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Kinetics of the Cu(II) catalysed reduction of Dichrmoate by hydrogen in aqueous solutions Hahn, Edmund Alexander 1960

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KINETICS OF THE Cu^ ^ 11  DICHROMATE  CATALYSED REDUCTION OF  BY HYDROGEN IN AQUEOUS SOLUTIONS  by EDMUND ALEXANDER.HAHN  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE-REQUIREMENTS FOR THE DEGREE OF '  :  MASTER OF APPLIED SCIENCE;  i n the Department of MINING AND METALLURGY  We a c c e p t " t h i s ' t h e s i s as conforming t o t h e standard-required' from-candidates f o r the Degree o f Master o f A p p l i e d  THE  Science  UNIVERSITY OF BRITISH COLUMBIA  March, i960  In the  presenting  requirements  of B r i t i s h it  this thesis for.an  Columbia,  freely available  agree that for  copying  gain  shall  Department  or  not  of  his  for reference  and  study.-  I  for  April  extensive be  granted  representatives. of  M i n i n g and  by  Metallurgy  Columbia,  of  the  It  this thesis  a l l o w e d w i t h o u t my  11. i960.  copying  of  University shall  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a , Date  the  Library  publication be  degree at the  p u r p o s e s may  D e p a r t m e n t o r by that  advanced  fulfilment  I agree that  permission  scholarly  in partial  make  further this  Head o f  thesis my  i s understood for financial  written  permission.  «. i _  ABSTRACT  The k i n e t i c s o f t h e C u hydrogen 200°C„  i n aqueous p e r c h l o r a t e A significant  + +  c a t a l y s e d r e d u c t i o n o f dichromate b y  s o l u t i o n s were i n v e s t i g a t e d between 160° and  dependence o f r a t e s on Cr  (VI) was observedo mechanism proposed t o account f o r t h e k i n e t i c s form  r-  dt  !—i  M  where t h e r a t e  ki =  The  r-  1.  T:  . .-i  +  -2^,900 RT  h  r a t e constant r a t i o s  k_^/k  x  2  gave r i s e t o a r a t e law o f t h e  /  T  , T  j3_[Cr(VlO  +  constant f o r t h e hydrogen  i L - e  r-  a c t i v a t i o n step,  k^, i s g i v e n by  -12a ^ Cl R  and k i / k =  3  a r e b e l i e v e d t o be temperature  independent i n t h e temperature range under c o n s i d e r a t i o n , and have values of  0.38 and 0 02 o  + +  approximate  respect!vely.  As a consequence for the C u  The  o f t h e s e s t u d i e s a s i m i l a r mechanism was proposed  c a t a l y s e d hydrogen-oxygen  by M c D u f f i e and co-workers.  recombination r e a c t i o n investigated  A c c o r d i n g t o t h i s mechanism an apparent  discrep-  ancy between t h e o b s e r v a t i o n s o f H a l p e r n e t a l and t h o s e o f t h e former workers  can be  explained.  - i i-  ACKNOWLEDGEMENT  The author wishes t o express  h i s g r a t i t u d e f o r t h e a d v i c e and  encouragement g i v e n b y t h e members o f t h e Department o f M i n i n g and Metallurgy.  I n p a r t i c u l a r he wishes t o thank Dr. E . P e t e r s f o r h i s s t i m u l a -  t i n g d i r e c t i o n o f t h i s i n v e s t i g a t i o n and f o r t h e c o n s t r u c t i v e c r i t i c i s m given d u r i n g the p r e p a r a t i o n o f t h e manuscript.  The a u t h o r  i s g r a t e f u l t o t h e Canadian N a t i o n a l Research C o u n c i l  f o r f i n a n c i a l a s s i s t a n c e and t o 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 o f Canada L i m i t e d f o r t h e Cominco F e l l o w s h i p h e l d i n 1959-60.  Company  SUMMARY OF STAFF COMMENTS ON THESIS EXAMINATION OF E.A. HAHN  T h i s was r e g a r d e d as a good t h e s i s .  The work i n v o l v e d an e x t e n s i v e  amount o f time p r e p a r i n g t h e r e a c t i o n v e s s e l so t h a t i t would y i e l d experiments.  good  The experiments were performed w i t h e x c e l l e n t p r e c i s i o n and t h e  r e s u l t s were good enough t o be i n t e r p r e t e d q u a n t i t a t i v e l y i n s p i t e o f t h e complex n a t u r e o f t h e  system.  No major c r i t i c i s m was made.  The complex p l o t s on pages 27, 28 and  29 were q u e s t i o n e d because t h e r e appear t o be d e f i n i t e t r e n d s among t h e i n d i v i d u a l experiments  p l o t t e d , and t h a t these t r e n d s r e p r e s e n t e d s u b s t a n t i a l  d e p a r t u r e s from t h e s t r a i g h t  l i n e s t h a t were drawn.  The reasons f o r t h i s  l a y i n t h e t y p e o f measurements and t h e form o f t h e f u n c t i o n used i n t h e p l o t , which r e s u l t e d i n a much p o o r e r q u a l i t y o f e x p e r i m e n t a l p o i n t near the ends of the l i n e s ,  e s p e c i a l l y t h e h i g h end, t h a n i n t h e m i d d l e .  T h i s type o f p l o t  c o u l d n o t have been made a t a l l except w i t h t h e most e x c e l l e n t  of rate  measurements„  The  c a n d i d a t e was asked a number o f q u e s t i o n s r e l a t e d t o t h e content  of t h e ' t h e s i S j ,  but n o t d i r e c t l y r e l e v a n t t o I t s d i s c u s s i o n o r c o n c l u s i o n s .  Among* t h e s e was a q u e s t i o n o f whether t h e r e would be any hope o f o b s e r v i n g the CuH  +  complex, one on whether any o t h e r mechanisms c o u l d b e p o s t u l a t e d t o  account  f o r t h e observed k i n e t i c s , and one on t h e s i g n i f i c a n c e o f t h e  of C u  and A g  + +  The  +  i n terms o f e l e c t r o n i c  activity  structure.  c a n d i d a t e ' s o r a l p r e s e n t a t i o n was a c c e p t a b l e and he was a b l e  t o answer t h e more r e l e v a n t q u e s t i o n s t h a t were d i r e c t e d t o h i m from t h e His t o t a l performance reservation.  was v e r y good and t h e t h e s i s was a c c e p t e d w i t h o u t  staff.  TABLE OF CONTENTS Page I N T R O D U C T I O N  o  o  o  Activation  o  o  o  o  o  o f Hydrogen  Effects  o f Complexing  Effects  of Solvent  o  o  o  o  o  o  o  o  o  o  o  o  o  o  O  O  O  O  .  .  O  .  .  .  .  .  .  .  .  .  . . . . . . . . . . . .  McL"ti ©l"*13,lS  O  O  O  A p p  0  0  0  3.1* c i t MS  O  O  O  O  0  0  O  d  0  O  O  0  „ .  O  O  0  E x p e r i m e n t a l Procedure RESULTS AND DISCUSSION  .  .  O  O  O  0  O  O  0  O  O  0  O  O  0  O  O  0  O  O  0  O  O  o  O  O  o  O  O  o  O  O  o  .  .  o  o  „ . <,  .  .  o  o  o  „ „ .  on Rates  O  o  O  O  o  O  O  o  O  o  p  O  o  O  O  o  .  „ .  .  .  .  .  .  .  .  „ „ . . . . . . . .  .  .  .  .  9  9  O  o  .  o  o .  Ion C o n c e n t r a t i o n on Rates . . . . . . . . . . .  33  Pressure, S t i r r i n g V e l o c i t y .  .  .  .  .  .  .  .  Catalysed  + +  .  and T i t a n i u m .  .  .  .  .  .  .  .  Hydrogen-Oxygen o o•  . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  R E F E R E N C E S  o  APPENDIX A  . . . . . . . . . . . . . . . . . . . . . . . . . . .  APPENDIX B  . . . . . . . . . . . . . . . . . . . . . . . . .  APPENDIX C  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  APPENDIX D  .  .  APPENDIX E  0  .  APPENDIX F  .  .  APPENDIX G  o  o  .  .  o  .  0  .  0  .  o  o  .  .  0  0  .  o  .  o  .  .  .  o  .  .  .  .  o  .  0  .  o  .  .  0  .  o  .  o  .  .  .  o  .  o  .  39  o  CONCLUSIONS  .  11  26  Recombination R e a c t i o n  0  11  . . . . . . .  Proposed Mechanism f o r t h e C u  0  9  16  S u r f a c e Area on Rates  .  8  . . . . . » < > .  o f Hydrogen  o  6  O  O  1  5  o  o . . «  O  o f Chromium V I Ion C o n c e n t r a t i o n on Rates  o  1  „ „ » .  O  Effect  Effect  o  . . . . . . . » . . . . . . . . . . <,  0  ,  O  o f Acidity  + +  o  . . . . . . . . . .  Effect  Effect o f C u  o  by M e t a l Ions i n Aqueous S o l u t i o n  Purpose and Scope o f t h e P r e s e n t I n v e s t i g a t i o n  E X P E R I M E N T A L  o  o  .  o  .  o  .  .  o  .  o  .  o  .  o  .  o  o  o  o  42 o  o .  o  hU-  o  4-6  .  47 49  9.  50  57  o o . o . o . o o o o c o o o .  .  .  .  .  .  .  .  .  .  .  .  .  ' 4 0  .  58 .  61  - iv LIST OF FIGURES Page 1  Dependence o f Rates on H  +  0  2  Dependence o f Rates on H  +  0  Concentration;  3<.  Dependence o f Rates on H  +  Concentration;  4.  Dependence o f R a t e "  on H  +  C o n c e n t r a t i o n ; 160°C . . . . . . . . . .  17  5.  Dependence o f Rate""' on H  +  C o n c e n t r a t i o n ; ISO C o o o o o o o o o o  -LS  60  Dependence o f . R a t e "  +  C o n c e n t r a t i o n ; 200°C . . . . . . . . . .  19  7.  P l o t s o f S l o p e s " , S, o f t h e Curves i n F i g u r e s 4,  -  1  on H  . . . .  1  Cr^ )  Concentration  1  80  1  C o n c e n t r a t i o n ; 160°C  P l o t o f l o g | i Versus T " Reduction o f C r (  V I  13  0  5 and 6 Versus  . . . . . . . . . . . . . . . . . . . . 1  )  f o r the C u  + +  21  C a t a l y s e d Hydrogen  . . . . . . .  . . . . . . .  25  9.  P l o t o f Rate F u n c t i o n , R, Versus C r (  V I  )  C o n c e n t r a t i o n ; 160°C  . . .  27  10.  P l o t o f Rate F u n c t i o n , R, Versus C r (  V I  ) C o n c e n t r a t i o n ; 180°C  . . .  28  11.  P l o t o f Rate F u n c t i o n , R, Versus C r ^ ^  . . .  29  12.  Schematic P o t e n t i a l E n e r g y Diagram f o r t h e A c t i v a t i o n o f H  13.  Dependence o f Rates on C u  + +  C o n c e n t r a t i o n ; 160°C; 0.1M.H+  34  14.  Dependence o f Rates on C u  + +  C o n c e n t r a t i o n ; 200°C; C.1M  H  +  35  15.  Dependence of Rates on C u  + +  C o n c e n t r a t i o n ; 200°C; 0.5M  H  +  16.  E f f e c t of C u  V I  + +  C o n c e n t r a t i o n ; 200°C 2  by C u  + +  .....  .  32  36  C o n c e n t r a t i o n on Rates a t S e v e r a l Temperatures, A c i d  C o n c e n t r a t i o n s and Cr (VI) 17.  Consumption o f H " Ions Due t o R e d u c t i o n  18.  Comparison  1  of C r ^ ^ V 1  Reduction  V e l o c i t y E f f e c t on Rates 19.  of C r ^ ^ . . . . . . . . . 1  Curves Showing N e g l i g i b l e  48  Stirring  „  59  Comparison o f Cr (VI)  R e d u c t i o n Curves Showing N e g l i g i b l e T i t a n i u m S u r f a c e Area E f f e c t on Rett QQ o o o o o a p o e o o a o o o o  60  -  V  LIST OF TABLES Page 1.  Values o f k-[_ C a l c u l a t e d from Mean I n t e r c e p t s o f F i g u r e s L, 5 and 6 and Other  2.  P e r t i n e n t Data  (a) Values o f  and  .  „  24  f r o m I n t e r c e p t s and Slopes o f P l o t s i n  F i g u r e s 9j 10 and 11 (b)  Values o f ^~1 and " l  from I n t e r c e p t s and Slopes o f P l o t s i n  k  ~"^2  30  ^ 3  3.  