separate standard eleo-trode i s used for the unpolarizable eleotrode. The po t e n t i a l of t h i s standard electrode has to be considerably more po s i t i v e than that of the amalgam i n order that the applied E.M.F. may be increased from zero i n one di r e c t i o n only ( i . e . making the potent i a l of the dropping electrode more negative), for which the ordinary polarographic connection s u f f i c e s . The vessel, which has the separate standard electrode affixed to the vessel with the dropping electrode, i s shown i n F i g . 3. The solution containing the kations of the metal used i n the amalgam i s plaoed i n the vessel B, into which the capi-l l a r y electrode (C) i s introduced through a rubber stopper. The side tubes of t h i s vessel serve for passing an in d i f f e r e n t gas ( i n t h i s case nitrogen) through the solution i n order to free i t from atmospheric oxygen. The amalgam accumulated by dropping i s l e t out from time to time through the tap E. The unpolarizable electrode i s plaoed i n the vessel A, where i t k e e p s — i n the form of a mercury l a y e r — i t s standard p o t e n t i a l . The current passes to t h i s electrode through a platinum wire sealed to a side contact, which i s f i l l e d with mercury. During the polarographio investigation the broad tap D i s kept open, so as to of f e r least e l e c t r o l y t i c resistance VIII between the vessels A and B. The tap F serves for the ex-change of the electrode solution. Fi^.'S E l e c t r o l y s i s vessel f o r amalgam polarography. The e l e c t r o l y t e i n the standard electrode was either O.ln potassium sulfate saturated with mercurous sulfate or i n potassium chloride saturated with calomel to matoh the anion of the el e c t r o l y t e surrounding the dropping electrode; The amalgams applied were those of copper, cadmium, lead and zinc i n concentrations not exceeding 0.005$. More concentrated amalgams were found to adhere to the walls of the glass c a p i l l a r y . The C-V curves obtained, were a l l of the type theore-t i c a l l y deduced. Fig.4 represents the curves polarographically recorded with lead, amalgam used i n the dropping electrode. Similar curves were obtained also with other amalgams. )NKCL 12 The straight l i n e passing through the middle of the polarogram denotes the 0 position of the galvanometer, i . e . the zero ourrent. At the beginning of the curves i n t h e i r lower branch the dropping amalgam electrode i s the anode, i . e . Pb atoms are transferred to the solution as Pb ions* The upper branch of the curve above the zero l i n e shows where the dropping amalgam eleotrode acts as eathode, i . e . deposits Pb*^ from the solution. Curve 1 has been obtained with amalgam dropping into a solution free from Pb hence, there i s only the anodic current shown. The cathodic one being p r a c t i c a l l y zero (the small ourrent above the zero l i n e i s due to traces of oxygen i n the s o l u t i o n ) . Curve 2 has been obtained with a more d i l u t e lead amalgam i n a solution 1 millimoles i n Pb"*"+. This curve shows the 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 of Pb from the amalgam as well as the oathodio branch caused by the electro deposit ion of Pb "^ . Curve 3 i s simply due to the eleotrodeposition of Pb at the drop-ping mercury electrode. It i s remarkable that #e of a l l three wafes coincide closely (corresponding to - 0.46 V from the p o t e n t i a l of the reference electrode H.C.E.).. The curves obtained with the same amalgams but at various times were not coinciding as far as the height of the l i m i t i n g anodic current i s concerned. This i s explainable by the i n s t a b i l i t y of the amalgams whioh are easily oxidized and thus lower t h e i r content of the dissolved metal* After shaking the amalgam a considerable decrease of the anodic current was produced. Interesting i s the s h i f t of the of 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 of the amalgam takes plaoe i n a solution i n whioh the metallic ion forms complexes. According to the general theory the E i should s h i f t to more negative p o t e n t i a l values i f the respective ion enters i n a complex. The same must of course hold also i n the case of the anodic wave. To investigate t h i s relationship the dropping lead amalgam eleotrode was surrounded by solutions of e l e c t r o l y t e s with which Pb^^form complexes. E i g . 5 shows the influenoe of the formation of complexes on the value of E i . Curve 1. lead amalgam with free Pb^T / 2-f\Gr. S x-t-± l l l l 1— S^o IN KCL +- O-OOIN PbCl^ 3- IN C IT KATE •« i< Curve 2, obtained with the same amalgam i n a l k a l i n e plumbite. Curve 3, effeot of c i t r a t e . A l l three curves referred to U.C .E. and the distance between two absoissal - 0.2/. The values of E i are therefore,(l)-0.46^. (2)-0.72K. (3)-0.53^ . These E i potentials coincide with those measured i n the catho-dic electrodeposition of Pb from (1) Free P b r 7 ^ i o n s (2) a l k a l i n e plumbite (4) lead s a l t i n excess o i t r a t e . Less regular are curves obtained when amalgam drops 21 i n a solution i n which the anodioally formed oations are pre-c i p i t a t e d , e.g. i f the dropping amalgam electrode (Pb) i s surrounded by d i l u t e a l k a l i or cadmium amalgam by d i l u t e ammonia. However, these i r r e g u l a r i t i e s are removed i f the concentrations of the p r e c i p i t a t i n g agents are inoreased so as to redissolve the precipitated hydroxides (Pb concentrated a l k a l i added, Gd concentrated ammonia added) $ The values are hereby again shifted to more negative values. The polarographic investigation of the anodio d i s -solution of 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 applications as f a r as q u a l i t a t i v e and quantitative analysis of traoe metals contained i n mercury i s concerned* We may imagine even a p o s s i b i l i t y of an analysis of a l l o y s i n whioh the a l l o y would not be dissolved i n an aqueaus solution but d i r e c t l y i n mercury and the amalgam would be polarographically investigated with the dropping anode. The m e t a l l i c components would be indicated by corresponding anodic waves of the G -V curve. Here an advantage over the ordinary polarographic analysis of metallic constituents i n solution even presents i t s e l f since i n the anodic d i s s o l u t i o n traoes of baser metals ( A l k a l i metals or zinc) may be shown with great s e n s i t i v i t y also i n the excess of the nobler metals (Cd,Pb,Bi,Cu,Au,Ag,Hg) whereas i n the kathodic polarographic investigation - just to the contrary - as a rule only the nobler constituents a r e more precisely estimated. How f a r amalgams may be prepared and successfully used for such an analysis with the dropping mercury anode remains to be s p e c i a l l y investigated. Here we mean just to XII hint to an inte r e s t i n g counterpart to the analysis of solutions with the dropping mercury cathode, v i z . to the polarographic analysis of amalgams by means of the dropping mercury anode, SUMMARY If the solution contains ions of the metal present in the amalgam, the o - curve has an anodic and cathodic branch and the equation of the curve i s where, i d ^ i s the anodic and idg i s the cathodic l i m i t i n g ourrent, k^ = d i f f u s i o n c o e f f i c i e n t of metal atoms i n meroury and kg = d i f f u s i o n c o e f f i c i e n t of metallic 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, nature, 142, 35 (1938) R.Strubl, G o l l . Czech. Ghem. Gommun, 10, 475 (1938) M. Spalenka, i b i d , 11, 146 (1939) K. Schwarz, Z. anal. ehem., 115, 161-174 (1939) J . Heyrovsky i n Bottgers Physikalische Methoden der analyt Chemio, Bd. I l l , p.428, Leipzig (1939) J.J.Lingane, J.A.C.S., 61, 976-977 (1939) Heyrovsky and Ilkovio, 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) 

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