Effect  4.  (a) E f f e c t o f P e r c h l o r i c A c i d C o n c e n t r a t i o n on the Rate o f the  o f Hydrogen P a r t i a l P r e s s u r e on Rates  Cu (b)  + +  C a t a l y s e d Hydrogen R e d u c t i o n o f C r (  lS  o  o  o  Slope Measurements o f R a t e and  60  50  )  Values o f S  (a) Order o f C u  o  e  vs H  - 1  V I  ) 52  . . . . . . . . . . .  Rate Measurements and Rate F u n c t i o n , R, at V a r i o u s XJ€ V 6  5.  V I  E f f e c t o f D i s s o l v e d C u p r i c P e r c h l o r a t e on the Rate o f C r ( R e d u c t i o n by Hydrogen  (c)  39  . . . . .  o  o  o  o  Cr^ ) 1  e  o  P l o t s o f F i g u r e s k,  +  o  o  e  o  5 and 6,  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  57  Dependence o f Rates, R e l a t e d t o Percent Change o f  + +  K + K' Qr*] + K + K' (b)  Order  of C r ^ ) 1  of  W  t  h  C  h  a  n  S  i  n  g  K  (i-' ' e  ) a t 200°C . .  61  Dependence o f R a t e s , R e l a t e d t o Percent Change  \¥lf\+ K + K»  at 200^0  i  w i t h Changing K' ( i . e .  fcr^^  )  62  p  o  o  KINETICS OF THE C u (  I T  ) CATALYSED REDUCTION OF  DICHROMATE BY HYDROGEN IN AQUEOUS SOLUTIOIS  INTRODUCTION  The  growing i n t e r e s t i n t h e a p p l i c a t i o n o f hydrogen 1  as a r e d u c i n g  agent f o r t h e p r e c i p i t a t i o n o f metals e„g„ N i , Co"") o r low v a l e n c e m e t a l o x i d e s 2,3 (e.g. V 0 , U0 2  3  ) f r o m h y d r o m e t a l l u r g i c a l l e a c h s o l u t i o n s has g i v e n r i s e t o  2  extended s t u d i e s o f t h e k i n e t i c s and mechanisms o f some o f t h e r e a c t i o n s  involved.  These s t u d i e s r e s u l t e d i n t h e a c c u m u l a t i o n o f a body o f evidence showing  that  hydrogen, which a t o r d i n a r y temperatures  i s q u i t e i n e r t , w i l l be a c t i v a t e d i n  both aqueous and non-aqueous s o l u t i o n s by c e r t a i n m e t a l i o n s and some o f t h e i r complexes.  F o r example, C u  + +  , Hg , Hg + +  + + 2  , Ag  +  anr* some o f t h e i r  complexes  were f o u n d t o a c t i v a t e hydrogen homogeneously,'*' e i t h e r i n t h e i r r e d u c t i o n t o the m e t a l l i c s t a t e ( e . g . H g ° , Ag°) o r i n t h e r e d u c t i o n o f s u b s t r a t e s t o a lower valence Cu  + +  ( e . g . 0T 0 z  = 7  to C r ^  1 1  ^).  Of s p e c i a l i n t e r e s t i n t h i s r e s p e c t i s t h e  c a t a l y s e d r e c o m b i n a t i o n r e a c t i o n o f hydrogen and oxygen i n aqueous  s o l u t i o n s a t temperatures between 200° and 300°C.^  T h i s r e a c t i o n may a t t a i n  i n d u s t r i a l importance due t o i t s p o s s i b l e a p p l i c a t i o n i n t h e r e c o m b i n a t i o n o f r a d i o l y t i c d e c o m p o s i t i o n p r o d u c t s o f water  i n homogeneous aqueous  nuclear  reactors. A c t i v a t i o n o f Hydrogen by M e t a l Iohs i n Aqueous S o l u t i o n .  As e a r l y as 1909,Ipa.tieff and Werschowski^ found t h a t c u p r i c  acetate  i n aqueous s o l u t i o n s c o u l d be reduced b y hydrogen t o m e t a l l i c copper a t h i g h temperatures and p r e s s u r e s .  However, a t t h a t time t h e k i n e t i c s were not s t u d i e d  i n d e t a i l and thus the, c a t a l y t i c  a c t i v i t y o f d i s s o l v e d Cu^-^) was not r e c o g n i z e d  as  such. Halpern and  Dakers  7  have shown r e c e n t l y t h a t  cupric acetate  a c t i v a t e hydrogen homogeneously i n aqueous s o l u t i o n s , the reduction  of Cu^"^  CuAc  + H  2  t o cuprous o x i d e w i t h t h e  —•  2  CuAc „H 2  r e s u l t being  the  f o l l o w i n g proposed mechanism:  (slow)  2  could  (a) 1  CuAc „H 2  + CuAc  2  2  + H0  —  2  Cu 0 + 4 HAc 2  (fast)  (b)  g S u b s e q u e n t l y Peters and  Halpern  found t h a t hydrogen reduced  mate i n aqueous s o l u t i o n s o f c u p r i c a c e t a t e , Cr 0 2  + 3 H  = 7  + 8 H  2  +  —  2 Cr  + + +  S i n c e t h i s r e a c t i o n would proceed o n l y acetate,  i t was  inferred that  the  the  dichro-  reaction being;  + 7 H Q.  2  2  i n the  l a t t e r was  p r e s e n c e of d i s s o l v e d  cupric  a c t i n g as a t r u e homogeneous  catalyst„ L a t e r i t was  shown t h a t d i s s o l v e d  cupric perchlorate  also  catalysed  Q the  hydrogen r e d u c t i o n  ClO^  -  of d i c h r o m a t e  In t h i s medium, complexing o f C u t +  0  i s b e l i e v e d t o be n e g l i g i b l e and t h e  k i n e t i c s were observed t o  c o n s i s t e n t w i t h a mechanism i n v o l v i n g t h e f o l l o w i n g sequence of  Cu  + +  CuH  +  + H  k-1 . Z ^ GuH+ + H  2  + Cu  + +  —-  2 Cu  +  by  be  steps:  (a)  +  + H  (b)  +  3  fast 6 Cu + C r 0 " + 14 H +  2  E q u a t i o n 3(a)  7  represents  +  —>  + +  + 2 Cr  a pre-equilibrium  s p l i t t i n g o f a hydrogen m o l e c u l e . the  6 Cu  + 7 H0 2  (c)  p r o c e s s i n v o l v i n g the h e t e r o l y t i c  S i n c e one  r e a c t i o n r a t e depends i n v e r s e l y on t h e  + + +  product  i s a hydrogen i o n ,  hydrogen i o n c o n c e n t r a t i o n  in  s o l u t i o n , and t h e r a t e of r e d u c t i o n o f dichromate e x p r e s s e d i n terms o f  the  s t o i c h i o m e t r i c hydrogen consumption i s g i v e n by t h e  expression  2 -d[y - m[cu++r[X|  which was equation  d e r i v e d by a s t e a d y s t a t e a p p r o x i m a t i o n o f CuH .  According to t h i s  +  r e a c t i o n r a t e s may  appear t o be e i t h e r f i r s t  depending on t h e r e l a t i v e magnitudes o f t h e  k_ /k Tw]  ^[pu+tl  - djH^ =  k3_[Cu 3[H ]  example, i f  ±  z  o r second o r d e r i n  two terms i n t h e  Cu  denominator.  + +  For  t h e n the r a t e e x p r e s s i o n w i l l reduce t o  the  form -  5  +  2  0  dt P e t e r s and  Halpern ^ 1  showed t h a t at 0.1M  range v a r y i n g f r o m 0.004M t o 0.10M t h e k i n e t i c s between 80°  and  the  Cu(C104) r a t e law  and  2  a HCIO4. c o n c e n t r a t i o n  given by Equation  5 described  140°C.  5 M c D u f f i e and h i s co-workers s t u d i e s on t h e 250°C.  found the same r a t e law t o h o l d i n t h e i r  c u p r i c p e r c h l o r a t e c a t a l y s e d hydrogen-oxygen r e c o m b i n a t i o n  T h i s k i n e t i c b e h a v i o u r i s a c t u a l l y unexpected i n terms o f t h e  mechanism s i n c e i n t h e i r work £ H [ ] ^ [ C u f ] h  >  +  t o o d i f f e r e n t f r o m t h a t found by H a l p e r n order  reaction in  Cu  + +  , and  and  i f the value 9  co-workers  7  at  above  of k_]/k  2  i s not  at 110°C, a second  would have been expected.  A number o f o t h e r m e t a l i o n s b e s i d e s  Cu  + +  have been found t o a c t i v a t e  hydrogen homogeneously i n aqueous s o l u t i o n s .  Of p a r t i c u l a r i n t e r e s t  hydrogen r e a c t i o n s c a t a l y s e d by A g ,  Hg  +  Hg  + +  and  + + 2  are  , and t h e oxyanion MnOi,. . -  11,12 Thus Webster and  Halpern  showed t h a t s i l v e r  perchlorate  will  c a t a l y s e t h e hydrogen r e d u c t i o n of d i c h r o m a t e o r o t h e r s u i t a b l e s u b s t r a t e s i n aqueous s o l u t i o n s by two  possible r e a c t i o n paths.  The  first  o r low  temperature  (50°  t o 90 C) p a t h i n v o l v e s p r e d o m i n a n t l y a t e r m o l e c u l a r C  rate determining  step  where hydrogen i s s p l i t h o m o l y t i c a l l y , e.g., k 2 A g •+ H  2 AgH  +  2  (slow)  +  (a)  6 AgH The  + substrate  +  -*• A g  +  + products  (fast)  (b)  second p a t h which predominates a t temperatures o f 100° t o 120°C i s b i m o l e -  c u l a r a n d - i n v o l v e s h e t e r o l y t i c s p l i t t i n g o f hydrogen, e.g.,  Ag  + H  +  kl ^ z t  2  k  AgH + H  +  (slow)  - l  7 k —»• i n t e r m e d i a t e 2  AgH + A g The  +' s u b s t r a t e  +  (a)  fast products, (b)  combined k i n e t i c s f o r both paths a r e r e p r e s e n t e d  "lM  k [ H j [Ag3  -  2  dt  +  k  n  [A g  [Hj  g  k_i[Hf[ k  +  by  .  8  [Ag+]  2  It should  be n o t e d t h a t t h e second term i n t h i s r a t e e x p r e s s i o n  t o t h e r a t e law proposed f o r t h e C u mate ( E q u a t i o n  The  + +  i s identical  c a t a l y s e d hydrogen r e d u c t i o n o f d i c h r o -  k).  second path was a l s o p o s t u l a t e d a s t h e r a t e d e t e r m i n i n g s t e p i n  s t u d i e s on t h e r a t e s o f a c t i v a t i o n o f hydrogen by s i l v e r s a l t s i n p y r i d i n e 13 solut ions, Another r e a c t i o n i n w h i c h AgH i s t h e hydrogen r e d u c t i o n Halpern ). 1 4  has been p o s t u l a t e d  o f MnCV" t o Mn0  2  as an  intermediate  i n a c i d s o l u t i o n (Webster and  The k i n e t i c s a r e o f t h e f o r m  and  +  D  ^  =  K  M |MWVD L V ]  the r a t e d e t e r m i n i n g s t e p i s b e l i e v e d t o be -  9  - 5 -  Ag  +  + MnO^-(or AgMnO^) + H  2  -* AgH  f o l l o w e d by f a s t r e a c t i o n s o f A g H Ag ,  + MnO^ + H  ID  +  and M n O ^ which y i e l d Mn0  2  and r e g e n e r a t e  The r o l e o f M n C V i n r e a c t i o n 10 may be r e g a r d e d as t h a t o f r e p l a c i n g  +  one  +  +  of the A g  +  i o n s i n r e a c t i o n 6; i t s e f f e c t i v e n e s s i n d o i n g so i s connected  with i t s high one-electron  affinity.  Permanganate w i l l a l s o r e a c t homogeneous-  l y w i t h hydrogen"^ whereby i t i s reduced t o Mn0  2  i n a c i d s o l u t i o n s and t o M n O ^  in basic solutions.  Also o f i n t e r e s t i s the H g hydrogen. Hg  + + 2  Thus, i n p e r c h l o r a t e  + +  and H g  s o l u t i o n s o f t h e s e i o n s , where b o t h H g  a c t i v a t e hydrogen s i m u l t a n e o u s l y ,  Hg (aq) + H  -  + +  2  catalysed a c t i v a t i o n of  + + 2  two mechanisms have been  Hg° + 2 H ( a q ) (slow)  + +  and  postulated, ^ 1  (a)  +  I Hg  II  + Hg  c  Hg  + + 2  + +  (aq) + H  -  2  Hg  —  + + 2  (fast)  (b)  2 Hg° + 2 H ( a q ) (slow) +  E q u a t i o n 11 suggests t h a t t h e r a t e d e t e r m i n i n g s t e p s two-electron  11  (c)  i n v o l v e i n each case a  r e d u c t i o n o f t h e m e t a l i o n w i t h r e l e a s e o f two p r o t o n s t o the  k solvent. there  Although t h e Hg° i n t e r m e d i a t e  seems f a v o u r e d on e n e r g e t i c  grounds  i s s t i l l some u n c e r t a i n t y about t h e mechanism o f a c t i v a t i o n .  E f f e c t s o f Complexing The  above d i s c u s s i o n has been concerned o n l y w i t h homogeneous  c a t a l y s i s o f hydrogen by m e t a l i o n s t h a t a r e b e l i e v e d t o be e s s e n t i a l l y uncomplexed. ions discussed  Experimental evidence ^*17*18 1  n  o  w  s  that  complexing o f t h e m e t a l  above has a profound i n f l u e n c e on t h e r a t e o f hydrogen a c t i v a -  t i o n by these ions. strength  s  The r a t e s a r e a f f e c t e d p a r t i c u l a r l y b y m e t a l - l i g a n d  and b y t h e degree o f b a s i c i t y o f t h e a n i o n i c s p e c i e s .  r a t e s w i l l be slowed down b y complexing agents e x h i b i t i n g h i g h  4  bond  In general, metal-ligand  bond s t r e n g t h , e s p e c i a l l y w i t h r e a c t i o n s i n v o l v i n g h e t e r o l y t i c s p l i t t i n g the hydrogen m o l e c u l e ( e . g .  a c t i v a t i o n steps  i  be enhanced w i t h  i n Equations  3 and  7), and  i n c r e a s e d b a s i c i t y o f t h e a n i o n because of p r o t o n  There are a l s o some m e t a l i o n s whose a c t i v i t y has  of will  stabilization.  been observed o n l y 19  i n the form o f complexes.  These a r e p a l l a d i u m and  rhodium chloro-complexes  which have been found t o c a t a l y s e t h e r e d u c t i o n o f f e r r i c c h l o r i d e . second o r d e r , b e i n g f i r s t a c t i v i t y o f these  order i n H  2  and  first  complexes i s b e l i e v e d t o be  a c t i v i t y of uncomplexed P d be measured d i r e c t l y due  + +  and R h  + + +  ,  o r d e r i n PdCl^"-or  evidence  20 '  They a r e  RhClg*.  The  f o r the p o s s i b l e  These a c t i v i t i e s , however, c o u l d  not  t o i n t e r f e r e n c e o f heterogeneous r e a c t i o n s r e s u l t i n g  from m e t a l l i c Pd o r Rh t h a t a r e p r e f e r e n t i a l l y p r e c i p i t a t e d when the i o n s  are  uncomplexed. E f f e c t s of  Solvent  C e r t a i n m e t a l s a l t s d i s s o l v e d i n non-aqueous s o l v e n t s have a l s o been shown t o a c t i v a t e hydrogen homogeneously. a c e t a t e t o be ing  the  F o r example, C a l v i n ^ found cuprous 1  c a t a l y t i c a l l y active i n quinoline solutions i n reactions involv-  r e d u c t i o n o f quinone t o hydroquinone and  Cu^"^  to C u ^ .  Cu^ ) 1  17 i t s e l f was  f o u n d t o be  inactive in this solution.  W e l l e r and M i l l s  ,  who  s t u d i e d the k i n e t i c s o f t h i s system i n d e t a i l , p o s t u l a t e d t h a t the r a t e d e t e r mining step i n v o l v e d the  complex f o r m a t i o n between a C u ^ )  dimer and  because o f t h e second o r d e r r a t e dependence on cuprous a c e t a t e . i v e n e s s o f the dimer as a homogeneous c a t a l y s t was t h a t due  to i t s e l e c t r o n i c s t r u c t u r e i t possessed  accommodating two hydrogen atoms s i m u l t a n e o u s l y  The  H  2  effect-  thought t o l i e i n the two  s i t e s capable  fact  of  permitting electron transfer  from t h e H atom t o t h e dimer i n t h e a c t i v a t i o n s t e p .  18 Recently  Chalk and H a l p e r n  r e p o r t e d t h e homogeneous a c t i v a t i o n of  hydrogen  by both cuprous and c u p r i c heptanoates  i n h e p t a n o i c a c i d and o t h e r  n o n - p o l a r media such a s d i p h e n y l and octadecane. were proposed b o t h o f which show h e t e r o l y t i c  Two d i s t i n c t  activation  s p l i t t i n g o f t h e hydrogen  e.g.,  paths  molecule,  . CuHp  2  + H  2  —  (CuH)Hp + HHp  (a)  + H  2  —  CuH + HHp  (b)  12 CuHp  The a c t i v i t y o f CuHp carboxylate s a l t s  i n t h e s e s o l u t i o n s i s much lower t h a n t h a t o f c u p r i c  2  f e . g . a c e t a t e , p r o p i o n a t e , b u t y r a t e ) i n aqueous s o l u t i o n . I t  21 is  suggested t h a t  requirement  *'.  t h i s behaviour i s probably r e l a t e d t o the  f o r s t r e t c h i n g o f t h e m e t a l l i g a n d bond i n t h e t r a n s i t i o n  s t a t e ; i n view o f t h e charge i n a n o n - p o l a r medium.  s e p a r a t i o n i n v o l v e d t h i s would r e q u i r e more  energy  Furthermore, t h e magnitude o f t h i s medium e f f e c t  should  depend i n v e r s e l y on t h e charge o f t h e m e t a l i o n : i n l i n e w i t h t h i s i t i s found t h a t t h e r a t i o o f the r e a c t i v i t i e s o f cuprous s a l t s t o t h o s e o f the c o r r e s p o n d i n g c u p r i c s a l t s i n c r e a s e s markedly  i n g o i n g from aqueous s o l u t i o n s t o non-  polar media. • 1  S i l v e r s a l t s have a l s o been found t o a c t i v a t e hydrogen solutions.  Thus Wilmarth and Kapanan  a c t i v a t e hydrogen AgH.  22  i n non-aqueous  .  observed that s i l v e r acetate w i l l  i n p y r i d i n e by h e t e r o l y t i c s p l i t t i n g o f H  2  and f o r m a t i o n o f  The a c t i v a t i o n e n e r g y i n t h i s s o l v e n t i s much s m a l l e r (^14  that o f the corresponding reaction involving A g  +  kcal) than  i n aqueous s o l u t i o n  (23 k c a l ) f  This d i f f e r e n c e . i s p r i n c i p a l l y ascribed t o the higher b a s i c i t y of the solvent r e s u l t i n g i n greater s t a b i l i z a t i o n o f t h e proton released during h e t e r o l y t i c s p l i t t i n g o f H . • T h i s means t h a t complexing o f A g 2  +  ions w i l l r e s u l t i n  h e t e r o l y t i c s p l i t t i n g becoming more f a v o u r a b l e than h o m o l y t i c s p l i t t i n g .  4  Hp = heptanoate;  HHp = h e p t a n o i c  acid.  - 8 Purpose and Scope o f t h e P r e s e n t  The  Investigation,  mechanism and r a t e  ing the kinetics of t h e C u  law (Equations  3 and 4> pages 2 and 3) d e p i c t -  c a t a l y s e d hydrogen r e d u c t i o n o f d i c h r o m a t e *  + +  9  a l s o been found t o a p p l y t o t h e p r e c i p i t a t i o n o f copper f r o m aqueous s o l u t i o n s as shown b y MacGregor the  t h i r d r e a c t i o n step  ZL  25 and MacGregor and H a l p e r n .  2 3  have  perchlorate  In t h i s  case,  3(c)) i s replaced by the d i s p r o p o r t i o n a t i o n  (Equation  reaction of Cu , i . e . , +  2 Cu" ^  Cu° + C u  13  + +  w h i c h a l s o i s b e l i e v e d t o be f a s t .  In these s t u d i e s v a l u e s  o f k i and k-1 were c a l c u l a t e d b y means o f k E q u a t i o n 4 f r o m r a t e measurements o b t a i n e d from t h e i n i t i a l p o r t i o n o f t h e 2  copper r e d u c t i o n c u r v e s .  I t was o b s e r v e d t h a t k i f o r 160°C^ was c o n s i s t e n t  thermodynamically with the value  9 by H a l p e r n e t a l a t 110°C.  obtained  lr  The r a t i o  ZL  -1  was f o u n d t o be between 0.97 and 1.7 a t 160°C  as compared t o 0.26 a t  110°C. The apparent i n c r e a s e o f t h i s r a t i o w i t h temperature s u g g e s t s t h a t t h e back r e a c t i o n i n t h e a c t i v a t i o n s t e p , i . e . , 7  - l ^Zt Cu  * 3-(a)  k  CuH + H  +  + +  + H  2  l  k  becomes f a v o u r e d , i n o t h e r words, t h e a c i d e f f e c t  i s enhanced by r i s i n g  tempera-  ture. M c D u f f i e e t a l ^ , however, w o r k i n g a t 250°C, f a i l e d t o f i n d an a c i d effect  on t h e r a t e s o f t h e C u  + +  catalysed  f o r s o l u t i o n s that-were 0.001 M i n Assuming t h a t a t e n p e r c e n t increase  t  i n a c i d i t y and t h a t  Cu  + +  hydrogen-oxygen r e c o m b i n a t i o n r e a c t i o n and from 0.005M t o 0.050M i n HCIO^.  decrease i n r a t e was o b s e r v a b l e due t o t h e t e n f o l d the oxygen r e d u c t i o n  o c c u r r e d b y a mechanism  - ( a ) denotes t h e back r e a c t i o n o f E q u a t i o n 3 ( a ) .  - 9 -  t o E q u a t i o n 3, t h e n t h e v a l u e o f j-1  analogous their  case.  must be l e s s t h a n 0,002 i n  T h i s shows an apparent  d e c r e a s e o f - l w i t h r i s i n g temperature and k i s i n c o n s i s t e n t w i t h t h e e a r l i e r p o s t u l a t e d temperature dependence o f t h e r a t i o . k  2  I n view "of t h i s apparent  d i s c r e p a n c y i t was d e c i d e d t o extend t h e  s t u d i e s o f t h e Cu + c a t a l y s e d hydrogen r e d u c t i o n o f dichromate  t o 200°C i n o r d e r  +  t o determine  if,  p o s s i b l y , a change o f mechanism t a k i n g p l a c e a t t h e h i g h e r  temperatures  might account f o r t h i s anomaly,,  EXPERIMENTAL  Materials. ' A l l m a t e r i a l s used were o f Baker and Adamson reagent S t o c k s o l u t i o n s o f c u p r i c p e r c h l o r a t e and sodium dichromate  grade q u a l i t y .  were made up and  used f o r p r e p a r i n g t h e e x p e r i m e n t a l s o l u t i o n s , t h e c u p r i c p e r c h l o r a t e s o l u t i o n b e i n g p r e p a r e d from c u p r i c oxide and d i l u t e d throughout.  HCIO^,  D i s t i l l e d water was used  Hydrogen and n i t r o g e n gases were s u p p l i e d by Canadian L i q u i d A i r  Company i n 2000 p s i g  cylinders.  Apparatus. The  e x p e r i m e n t a l apparatus  comprised  a 1 g a l l o n , 1200 p s i g  l e s s s t e e l a u t o c l a v e manufactured b y A u t o c l a v e E n g i n e e r s sampling  system and gas i n l e t  autoclave cover.  and  Thermowell,  connections were made t h r o u g h t h e  The s t i r r e r was d r i v e n b y a 3/4 H.P. e l e c t r i c motor v i a a  s t i r r e r shaft f i t t e d through cover.  and o u t l e t  Inc.  a pressure gland i n the center of the autoclave  A l l p a r t s i n contact w i t h t h e s o l u t i o n , e.g., s t i r r e r ,  sampling  stain-  system, were made o f t i t a n i u m ,  titanium liner f i t t e d  thermowell,  The s o l u t i o n s were c o n t a i n e d i n a  into the autoclave vessel,  The l i n e r was p r o v i d e d w i t h  b a f f l e s made o f t i t a n i u m sheet i n o r d e r t o ensure s u f f i c i e n t  gas-liquid  - 10 interface during s t i r r i n g diffusion  thus p r e v e n t i n g h y d r o g e n a t i o n r a t e s from becoming  controlled.  The use o f t i t a n i u m was temperatures  e s s e n t i a l s i n c e i t was  found t h a t a t t h e  and p e r c h l o r i c a c i d c o n c e n t r a t i o n s used i n the experiments  l e s s s t e e l would be a t t a c k e d and  stain-  cause r a p i d r e d u c t i o n o f dichromate by  iron  ft i n t h e absence  o f hydrogen.  Moreover, a t e f l o n s h i e l d was  p l a c e d on t o p o f  the t i t a n i u m l i n e r t o prevent s p l a s h i n g o f t h e s o l u t i o n s a g a i n s t t h e  stainless  s t e e l a u t o c l a v e c o v e r and t h e r e b y cause r e d u c t i o n o f d i c h r o m a t e . The s o l u t i o n s were h e a t e d e x t e r n a l l y by a s e t o f two b u r n e r s o f which one s e r v e d as a p i l o t  r i n g - t y p e gas  b u r n e r and t h e o t h e r as a b o o s t e r . twin  Gas  f l o w t o t h e b u r n e r s was  r e g u l a t e d by means o f a Brooksmite  flowmeter.  Temperature c o n t r o l was  m a i n t a i n e d w i t h a Leeds and N o r t h r u p Micromax C o n t r o l l e r -  R e c o r d e r , w h i c h c o n t r o l l e d gas f l o w t o t h e b o o s t e r b u r n e r by means o f an a u t o matic v a l v e .  I n o r d e r t o p r o v i d e s u f f i c i e n t heat c o n d u c t i v i t y f o r good tempera-  t u r e c o n t r o l between t h e a u t o c l a v e v e s s e l and  the s o l u t i o n , t h e space between  t h e t i t a n i u m l i n e r and t h e v e s s e l ( a p p r o x i m a t e l y 1 / 1 6 " ) was  f i l l e d with  240  ftft mesh s i l i c o n - c a r b i d e powder.  The powder was  prevent i t from s p i l l i n g i n t o the s o l u t i o n . of  ±0.3°C a t  200°C was  t h e n covered w i t h g l a s s w o o l t o I n t h i s way  a temperature  control  obtained.  Hydrogen gas p r e s s u r e was  m a i n t a i n e d and r e g u l a t e d w i t h a s t a n d a r d  t y p e gas b o t t l e p r e s s u r e r e g u l a t o r and measured w i t h a Bourdon°type gauge t o an a c c u r a c y o f * Jja.  ft Two grams o f S t a i n l e s s s t e e l : f i l i n g s i n a 2.5 x 1 0 ~ % C r 0 = s o l u t i o n o f pH » 0 caused complete r e d u c t i o n o f t h e dichromate i n a p p r o x i m a t e l y 50 minutes at 200°C. ;  2  7  ftft S i C has. good t h e r m a l c o n d u c t i v i t y and e x c e l l e n t c h e m i c a l s t a b i l i t y a t high temperatures (J.W. M e l l o r s A Comprehensive T r e a t i s e on I n o r g a n i c and T h e o r e t i c a l C h e m i s t r y , V o l . V, p. 883) t h u s making i t u n r e a c t i v e w i t h r e s p e c t to the experimental s o l u t i o n s used. I t a l s o does not seem t o have any measurable e f f e c t on r a t e s .  - 11 -  j Experimental Procedure,  The e x p e r i m e n t a l procedure comprised t h e f o l l o w i n g s t e p s ;  (l) flushing  t h r e e times o f t h e a u t o c l a v e w i t h n i t r o g e n t o remove a l l r e s i d u a l a i r from the space above t h e s o l u t i o n so t h a t t h e atmosphere at temperature and b e f o r e hydrogen a d d i t i o n would c o n s i s t o f steam and a l i t t l e h e a t i n g t o the d e s i r e d temperature,, (two t o t h r e e t i m e s ) b e f o r e hydrogen  residual'nitrogen,  (3) sampling o f s o l u t i o n at  (2)  temperature  a d d i t i o n to t e s t the s t a b i l i t y of d i c h r o -  mate, (4) a d d i t i o n o f hydrogen t o the d e s i r e d pressure,, (5) p e r i o d i c  sampling  of the s o l u t i o n t o f o l l o w the c o u r s e o f t h e d i s a p p e a r a n c e o f d i c h r o m a t e .  The  sample s o l u t i o n s were passed t h r o u g h a c o o l i n g c o i l of t i t a n i u m t u b i n g immersed i n a beaker o f c o l d t a p water b e f o r e t h e y  entered  o r d e r t o prevent t h e i r f l a s h i n g and consequent  t h e sampling b o t t l e s i n  l o s s o f steam.  A n a l y s e s were made as f o l l o w s ? the samples were d i l u t e d and t h e a c i d i t y a d j u s t e d .  Then the dichromate content, o f each sample was d e t e r -  mined w i t h a Beckman Model D,U, the  volumetrically  spectrophotometer a t a wavelength  a b s o r p t i o n peak f o r dichromate,  r e a d i n g a t t h e a c i d i t y chosen  Cr  + + +  or C u  + +  o f 350  m/^  d i d not give a r e s i d u a l  f o r making the s p e c t r o p h o t o m e t r i c d e t e r m i n a t i o n .  A c i d i t i e s o f t h e u n d i l u t e d sample s o l u t i o n s were measured by p o t e n t i o m e t r i c  ± t i t r a t i o n w i t h a 0.1N t i o n was  sodium t e t r a b o r a t e solution..  The  cupric ion concentra-  d e t e r m i n e d g r a v i m e t r i c a l l y by d e p o s i t i o n o f copper on p l a t i n u m  electrodes„ RESULTS AND  Early in this the  ±  i n v e s t i g a t i o n i t was  r e d u c t i o n o f C r 0 7 ~ by hydrogen 2  Ac Vogels  Textbook  DISCUSSION  observed t h a t t h e p l o t s  i n t h e presence o f C u  + +  depicting  i o n s were not  o f I n o r g a n i c Q u a n t i t a t i v e Chemical A n a l y s i s , 2nd Ed„,p„231  straight  l i n e s , as found p r e v i o u s l y by P e t e r s  a definite  range of 160°  an i n i t i a l  4  2  180°, and  7  .  The  in Cu  + +  and an  200°C r e s p e c t i v e l y show t h a t , w i t h  to t h i s  simply determining a p p l i e d i n the  present  case;  r a t h e r , i t was  curve  best  3  + +  t o 4,0  respect to  necessary  at s e v e r a l C r ^ ^  x 10"%  Cr(  V I  of 3 the  Cr^"^ ^ 0  by  be  to o b t a i n r a t e measureI n o r d e r t o minimize  smooth curve was  drawn t h r o u g h  the  a f l e x i b l e r u l e r , a f t e r w h i c h tangents were levels  a c c u r a c y o f s l o p e measurements was x 10"  concentration  increasing acidity,  of t a n g e n t s t o t h e r e d u c t i o n c u r v e s .  p o i n t s of a r u n w i t h  plotted to this  initial  l i n e a r r e d u c t i o n p l o t s could not  e r r o r s i n t h e s e r a t e measurements, t h e  1,6  Cu  development, t h e e a r l i e r method o f measuring r a t e s  t h e s l o p e s of t h e  ments f r o m the s l o p e s  experimental  observations  r e d u c t i o n p l o t s d e p i c t e d In F i g u r e s 1, 2, and  r a t e s t e n d t o s h i f t f r o m z e r o - toward f i r s t - o r d e r w i t h  Due  These  showed  t o 200°C f o r s o l u t i o n s c o n t a i n i n g about 0„02 M  w i t h s o l u t i o n s 0„1M  about 5 x 1CT M C r 0  best  9 e t a l , but  c o n c e n t r a t i o n o f 3 x l C T - % CrgO?" whereas the e a r l i e r measurements  were made at 110°C  f o r 160°,  Halpern  dependence o f r a t e s on dichromate concentration,,  apply to the and  and  J  by t h e m i r r o r image method.  obtained  ) ) although  at i n t e r m e d i a t e  t h i s u s u a l l y was  levels  the r e g i o n  The  (i„e„, of  j  greatest curvature (i,e,, in  5,2  x 10"3  of the r e d u c t i o n p l o t s . t o 6,0  At h i g h C r ^ ^ 1  x 10~^M) toward t h e s t a r t  r a t e measurements f e l l o f f , which may  be due  concentrations  o f r e d u c t i o n the  accuracy  t o such t r a n s i e n t phenomena  as the time l a g i n v o l v e d i n the s a t u r a t i o n of s o l u t i o n w i t h hydrogen. levels  below 1,6  x 1 0 " m e a s u r e m e n t s a g a i n became l e s s a c c u r a t e  the d i f f i c u l t y i n o b t a i n i n g s u f f i c i e n t e x p e r i m e n t a l run.  ±  T h i s was  p a r t i c u l a r l y so i n f a s t  In  Cr^ ^ 1  because o f  p o i n t s near t h e end  r e d u c t i o n experiments.  At  of a  general,  The term, G r ( l ) , r a t h e r t h a n C r 0 7 ~ , w i l l be used f r o m here on because the e x a c t nature o f t h i s s p e c i e s i s not known at the temperatures at which t h e p r e s e n t experiments were conducted. F o r example, Tong and K i n g ^ " have shown t h a t at room temperature t h e predominant C r ( ^ - 0 s p e c i e s i n a c i d i c aqueous s o l u t i o n s of u n i t i o n i c s t r e n g t h i s HCrOv"", v  2  Time - Minutes Fi£o__l  0  Dependence o f Rates on H  +  C o n c e n t r a t i o n ! 160°C  0  10 atm„ H ; 2  0.02M C u ( C 1 0 ) 4  1 2  Time - Minutes  Dependence o f Rates on H C o n c e n t r a t i o n ; 10 atm. H ; 0„02M Cu(C10 ) "> +  2  4  2  200°C  - 16 about L t o 10 r a t e measurements, each associated with a g i v e n C r ^ ^ 1  (not n e c e s s a r i l y an e x p e r i m e n t a l point;, were taken f o r a s i n g l e  level  experiment.  E f f e c t o f A c i d i t y on Rates A s e r i e s o f e x p e r i m e n t s , i n w h i c h t h e a c i d i t y o f t h e s o l u t i o n s was v a r i e d , was conducted at each temperature r e s u l t i n g r e d u c t i o n p l o t s depicted  i n F i g u r e s 1, 2 and 3* show, not o n l y t h a t  r a t e 3 d e c r e a s e , but a l s o that t h e C r ^ )  dependence o f r a t e s s h i f t s  1  toward f i r s t  ( i . e . 160°, 180° and. 200°C) and t h e  increasingly  order w i t h higher a c i d i t y .  A c c o r d i n g t o t h e mechanism and r a t e law proposed b y H a l p e r n and c o workers  7  (see E q u a t i o n s 3 and 4, pages 2 and 3) a p l o t o f r a t e ~  x  vs H  +  s h o u l d y i e l d a s t r a i g h t l i n e of s l o p e k.! k and  x  1 kl[Cu -] [H ] +  2  2  2  intercept  i[? ]Ef  k  u++  F i g u r e s 4, 5, and 6 show p l o t s o f t h i s kind f o r t h e t h r e e e x p e r i m e n t a l temperatures r e s p e c t i v e l y .  Rates measured a t f o u r d i f f e r e n t C r ^ )  l e v e l s o f each r e d u c t i o n curve y i e l d f o u r s t r a i g h t common i n t e r c e p t a t  *  **  1  l i n e s on t h i s p l o t w i t h a  = 0, but w i t h s l o p e s t h a t d e c r e a s e - w i t h i n c r e a s i n g  A f t e r c o m p l e t i o n o f t h e 1.5M HCIO^, r e d u c t i o n experiment (see F i g . 3) a w h i t e p r e c i p i t a t e was found t o adhere t o a l l t i t a n i u m p a r t s i n c o n t a c t w i t h the s o l u t i o n . T h i s powder may have been some f o r m o f h y d r a t e d t i t a n i u m o x i d e formed b y t h e o x i d a t i o n o f t h e m e t a l b y p e r c h l o r i c a c i d a l t h o u g h no c o n c l u s i v e a n a l y s i s j o u l d be made on i t . Rate"  1  = I- d[H ]^ 2  dt  - 17 -  b  U^l  Cv?—  073  :  HCIO^ - Mole - L i t e r " Fig. 4. Dependence of Rate  -1  on H  +  074"  075"  X  Concentration at Several  C r ( ) Levels; 160°C. 0.02M Cu(C10 ) ; 10 atm. H . VI  4  2  2  - 18 r  F i g . 5.  Dependence o f Rate on H C o n c e n t r a t i o n a t S e v e r a l C r ( V I ) L e v e l s ; 180°C. 0.02M C u ( C 1 0 j ; 10 atm. H . +  2  2  - 19 -  HC1C> M o l e - L i t e r - l F i g . 6.  Dependence o f R a t e " on H C o n c e n t r a t i o n a t S e v e r a l C r ( V I ) L e v e l s ; 200°C. 0.02M C u ( C 1 0 ) ; 10 atm. H . 1  +  4  2  2  - 20  concentration.*  This v a r i a t i o n of slope with C r ^ ) 1  together with the greater-than-zero the e a r l i e r mechanism cannot be  concentration  dependence of r a t e s on C r ^ )  suggest  1  invoked  f o r the p r e s e n t  -  case, although  a p p l y at [H"f] = 0, because t h e common i n t e r c e p t i n d i c a t e s t h a t t h e  that  i t may-  Cr (VI)  dependence d i s a p p e a r s  at t h a t p o i n t .  I n view o f t h e i n v e r s e r e l a t i o n s h i p between C r ^ )  concentration  1  the s l o p e s o f F i g u r e s 4, against C r ^ ) , 1  and,  5 and  Each o f t h e s e  p l o t s may  f o r each  be r e p r e s e n t e d b y  an  form S = Slope"  C and  l a t t e r were p l o t t e d  as shown i n F i g . 7, t h r e e l i n e a r p l o t s , one  temperature, were o b t a i n e d . E q u a t i o n o f the  6, the r e c i p r o c a l s , S, o f the  and  1  = C + C»  [cr^^  14  C» a r e , r e s p e c t i v e l y , t h e temperature dependent i n t e r c e p t and s l o p e o f  any one  of the three  plots.  From E q u a t i o n of the r a t e  - 1  vs H  14 i t i s e v i d e n t t h a t t h e r e c i p r o c a l s , S, of t h e  p l o t s i n F i g u r e s 4,  +  5, and  slopes  6 c o n s i s t o f a Cr (VI) independent  t e r m C and  a Cr (VI) dependent t e r m  ion of C r ^ ) 1  C'[cr(VI)].  by hydrogen t a k e s p l a c e v i a two  independent one,  and  a Cr(  V I  )  dependent one.  T h i s suggests distinct  that the  reduct-  p a t h s , namely, a  Assuming t h e  Cr^ ^ 1  Cr (VI)  independent r e d u c t i o n p a t h i s a c c o r d i n g t o the mechanism o f Halpern and co-workers' " ( E q u a t i o n 3* page 2 ) , i t can be shown t h a t t h e t e r m C i s e q u a l t o 2 ^2 x ^[cu"1"^ \j}z} * 14 may! be r e - w r i t+t e n as f o l l o w s : 7  a n c  k_x  ^Jkl|Cu f| UllCuH  S-/«2 4  [HJ + C'[cr(VlJ JHol C « | C r ^ J L v ±  +  15  S l i g h t adjustments o f a c i d i t y were made f o r each Cr (VI) l e v e l at which r a t e s were measured t o account f o r H i o n d e p l e t i o n owing t o r e d u c t i o n o f C r ( V l ) . HCIO4 c o n c e n t r a t i o n s were e s t i m a t e d f o r each l e v e l from i n i t i a l a c i d measurements by use o f F i g . 17, Appendix B. +  P-* 7»  P l o t s of S l o p e s " , 3, o f the Curves i n F i g u r e s 4, 5 and 6 Versus C r ( ) C o n c e n t r a t i o n f o r 160°, 180° and 200°C. 1  V I  - 22  The  second  Cr  t i o n o f hydrogen by C r ^ ^  or d i r e c t r e a c t i o n o f Cr(VI) with the CuH  s i m u l t a n e o u s l y w i t h t h e r e d u c t i o n of Cr^^"^ by C u The f i r s t  o f these,two p o s s i b i l i t i e s , analogous 14  Webster and H a l p e r n , involve the  seems u n l i k e l y .  •&  The  +  +  intermediate, t a k i n g place  (see E q u a t i o n 3 ( c ) , page 2 ) ,  t o t h a t observed f o r MnO*, by -  second,more probable,one  would  reaction k _> i n t e r m e d i a t e s  /TT-p\  CjAViJ By combining et a l  activa-  by e i t h e r h e t e r o l y t i c o r h o m o l y t i c s p l i t t i n g o f t h e  1  molecule,  dependent p a t h c o u l d i n v o l v e e i t h e r d i r e c t  (VI)  -  +  C  u  H  +  fast -+ C u  + +  E q u a t i o n 16 w i t h the C r ^ ) -independent 1  + Products .  ,16  mechanism of H a l p e r n  ( E q u a t i o n 3) t h e f o l l o w i n g sequence i s o b t a i n e d :  9  l  k  Cu  + +  + H ^ Z ± CuH k-1  + H  +  2  k —  (a)  +  2  CuH  +  + Cu  CuH  +  + Cr^  + +  V I  2 Cu k —  ^  + H  +  (b)  +  fast Intermediates — Cu  3  1  + +  + Products  7  (c)  fast Cu  &  +  + Cr(  )  V I  —  Cu  + +  + Products  (d)  D i r e c t a c t i v a t i o n o f hydrogen by C r ^ ) i s u n l i k e l y i n the l i g h t o f t h e s i g n i f i c a n c e of t h e p l o t s i n F i g u r e s 4* 5, and 6. These p l o t s show t h a t the s e n s i t i v i t y o f r a t e s t o Cr(VI) c o n c e n t r a t i o n r i s e s w i t h i n c r e a s i n g acidity. I f a c t i v a t i o n of H by C r ( ^ I ) would take p l a c e by h e t e r o l y t i c s p l i t t i n g of t h e molecule a c c o r d i n g t o 1  2  Cr< ) V I  +  H ^! 2  C r ^ H "  + H+  ^Products  then p l o t s o f r a t e " vs H ( F i g s . 4, 5 and 6) s h o u l d show an e f f e c t o f that i s decreasing, rather than increasing, with i n c r e a s i n g a c i d i t y . A l s o i f a c t i v a t i o n by C r t v l ) s h o u l d i n v o l v e h o m o l y t i c s p l i t t i n g o f H after 1  +  2  2 Cr(  V I  )  + H  2  2 Cr(  V I  )H  f  -^ Products St  t h e n changes i n a c i d i t y would not be expected t o a f f e c t t h e C r ^ ) dependence o f t h e r a t e s a t a l l which, t o o , i s c o n t r a r y t o e x p e r i m e n t a l observations. 1  - 23 -  which l e a d s t o a r a t e e x p r e s s i o n o f t h e form  "  d  [  H 2  ] -  kiTcu^fra]  j i a [Cu++] + ±1  [cr^l  18  dt  d e r i v e d by a s t e a d y s t a t e a p p r o x i m a t i o n  o f t h e CuH  intermediate.  +  On i n v e r t i n g  and r e a r r a n g i n g , E q u a t i o n 18 i s changed t o -  <- d j d l "  1  -  M  *  1  which i s t h e e q u a t i o n o f a s t r a i g h t l i n e whose dependent and variables are r a t e  and  - 1  respectively,  H  +  19  independent  r e s p e c t i v e l y , and whose s l o p e and i n t e r c e p t a r e ,  l[ ] M v(I*—1  +~1 [cr™]! J  k Cu++  19(a)  kl[cu3 [}Q  and  19(b)  +  I t i s now apparent t h a t each o f the f a m i l i e s o f s t r a i g h t - l i n e p l o t s i n F i g s . L  }  5 and 6 a r e r e p r e s e n t e d by E q u a t i o n 19 and t h e i r C r ( ^ - ) dependent s l o p e s  g i v e n by 19(a).  On i n v e r t i n g e x p r e s s i o n (19a) E q u a t i o n 20, which i s e q u i v a l e n t  t o 15, i s o b t a i n e d , i . e . ,  > .  Thus, i t may be seen t h a t t h e c o n s t a n t C i n E q u a t i o n 15 i s C  20  (which r e p r e s e n t s s l o p e s i n F i g . 7)  = k i f C u + g [ H ] 2i_ 2  k  .  20(a)  - l  *-l kk -n "-1 — and 2=. V a l u e s o f t h e r a t i o s — ^<2 - and _^ ji± 3 f o r t h e t h r e e e x p e r i m e n t a l temperatures  which  can be c a l c u l a t e d by E q u a t i o n 20 from i n t e r c e p t s and s l o p e s i n F i g . 7, a r e shown i n Table 2 ( b ) ,  - 24 I t i s now a l s o apparent  that t h e e x p r e s s i o n 19(b) f o r t h e common  i n t e r c e p t s o f t h e p l o t s i n F i g u r e s 4,  5 and 6 i s i d e n t i c a l t o t h a t d e r i v e d from  t h e e a r l i e r mechanism (see e x p r e s s i o n o f i n t e r c e p t ,  page 1 6 ) . With t h i s  e x p r e s s i o n , v a l u e s o f k]_ a t 1 6 0 ° , 180° and 200°C weie c a l c u l a t e d from t h e mean i n t e r c e p t s i n t h e above F i g u r e s and a r e shown i n Table 1.  TABLE 1 V a l u e s o f k]_, C a l c u l a t e d f r o m Mean I n t e r c e p t s o f F i g u r e s 4. 5 and 6, and Other Pert^nerr' Data.  Inter- cept.,  Temp. °C  ^-min-mol  kiDu+liXl JrS  (I3.1±1.0)xl0  18©°  (3.32±0.2)xl0  200°  (0.92±0,05)xl03 .See Reference Obtained  1  JL-mol-^-sec"!  -  9.5 xlO-5  IxlO"  1  5  2xl0-  2  1.18x10-2  (5.40±0.73)xlO"3  (3.01±0.18)xlO~ '  2xl0"  2  1.35xl0"2  (l.83 0.22)xl0-2  (1.09 0.06)xl0-3  2xl0-  2  1.58x10-2  (5.74 0.67)xlO-  /  3  kl  1  mol-^"  1  (7.6.':i0.58)xl0-  3  ^  1  -  160°  (b)  1  mol-Z~~ -min~  - 1  110°  (a)  [Cu-J. mol-^T -  I n t e r c e p t --  ±  (  b  )  ±  ±  27  from Reference  9.  A good A r r h e n i u s p l o t o f l o g ' ^1 T from t h e s e v a l u e s o f k-j_.  vs 1 T  d e p i c t e d i n F i g . 8, i s o b t a i n e d  The a c t i v a t i o n e n t h a l p y e s t i m a t e d from t h e s l o p e o f  this plot i s AH*  =  24.9*1.7  kcal/mol.  which i s i n good agreement w i t h t h a t g i v e n by Peters23 who o b t a i n e d kcal/mol.  2  A H * = 24.6  The c o r r e s p o n d i n g e n t r o p y o f a c t i v a t i o n , A S  f  =  12.1*4.5  c a l - "K"  - mol" ,  1  1  which a l s o agrees . w e l l w i t h P e t e r s ' v a l u e , i . e . , A S * c o n s i d e r e d normal f o r a b i m o l e c u l a r r e a c t i o n .  = -13.1  e.u., i s  Hence, k i may be r e p r e s e n t e d by R  21  2  '  1  2  '  2.3  2  2.4  1 x IO  2.5  2.6  2.7  3  T 1  kl Plot of l o g - y -  Ve-Rus T  Reduction of C r ™ .  f o r the C u  + +  C a t a l y z e d Hydrogen  0.02M C u ( C l C V ) ; ±0 atm. 2  H; 2  - 26  where k and  h a r e Boltzman's and  The  Planck's constants  uncertainty i n estimating Appendix C f o r e r r o r  is  vs j C r (  V I  )]for  9,  160",  10,  180°  and  are a s c r i b e d t o i s assumed  the  (see  and  on  Rates.  r a t e s on  concentration  in solution  11 i n t h e f o r m of p l o t s o f t h e r a t e f u n c t i o n , 200°C r e s p e c t i v e l y .  d e r i v e d from t h e r a t e e x p r e s s i o n , linear  AS*  and  estimations).  dependence o f r e d u c t i o n  seen i n F i g u r e s  respectively.  k]_, f o r w h i c h a t o t a l e r r o r of ±13$  E f f e c t o f Chromium VI Ion C o n c e n t r a t i o n The  & H*  f a i r l y large errors, both i n  -  E q u a t i o n 18,  T h i s r a t e f u n c t i o n , which  i s r e l a t e d to C r ^ ) 1  "iy  R, was  the  equation  M  fcu+jl +  R = (Rate) x (Ro - Rate)  « k, k_i  where Rate = -dJHgj/dt and  [c( )]  = k i [ C u ^ ] Qi^].  Ro  r  k^ k_]_  +  VI  .  22  Values o f R were c a l c u l a t e d from  r a t e measurements of a t l e a s t three experiments,each of d i f f e r e n t a c i d i t y , at each o f t h e t h r e e t e m p e r a t u r e s , w i t h Ro intercepts i n Figures  The  L,  5, and  plots i n Figures  the r e g i o n of (0.4 t o 4.0)  b e i n g the r e c i p r o c a l of the  6.  9,  10,  x 10"3M  and  11 show r e a s o n a b l y good l i n e a r i t y i n  C r ( l ) , w i t h t h e p o i n t s o f the i n d i v i d u a l v  runs c o i n c i d i n g q u i t e w e l l i n t h a t r e g i o n . i t y and the  spreading  respective  o f p o i n t s at h i g h e r  r a t e measurements become i n a c c u r a t e  The  l a r g e r d e v i a t i o n s from  linear-  C r ( V l ) l e v e l s r e f l e c t the f a c t  in that region.  From i n t e r c e p t s and  that slopes  r a t i o s ^-J, and k - l may be c a l c u l a k k t e d f o r each o f t h e e x p e r i m e n t a l t e m p e r a t u r e s , s i n c e from E q u a t i o n 22, of Figures  9,  10,  and  11, t h e  rate constant  2  Intercept  and  Slope  = kg_ [Cu "^ +  =  k_3 k  - l  .  3  22(a)  22(b)  - 27 -  2 Cr( F i g . 9.  V I  4  ) x 10  3  Mole-Liter-  6 x  P l o t o f Rate F u n c t i o n , R , V e r s u s C r ( V I ) C o n c e n t r a t i o n ;  0.02M  CuCClO^^j  10  atm. H ; 2  l60 C e  - 20 -  2  o C  F i g . 10  R  ( V I )  n X  :  6  Mole-Liter"!  IQ3  P l o t o f Rate F u n c t i o n , R, V e r s u s C r ^ ^ V I  0.02M C u ( C 1 0 ) ; 10 atm. H ; if  2  2  Concentration; 180°C.  - 29 -  o.5r HClO^(initlal)  O A • O  0.20 0.35 0.50 0.50  Cu(C10 ) 4  M  2  0.02 M 0.02 • 0.02 0.01  0.4 H 1  U I  HQ> »  o.i  2 Cr( F i g . 11.  V I  4  ) x 10  3  Mole-Liter"  P l o t o f Rate F u n c t i o n ^ V e r s u s 10 atm. H ; 200°C„ 2  1  Cr(  V I  )  Concentrat i o n ;  - 30 -  Values of t h e s e r a t i o s s h o u l d agree w i t h t h o s e o b t a i n e d i n a s i m i l a r f a s h i o n from t h e i n t e r c e p t s and s l o p e s i n F i g . 7 and the c o r r e s p o n d i n g i n t e r c e p t s l o p e e x p r e s s i o n s i n E q u a t i o n 20.  Table 2, which l i s t s  k  - l  and ^-1,  and  obtained  by both methods, shows t h a t t h e agreement i s q u i t e good indeed, d e s p i t e t h e f a c t t h a t t h e u n c e r t a i n t i e s i n measurements are q u i t e h i g h f o r both f o r ^1 k  i . e . , *19$  and ±8% f o r  2  ^1. k 3  W i t h i n l i m i t s o f e r r o r , both  k  - l k  temperature  ratios,  between 160° and 200°C.  arrf  2  ^-1 appear t o be k  independent  3  The v a l u e o f 0.26  f o r k - l at  110°C  suggests t h a t t h i s r a t i o i s c o n s t a n t i n t h e range o f 110° t o 200°C. r e s u l t s indicate that the reaction steps - ( a ) * ,  (b) and  These  (c) o f E q u a t i o n  17.  TABLE 2 (a)  Values o f - l and ~ l from I n t e r c e p t s and • k k o f P l o t s i n F i g u r e s 9, 10, and 11, k  k  2  Temperature °C  Intercept  = k /k_ Vf]  mol-l"  2  lL  110°  1  Slopes  3  Slope  " k /k_i 3  .  — .  k_i/k  2  0.26^*  160°  0.054*0.01  44*6*4,0  0.'37*0.07  (2.24*0.20) x  -2 10*  180°  0.053*0.01  51.0±4.0  0.38±0„08  (1.96*0.18) x  -2 10"  200°  0.051*0.01  49.6*4.0  0.39*0.08  (2.02*0.16) x  -2 10"  4  R e a c t i o n s t e p - ( a ) denotes t h e back r e a c t i o n of (a) i n E q u a t i o n  ±k  See Reference  9.  17.  of  - 31 TABLE 2  (b)  Values o f k-1 k  a  n  d  k  2  - l k  (cont'd.)  from I n t e r c e p t s and S l o p e s 3  of P l o t s i n F i g . 7.  Slope  Intercept  Temp,  k-l/k  2  k.]/k  3  k_i  <-l mo l 2 - J e - 2 m i n - 1  mol-jET^min**  160°  4.10xl0~  3.25x10-3  0.37  2.36x10',-2  180°  1.36x10-  1.6lxl0-  2  0.44  1.86xl0~  2  200°  5.60x10"  0.53X10"  0.39  2.04xl0"  2  6  5  1  1  5  a l l have a p p r o x i m a t e l y t h e same a c t i v a t i o n energy, which i s e v i d e n t from t h e following.  Consider t h e equations -  log  k-1 = '•  log A_-L  2  and  -  2  -  lf3  where  A_]_^2  and  23  (E_! - E ) 2.3 RT  (b)  3  3  A_-j_  (a)  a  2.3 RT  i o g k _ i = l o g A_ k  (E-i - E )  '  k  ^ a r e r a t i o s o f the frequency f a c t o r s f o r t h e r e a c t i o n s  .(see E q u a t i o n 17) i n v o l v i n g r a t e c o n s t a n t s k _ i , k are t h e c o r r e s p o n d i n g a c t i v a t i o n  energies.  2  and k , and E_]_, E 3  straight  and E  k l ~  a p l o t o f t h e i r logarithms against T ~ l should r e s u l t i n a  l i n e o f a p p r o x i m a t e l y zero s l o p e , wherefrom i t f o l l o w s t h a t + E. ~  0  + E  3  ~  0  E _ =* E  2  ^ E  —3_  1  •  (a)  and  -3_1 hence  x  (b)  3  3  S i n c e k _ i and k-1 a r e n e a r l y tempera-  k7" t u r e independent,  2  (c).  2  4  - 32 The s i m p l e s t c o n c l u s i o n t o be drawn f r o m t h i s r e s u l t  (c) o f E q u a t i o n 17  p o s s i b l y a l l z e r o , i . e . , r e a c t i o n s ( a ) , (b) and a c t i v a t i o n e n e r g i e s , and k_]_, k  2  and k  i s t h a t E_;j_, E  are temperature  3  2  and E  3  are  have no  dependent o n l y w i t h  respect to t h e i r e n t r o p i e s of a c t i v a t i o n .  A p o t e n t i a l energy diagram f o r the proposed  a c t i v a t i o n mechanism  may  a c o n c e i v a b l y be r e p r e s e n t e d  as shown i n F i g . 129  CuH + +  H  where E-j_ i s the  activation  +  Products Reaction  F i g . 12  Schematic  Coordinate  P o t e n t i a l Energy Diagram f o r the A c t i v a t i o n of H by C u + +  2  energy o f r e a c t i o n  (a) E q u a t i o n 17.  T h i s scheme i m p l i e s t h a t  CuH  +  i s the  a c t i v a t e d complex and t h a t t h e r e a c t i o n o f t h i s complex w i t h each o f the s p e c i e s H , +  Cu  + +  o r C r ( V l ) i n v o l v e s o n l y a d i r e c t decrease i n energy.  i n t h e magnitudes of t h e r a t e c o n s t a n t ? k_-^, a consequence o f the d i f f e r e n c e s  K  i n t h e bucropy  2  and k , 3  The  differences  t h e r e f o r e , would be o n l  changes r e s u l t i n g f r o m t h e  r e a c t i o n of t h e s e s p e c i e s w i t h CuH . +  ft These c o n d i t i o n s do not r e j e c t t h e p o s s i b i l i t y t h a t CuH i s i n f a c t more s t a b l e t h a n the a c t i v a t e d complex i t s e l f . However, i n s u c h a case the p o t e n t i a l energy curve would be a p p r o x i m a t e l y s y m m e t r i c a l about t h e (CuH + H ) c o n f i g u r a t i o n t o account f o r a p p r o x i m a t e l y e q u a l a c t i v a t i o n e n e r g i e s i n a l l d i r e c t i o n s . +  +  +  - 33  Effect  of C u  Ion C o n c e n t r a t i o n on Rates  + +  F i g u r e s 13,  14 and  15 i l l u s t r a t e the dependence  c o n c e n t r a t i o n i n s o l u t i o n at 160°  and 200°C.  shown, two were c a r r i e d out a t 200°C, one The  -  160 C s e r i e s was  0.1M  C  i n c r e a s e , and  i n HCIO^.  of r a t e s on C u  ion  + +  Of t h e t h r e e s e r i e s o f experiments  a t 0.1M  HC10 , the o t h e r at 0.5M 4  HCIO4.  I t i s e v i d e n t t h a t (1) r e d u c t i o n r a t e s  (2) t h e dependence o f r a t e s on Cr (VI) decreases  first  o r d e r toward zero o r d e r , w i t h i n c r e a s i n g C u  son o f F i g u r e s 1 4 and  by i n c r e a s e d - C u In F i g . 16,  against C u of  r a t e s on C u  r a t e s had It  + +  ion concentration.  + +  r a t e s measured at the  ( F i g . 1 5 ) , i t becomes n e v e r t h e l e s s  4x10"3 Cr^^"^  i s evident.  An apparent  l e v e l a r e shown p l o t t e d  first  o r d e r dependence  I n a d d i t i o n t o these t h r e e p l o t s i s one f o r which  been measured a t t h e 1 . 6 x l O M C r ^ _3  V I  ^  l e v e l f o r the 0.5M  i s seen t h a t a s h i f t o f r a t e dependence f r o m apparent  order i n C u  first-  HCIO^ s e r i e s .  toward second-  o c c u r s when r a t e measurements are made a t t h e lower C r ( V l ) l e v e l .  + +  T h i s s h i f t t o g e t h e r w i t h the d e c r e a s i n g dependence o f r a t e s on C r ^ ) 1  increasing C u  + +  i o n c o n c e n t r a t i o n w i l l now  e x p r e s s i o n E q u a t i o n 18 which reads fk  - djHj dt  Compari-  ion concentration.  + +  f o r each of t h e t h r e e s e r i e s .  + +  apparent  15 i n d i c a t e s a l s o t h a t , a l t h o u g h the C r ( ^ l ) e f f e c t i s  enhanced c o n s i d e r a b l y w i t h t h e h i g h e r a c i d i t y suppressed  from  be e x p l a i n e d i n terms o f t h e  rate  k  2  3  \  ki[Cu+tl [ H 3 1 * - I [ C U > k_i§r(vl)jf (H+n iS2_ICu t] + k 3 _ [ C r T O ] + +  .  18  +  +  - l  k  I n E q u a t i o n 18  with  - l  k  c o n s i d e r the e x p r e s s i o n k  |cu 3 + +  2  *Cl  H  +  k  k  18(a)  ^1  a Qu ''ll +  k  [crO/I))  3  -l  which r e - w r i t t e n f o r s i m p l i c i t y ,  +  k  3 rCr(VPl k  - l  becomes  K + K' + K + K»  18(b)  Time - Minutes F i g . 13o  Dependence o f Rates on Cu + C o n c e n t r a t i o n ; +  O.IM HClOi,  (initial).  160°C. 10 atm.H ; 2  .  1  1  1  r  Time - Minutes F i g . 14.  Dependence o f Rates on C u C o n c e n t r a t i o n ; 200°C 10 atm. H ; 0.1M HC10 (initial) + +  2  4  - 37 -  F i g . 16.  E f f e c t of C u C o n c e n t r a t i o n on Rates at S e y e r a l Temperatures, A c i d C o n c e n t r a t i o n s and C r A ^ ' L e v e l s ; 10 atm. H . + +  1  2  - 38 -  where K =  k  \cu +\ +  2  k  and  K*  =  - l  k  k  lcr( )l VI  3  - l  I t i s found t h a t the o r d e r o f t h e dependence o f r a t e s on C u  is a  + +  f u n c t i o n o f the magnitude of t h e change i n t h e n u m e r i c a l v a l u e o f e x p r e s s i o n 18(b) as K ( i . e . ,  [Cu" "^) i s v a r i e d , w h i l e 1  [~H] +  and K» a r e kept c o n s t a n t .  S i m i l a r l y , t h e o r d e r o f t h e dependence o f r a t e s on C r ^ " ^ i s a f u n c t i o n o f t h e magnitude o f t h e change i n t h e n u m e r i c a l v a l u e o f 18(b) as K' is varied, while  [k ]] and K are kept c o n s t a n t . +  (i.e.,  [Cr^^)  The magnitude o f the change i n  the n u m e r i c a l v a l u e of 18(b) depends i n both cases on t h e r e l a t i v e magnitudes of  (1) t h e sum o f t h e two terms t h a t a r e h e l d  0"^]  + K ) , and  It - K + K* f H J + K + K»  (•£) t h e t e r m t h a t i s v a r i e d  i s shown i n Appendix  constant ( i . e . ,  [ j " " ^ + K'  or  ( i . e . , K o r K*)»  G, T a b l e 6(a) t h a t i f t h e change i n  i s s m a l l as K ( i . e . ,  |Cu 'H ) i s v a r i e d , then r a t e s appear t o be +  +  first is  o r d e r i n [Cu "*[] (see F i g . 16, curves A and B ) .  l a r g e , the r a t e s w i l l s h i f t toward  F i g . 16, curve C ) .  Similarly,  dependence of r a t e s on  apparent second  i t i s shown i n Apoendix  t  S\  K + K' CH J +  [Cu f] +  G , Table 6(b), that the  i s s m a l l as K'  (see F i g . 15, curve E and F i ^ . 3, curve F ) .  f i r s t - t o second-order i n (Cu ]]and f r o m z e r o - t o f i r s t - o r d e r i n ++  combination  of t h e s e p o s s i b i l i t i e s ,  expression  M  +  v a r y from  [cr(VD],  or a  depending on the s e n s i t i v i t y o f the  t o changes i n e i t h e r K o r K», K + K»  6  These o b s e r v a t i o n s e x p l a i n the f a c t t h a t P e t e r s and observed no  (i.e.,  apparent f i r s t o r d e r i f t h i s  Consequently i t i s noted t h a t t h e r a t e e q u a t i o n 18 may  Jj [H >  (see  + K + K«  [Cr(VI)J ) i s v a r i e d , and t h a t i t s h i f t s toward change i s l a r g e  order i n  change  appears t o be zero o r d e r (see F i g . 15, curve A  and F i g . 3, curve A) i f t h e change i n r  However, when-this  +  CrOHO  . e f f e c t , no a c i d e f f e c t and j u s t a f i r s t  9  r a t e s , a n d t h a t H a l p e r n et a l  (  \  a l s o observed no C r ^ ) 1  Halpern ^  order C u  1  + +  effect  on  e f f e c t although they d i d  - 39 -  f i n d an a c i d e f f e c t and a pseudo second o r d e r e f f e c t o f C u be v e r i f i e d by a p p l y i n g the p r e s e n t r a t e law a u t h o r s * d a t a and  c a l c u l a t i n g changes i n  + +  .  T h i s may  ( E q u a t i o n 18) t o t h e  K + K* £H+] + K + K»  preceding  as shown i n Appendix G.  E f f e c t o f Hydrogen P r e s s u r e . S t i r r i n g V e l o c i t y and T i t a n i u m S u r f a c e on  easily  Area  Rates. The d a t a f o r r a t e measurements at 5 and  p r e s s u r e a t each e x p e r i m e n t a l temperature, rates are f i r s t  o r d e r i n PH «  10 atm.  hydrogen  e x h i b i t e d i n Table 3*  partial  indicate that  T h i s not o n l y i s i n agreement w i t h t h e  2  earlier  r e s u l t s o f P e t e r s and H a l p e r n , ^ but a l s o adds support t o the proposed . 1  mechanism ( E q u a t i o n 1 7 ) .  ; TABLE 3  E f f e c t o f Hydrogen P a r t i a l P r e s s u r e  on-Rates.  C ( V I ) l e v e l » 4X10 3MV _  r  Temp. °C 160° 160° 180° 180° 200° 200°  Two  H atm. P  2  mol-Jr  mol-J-  0.02  0.1  1  5 10 5 10 5 10  experiments,  Rate = mol-  1  -dM/dt mn"  1  .2.66x10-5 5.82x10-5 l.lOxlO" 2.34xl0 3.86xlO" 7.50xlO 4  - 4  4  - 4  performed t o study t h e e f f e c t s o f s t i r r i n g  velocity,  and o f s u r f a c e a r e a o f t i t a n i u m i n c o n t a c t w i t h t h e s o l u t i o n gave t h e f o l l o w i n g r e s u l t s at 200°C.  Reduction  of t h e s t i r r i n g v e l o c i t y f r o m t h e u s u a l 620  t o i+10 rpm had no e f f e c t on t h e r e d u c t i o n r a t e s except t o i n c r e a s e t h e  rpm  time  required f o r saturation of the s o l u t i o n with H  2  as shown i n F i g . 18, Appendix F.  T h i s i n d i c a t e s t h a t t h e s t i r r i n g v e l o c i t y was  s u f f i c i e n t l y high to eliminate  any p o s s i b i l i t y o f r a t e s b e i n g d i f f u s i o n c o n t r o l l e d .  Doubling the surface  a r e a of t i t a n i u m i n c o n t a c t w i t h t h e s o l u t i o n by a d d i t i o n of s u f f i c i e n t "  fine  - 40 -  t i t a n i u m t u r n i n g s a l a o had no e f f e c t that  on t h e r a t e , which confirms t h e  s u r f a c e e f f e c t s on r e d u c t i o n r a t e s are n e g l i g i b l e  Proposed  Mechanism f o r the Qii  t h e i r k i n e t i c s t u d i e s on t h e C u  r e c o m b i n a t i o n , M c D u f f i e and  co-workers^  + +  Reaction.  c a t a l y s e d hydrogen-oxygen  had found - as d i s c u s s e d i n t h e  d u c t i o n - t h a t r a t e s were s e e m i n g l y f i r s t were w i t h o u t  (see F i g . 19, Appendix F ) .  C a t a l y s e d Hydrogen-Oxygen Recombination  ++  In  assumption  order i n C u  e f f e c t on r a t e s , w h i c h i s i n apparent  + +  Intro-  and t h a t a c i d i t y  disagreement  with the  changes obser-  9 v a t i o n s o f H a l p e r n et a l . the r a t i o k _ ] / k  Hence, t h e i r o b s e r v a t i o n s seemed t o i n d i c a t e t h a t  (see E q u a t i o n 4) became n e g l i g i b l y s m a l l a t 250°C.  2  words, the back r e a c t i o n - ( a ) (see E q u a t i o n 3) became unimportant. c o n t r a s t t o t h e f i n d i n g s o f MacGregor and H a l p e r n ^ who 2  from 0.25  (at 110°C) t o 1.3  ( f o r 160°C), s u g g e s t i n g t h a t the back  r e a c t i o n becomes i n c r e a s i n g l y important as t h e temperature Assuming t h a t t h e temperature present  investigation,  independence o f  i s raised.  k_j/k , z  as found i n t h e  (see Table 2) a l s o a p p l i e s a t 250°C, i t i s s u g g e s t e d  t h a t t h e r e s u l t s o f M c D u f f i e e t a l can be r e c o n c i l e d w i t h those o f et for  This i s i n  noted an i n c r e a s e i n  2  k_i/k  In o t h e r  a l by p r o p o s i n g f o r t h e r e d u c t i o n o f 0 ,  an analogous  2  the r e d u c t i o n o f C r ^ ^ ^ s e e  Equation 1?).  Halpern  mechanism, t o t h a t  T h i s mechanism can be w r i t t e n  as f o l l o w s * kl Cu  + +  + H  ^=±  2  CuH  + H  +  (a)  +  k-1 CuH  +  + Cu  CuH+ + 1/2  0  2  + +  i  2 Cu  2  + H  ^  +  +  Cu  + H + +  ( )  +  b  + H0  (c)  2  fast 2 Cu  The  +  + 1/2  0  2  + 2 H  +  —  2 Cu  c o r r e s p o n d i n g r a t e law b e i n g —  + +  + H0 2  (d)  24  - 41 -  - US  =  M 1^1 ^ 1 [0J CH+]+ fei- t] fe M  kl  dt  ]Cu+tl  fax+*\*  +  ^5  +  E q u a t i o n 25 c o n t a i n s t h e e x p r e s s i o n  fe  |u+g  fe[o i 2  +  25(a)  H+l + ^[cV+I + hJ[o which may  be w r i t t e n as K + K«»  25(b)  [H ] + K + K» +  [Cu 3 +  where K i s a g a i n  McDuffie  and K»»  [jb ~J  =  e t a l worked w i t h s o l u t i o n s t h a t were 0.00IM i n  Cu  + +  and  initially  4 about  0,076M i n  0  2  .  ( i n i t i a l oxygen p a r t i a l p r e s s u r e :  a c i d i t y r a n g i n g from 0,005 t o 0.05M i n HC10/,.. k_]_/k^.  400 p s i g ) w i t h t h e  Knowing k _ i / k  2  and  assuming  t o be a p p r o x i m a t e l y the same as k_^/k , i t can be shown t h a t t h e 3  change i n the e x p r e s s i o n  K + K''  i s o n l y about 1 p e r c e n t as a r e s u l t  [JH 1. + K + K " +  of the t e n f o l d i n c r e a s e i n a c i d i t y , f r o m w h i c h i t i s c l e a r t h a t no a c i d on r a t e s can p o s s i b l y be d e t e c t e d . Moreover, the n u m e r i c a l v a l u e of K + K  ,f  Dr*"l + K + K»»  effect  i s so c l o s e t o u n i t y (0.99) under the g i v e n c o n d i t i o n s t h a t  t h e r a t e law must r e a d  - dJHjj =  ^[Cu+3 [HjJ  5  dt as i n f a c t observed  by M c D u f f i e .et a l .  No e x p l a n a t i o n can be g i v e n f o r the i n c r e a s e o f k_;j/k  4  Solubility of 0  2  was  e s t i m a t e d from d a t a of Pray, Schweichert  2  with  and  Minnich  temperature as observed b y MacGregor and H a l p e r n .  T h e i r value  i s admittedly  o f low p r e c i s i o n because o f t h e method used f o r measuring r a t e s , w h i c h was t h e estimation analysed  of i n i t i a l s l o p e s on r a t e curves t h a t were n o t m a t h e m a t i c a l l y  along t h e i r e n t i r e l e n g t h .  explanation  I f the high value  i s i n fact v a l i d , the  must l i e i n a y e t u n e x p l a i n e d d e v i a t i o n i n t h e mechanism when copper  i t s e l f i s being  reduced.  CONCLUSIONS  The  k i n e t i c s o f t h e homogeneous a c t i v a t i o n of hydrogen by C u  + +  i n aqueous s o l u t i o n were i n v e s t i g a t e d i n t h e temperature range o f 160° t o 200°C.  A s i g n i f i c a n t dependence o f r a t e s on  concentration  was  o b s e r v e d and a mechanism, s i m i l a r t o t h a t developed e a r l i e r by H a l p e r n and co-workers,  9  The  was proposed t o account f o r t h i s  r a t e constant  r a t i o s o f rate constants f o r 160°,  observation.  k-|_ f o r t h e hydrogen a c t i v a t i o n step and t h e  o f subsequent steps,' k_^/k  2  and k_]_/k , were determined  180° and 200°C by means o f t h e r a t e e x p r e s s i o n  3  derived from the  above mechanism.  The  e n t h a l p y o f a c t i v a t i o n c a l c u l a t e d from t h e s l o p e o f a l o g ^1 T vs i p l o t was t h e same w i t h i n l i m i t s o f e r r o r as t h a t found by P e t e r s ^ i n a T "v 2  similar  study.  The  ratios k_i/k  2  and k_]_/k were found t o be temperature independ3  ent w i t h i n l i m i t s o f e r r o r s u g g e s t i n g r e a c t i o n s with rate constants  k.^, k  b l y small, which implies that  CuH  +  that t h e a c t i v a t i o n energies 2  and k  3  for the  a r e e q u a l and p o s s i b l y n e g l i g i -  may be t h e a c t i v a t e d  complex.  - L3 I t was shown t h a t a mechanism s i m i l a r t o t h a t found i n t h i s g a t i o n may e x p l a i n s a t i s f a c t o r i l y t h e apparent d i s c r e p a n c y kinetics of the C u  + +  oxygen r e c o m b i n a t i o n  investi-  between t h e  c a t a l y s e d hydrogen r e d u c t i o n o f C r ^ ^ and the hydrogen1  reaction.  On t h e b a s i s of t h e o b s e r v a t i o n s  i n this  i n v e s t i g a t i o n and the  c o n c l u s i o n s d e r i v e d t h e r e o f a g e n e r a l mechanism f o r t h e a c t i v a t i o n o f H Cu  + +  and t h e o x i d a t i o n o f t h e i n t e r m e d i a t e k  Cu  + +  + H  CuH  +  2  may be w r i t t e n as f o l l o w s ?  I CuH  P  +  + H  (a)  +  26  Zkji CuH  where  +  + ZOx  —•  Intermediates  S ) x i s t h e sum o f a l l o x i d a n t s  t h e sum o f t h e c o r r e s p o n d i n g  rate  fast -»• Products  capable  constants.  by  (b)  o f o x i d i z i n g CuH  +  and J J C T J  - 44 REFERENCES  Can. I n s t . M i n . and Met. B u l l . , ^6: 677  1.  F.A. Forward,  (1953).  2.  R.N. O ' B r i e n , F.A. Forward  3.  I.H. Warren, t o be p u b l i s h e d .  4.  J . H a l p e r n , Advances i n C a t a l y s i s , 11:301 (1959).  5.  H.F. .McDuffie and Co-workers, J . Phys. Chem. 26:1030 (1958).  6.  V.N. I p a t i e f f  7.  J . H a l p e r n and R.G. Dakers, J . Chem. Phys. 22:1272 (1954).  '8.  E . P e t e r s and J . H a l p e r n , Can. J . Chem. 3_3j356 (1955).  9.  J . H a l p e r n , E.R.-MacGregor and E . P e t e r s , J . Phys. Chem. 60:1455  and J . H a l p e r n , T r a n s . C.I.M.M., £6:369 (1953).  and W. Werschowski, Ber. ^2:2078  (1909).  (1956).  10.  E . P e t e r s and J . H a l p e r n , J . Phys. Chem. J59/-793 (1955).  11.  A.H. Webster and J . H a l p e r n , J . Phys. Chem. 60:280 (1956).  12.  A.H. Webster and J . H a l p e r n , J.. Phys. Chem. 61:1239 (1957)  13.  L. Wright, S. W e l l e r and G.A. M i l l s ,  14.  A.H. Webster and J . H a l p e r n , T r a n s . F a r a d . S o c , 53_:51 (1957).  15.  G . J . K o r i n e k and J . H a l p e r n , J . Phys. Chem. 60:285 (1956)  16.  M. C a l v i n , J . Am. Chem. Soc. 61:2230 (1939)  17.  S. W e l l e r and G.A. M i l l s , J . Am. Chem. Soc. 25_ 769 (1953)  18.  A . J . Chalk and J . H a l p e r n , J . Am. Chem. Soc. 81:5846, 5852 (1959  19.  H. H a l p e r n , J . F . Harrod and P.E. P o t t e r , Can. J . Chem. 3.7.1446 (1959).  20.  J . F . Harrod and J . H a l p e r n , Can. J . Chem. 3_7_:1933 (1959).  21.  J . H a l p e r n , J . Phys. Chem. 63j398 (1959).  22.  W.K. Wilmarth  23.  E. P e t e r s , Ph.D. T h e s i s , The U n i v e r s i t y o f B r i t i s h Columbia, 1956  24.  E.R. MacGregor, Master's  25.  E.R. MacGregor and J . H a l p e r n , T r a n s . A.I.M.E. 212:244 (1958).  26.  J.Y-P. Tong and E . L . K i n g , J . Am. Chem. Soc. 7£:6l80 (1953)  J . Phys. Chem. j£:1060 (1955)  ;  and A.F. Kapanan,  J . Am. Chem. Soc. 7Jhl308  (1956)  T h e s i s , The U n i v e r s i t y o f B r i t i s h Columbia,  1956.  - 45 -  REFERENCES  (cont'd.)  27.  R.T. McAndrew,  private  communication.  28.  H.A. Pray, C.E. Schweichert and B.H. M i n n i c h , I n d . Eng. Chem. L±tllk6  (1952)  - U6 APPENDIX A  Compounds T r i e d f o r P o s s i b l e Use as S u b s t r a t e s S e v e r a l compounds  besides N a C r 0 2  2  7  were t r i e d t o determine i f any  might s e r v e as s u i t a b l e s u b s t r a t e s f o r o b s e r v i n g t h e r a t e of a c t i v a t i o n o f hydrogen by C u  + +  ions.  The f o l l o w i n g r e s u l t s were o b t a i n e d :  Re s u i t  Compound Na Cr 0 2  2  was found t o be s t a b l e i n s o l u t i o n and r e a d i l y  7  r e d u c i b l e by hydrogen.  NaV(OH)^  On h e a t i n g V ( 0 H ) 4 ~ decomposed w i t h t h e f o r m a t i o n o f a r e d d i s h brown p r e c i p i t a t e , presumably V 0 . 2  NalO,  Reduction loss of I  NaCIO,  o f I 0 ~ t o both 3  2  I " and I  2  5  took p l a c e  by e v a p o r a t i o n .  C 1 0 ~ decomposed on h e a t i n g t o C l ~ and p r o b a b l y 3  (solution turned yellowish green).  NaBrO.  B r 0 ~ decomposed t o B r 3  solution.  causing  2  and B r ~ upon h e a t i n g o f  C10  2  - 47 APPENDIX B  Consumption o f H  H  +  +  Ions Due t o R e d u c t i o n o f C r ^  V I  ^  i o n s w i l l be consumed upon hydrogen r e d u c t i o n o f Cr (VI)  Assuming f o r convenience  t h a t Cr  K  (VT) J  i s mostly HCrCV,  26  this reduction  w i l l take p l a c e a c c o r d i n g t o t h e e q u a t i o n ;  HCrOiT + 3/2 H  2  + 4 H  +  —  Cr  + + +  . + 4 H0  (27)  2  T h e o r e t i c a l consumption c u r v e s and e x p e r i m e n t a l p o i n t s o b t a i n e d , by p o t e n t i o m e t r i c t i t r a t i o n w i t h 0.1 N borax s o l u t i o n , from runs at 160°, 180° and 200°C a t s e v e r a l i n i t i a l a c i d l e v e l s , are d e p i c t e d i n F i g . 17. appears  t h a t i n most cases t h e a c i d consumption i s l e s s than  which i s p r o b a b l y of  Cr  + + +  .  a result of p a r t i a l regeneration of H  +  It  theoretical  i o n s by h y d r o l y s i s  6  i  u ©  I .a  o  Q  o  o 2 -  P  A  0.1  0.05  0.2  0.3  0.35  0.4  0.5  M o l e - L i t e r -1 Fig-  17.  Consumption o f H  +  Ions Due t o R e d u c t i o n o f Cr  (VI) — T h e o r e t i c a l Curves; O • A P o i n t s O b t a i n e d from V a r i o u s Experiments at 160°, 180° and 200°C.  i i  - 49 APPENDIX C  Estimation o f Errors Occurring i n the Evaluation of k i  Based on t h e maximum d e v i a t i o n s o f t h e i n t e r c e p t s i n F i g u r e s 4, 5 and  6 and on e r r o r s i n hydrogen s o l u b i l i t y and hydrogen p a r t i a l  measurements, t h e average e r r o r i n l a t i o n o f these v a l u e s  was estimated  t o be il3%o  pressureIn the c a l c u -  i t was assumed t h a t the s o l u b i l i t y o f hydrogen  was measured f o r d i s t i l l e d water) was e s s e n t i a l l y u n a f f e c t e d by 3 x  (which  10"%  -3 N a C r 0 , 2 x 10 1 2  2  7  Cu(C10 ) if  2  and 0.05  t o 0.5M  HCIO4 i n s o l u t i o n .  I t was  f u r t h e r assumed t h a t Henry's Law was obeyed i n t h e r e g i o n o f p r e s s u r e s i . e . , 5 t o 10 atm, H  2  used,  gas.  The f o l l o w i n g e r r o r s were taken i n t o account:  1)  Errors i n the concentration of H o f accuracy  of pressure  3)  Errors i n cupric perchlorate  4)  *3$.  27 s o l u b i l i t y measurements ±3%.  Errors i n H  not  d i s s o l v e d i n s o l u t i o n due t o t h e l i m i t  gauge r e a d i n g s  2)  2  2  c o n c e n t r a t i o n were l e s s t h a n 0.5$  and were  considered.  E r r o r s due t o i n a c c u r a c y i n d r a w i n g o f t h e r e d u c t i o n curves and i n a n a l y s i s were estimated t o be o f t h e o r d e r o f greatest curvature of the reduction p l o t s .  [Jr^^J  w i t h i n the region of  These e r r o r s were g r e a t e r a t  b o t h ends o f t h e r e d u c t i o n p l o t s ( F i g u r e s 1, 2 and 3) p a r t i c u l a r l y a t the start of reduction.  Hence, r a t e measurements f o r d e t e r m i n a t i o n  were c o n f i n e d t o t h e r e g i o n o f h i g h e s t  o f k]^  curvature o f t h e r e d u c t i o n p l o t s .  5)  E r r o r s i n r a t e measurements by t h e mirror-image method *3%.  6)  E r r o r s i n i n t e r c e p t measurements ( F i g u r e s 4, 5 and 6) *6$.  Since e r r o r s  4) and 5) are i n h e r e n t i n 6), an average e r r o r o f (6% + 3% + 5 % ) * 2 =r7% was  assumed.  - 50 -  APPENDIX D Summary of Rate Measurements TABLE 4 (a)  Effect of Perchloric Acid Concentration on the Rate o f the C u Catalyzed Hydrogen Reduction of C r ( ) . Cu(C10^) " 0.02M, P = 10 atm. ++  V I  2  Q-cioJJ mol-JT  Expt. No.  1  (CrCVlOlevel mol-X" 1  (i) ~> 0.009 1t tl 0.01  '• •  Ac ^ 1  1  A  1 6 0  -,-,  Ac — 1 1  Ac ! ^ 1  0  Ac ! ^ 1  4  0  .d[Hj/dt** mol-_£- -niirrJi  L  (-d[H3 / d t j -  1  j^-min-mol"- 1  160°C (Fis. U) •  1.6x10-3 2.4 3.2 4.0  »» •' » t  1.6  tt  0.045 0.047  2.4 3.2 4.0  " " "  0.087 0.090 0.092 0.094  1.6  t »  2.4 3.2 4.0  " " "  0.1B9 0.191 0.193 0.195  1.6  »»  2.4 3.2 4.0  " " "  0.345 0.346 0.348 0.350  1.6  "  2.4 3.2 .4.0  »»  0.484 0.487 0.490 0.493  1.6  "  2.4 3.2 4.0  " " »»  0.039 0.042  Ac ^  H  t.  ««  6.95x10-5 7.43 " 7.65  8.06  "  1.44x10^ 1.34 " 1.31 " 1.24  "  5.23 " 5.47 " 5.73 " 5.92 ••  1.91 1.83 1.74 1.69  " " " "  4.63 5.02 5.35 5.82  2.16 tt 1.99 " 1.87 ' t 1.72 tt  " " " "  "  3.20 2.86 2.62 2.31  tt tt tt "  1.92 2.34 2.72 3.07  " " tt "  5.22 4.28 3.67 3.26  tt " t,  1.50 1.77  " tt  6.66 " 5.63 " 4.85 »• 4.18 t,  3.12 3.49 3.82  tt  4.32  2.06  2.31  tt  "  tt "  tt  Slight adjustments of acidity which were made for each Cr (VI) level at which rates were measured were estimated from Fig. 17 Appendix B, and i n i t i a l acidities. 5  dpj/dt -  3/2  x^d&rO^  (Table 4 continued  - 51 APPENDIX D - T a b l e 4 (cont'd.) Expt. No. .  •  DiClOj mol-/-1  (Gr(VI)J l e v e l mol-2.-1  r.  130 Ac - 2  180 Ac - 1  180 Ac - 5  180 Ac - 4  180 Ac - 3  .(ii)  -dfHj/dt mo 1-2-1 -min-1  - d ^ / d t X-min-mol-I 1  180°C ( F i g . 5)  1.6x10-3  2.21x10-4  " " "  2.29  "  0.045  2.4 3.2 4.0  2.43 2.50  " "  0.087 0.090 0.092 0.094  1.6 2.4 3.2 4.0  " " " ''  1.80 2,02 2.18 2.34  " " " "  0.189 0.191 0.193 0.195  1.6 2.4 3.2 4.0  " " " "  1.26 1.45 1.60 1.75  "  7.97  "  " "  6,23 5,70  " "  0.341 0.343 0.345  0.346  1.6 2.4 3.2 4.0  " '* " "  0.826 1.01 1.20 1.32  '' •» »• »*  12,1 9.90 8.34 7.58  " " " "  0.484 0.487 0.490 0.493  1.6 2.4 3.2 4.0  " " "  0,606  "  0.793 0.886 1,00  " »' ««  0.035 0.038 0.041  ft  4,52x103 4.36 " 4.12 " 4.00 " . 5.50 " 4.95 " 4.58 «• 4.27 "  6.90 "  16.5 12.6 11,3 10.0  " " '' ''  ( i i i ) 200°C (F i g , 6) Ac2Q0  2  0.045 »' • '  :  »» »»  200 Ac - 7  200 Ac - 6  0.088  0.090 0,092 0.095  2  200 Ac - 4  1.6 " 2.4 " 3.2 " 4.0 "  6.66x10"  1.50xl03  7.08  1.41  ;  0 9 9 9 » 9  N.B, used average r a t e and a c i d i t y values. 4  7.29 7.50 4.18  0.193 0.195  0,340 0,343 0,345 0.346  1.6 2.4 3.2 4.0  " " " "  3.06 3.69 4.16 4.47  0.484 0.488 0.490 0.493  1.6 2.4' 3.2 4,0  " " " "  2.27 2.79 3,24 3,65  0.191  Ac °°3  9,0x10T4-  1.6 " 2.4 " 3.2 «» 4.0 "  0.189  1.11x103  1,6x10-3 2.4 " 3.2 " 4.0 "  4.74 5.66 6.13  « » ? ?  11  »t »t  »t »»  » »  »t  i»  •i  r  • »t »»  »»  1.37 1.33 t ? 2.39 «t 2.11 1 1 1.77 » t 1.63 »t 3.26 2,71 2.40  »?  ? i »?  2.24  »«  »?  4.40  » 9  « ?  3.58  9 9  2,74  9 9  »?  t«  3.08 t t  - 52 APPENDIX D - Table 4  (b)  (cont'd.)  E f f e c t o f D i s s o l v e d C u p r i c P e r c h l o r a t e on t h e Rate o f C r ( V l ) R e d u c t i o n by' Hydrogen. PH  2  = 10 atm.  (Fig. 16).  a  9 Expt. No.  Initial'  [0u++ ]  [Hcial mol-/ ~  L  0.1 »t  Cu' - 2  »t 11 11  200-  0.1  Cu - 2 Ac . ?  »t  4.0xlO"  0.06  »i  ,0.08 0.10  i»  Cu °5  « »  Cu °°I 20  2  0  20  4>  G  t! tt 0.5  Ac - L  »1  »t  Cu 2°8  J 1  Cu °°9  » t  2  2  1 « t t  u °°8 Cu 2° 2  2  9  tt tt t t  0.0074 0.01 0.02 0.03 0.04 0.01 0.02 0.04  0.06  1  3  it  2  mol--min"  1  .0.582x10""-*  1.12 1.53 2.02  11  " " »»  2.54  200°C 4.0xl0-  3  i»  11  «i • i  » i  ?t 11  0.01 0.02 0.04  1.6x10-3  0.08  11  11  •t  10.9  "  15.7  "  14.8  «»  11  2.84x10"^ 4.11 " 7.50 "  1.84 3.65 6.98 9.75  11  0.08  0.06  -d[H ]/dt  160°C  0.02 0.04  (ii) r  level  mol-X"  mol-X~^" (i)  160 Ac - 5  [ C r ™ ]  '* , " " " t i  1.01  t i  2.27 5.06  t i  8.13  11.4  Continued,......  " "  "  - 53 APPENDIX D - Table 4 (cont'd.)  (c)  Rate Measurements and Rate F u n c t i o n R* at V a r i o u s C r ^ ^ L e v e l s . 1  (i)  160°C, [ C u + + J  =.0.02 mol, P  = 10 atm ( F i g . 9)  H  k [ C u ] ] JH ] = 1.27x10-6 m o l - i - 1 - s e c - 1 ++  x  Expt. N o  mol-/"  AO - !! 1  r  1  0.186 0.187 0.188 0.189 0.190 0.191 0.192  60  0.193 0.194 0.195 0.196 0.198 0.199 0.338 0,339  0.340  0.341 0.342 0.343 0.344 0.345 0.345 0.346 0.347 0.348 0,349  160  0,480 0,481 0,483 0.484 0,486 0.487 0,489 0.490  Ac - 13  0.492 0.493 0,495 0.496 0,498 £  IdQjJ/dt  [c (VIlevel  [HClOj  '  2  R « (Rate) xCH + H (Ro - Rate)  mol-X"  mol-^"  1  0.4x10-3 0.8. "  1.2  »» " »' ' • " " " " "  0.4 0.8 1.2 1.6 2.0 2.4 2.8 3,2 3.6 4.0 4.4 4.8 5.2  *' »» »• " '' " «• " " " " " •»  0,4 0.8 1.2 1.6 2.0 2,4 2,8 3.2 3.6 4.0 4.4 4.8 5.2  "  wh  =  H  " " •» »• "  0,236 0,243 0,299 0,320 0,364 0.389 0,421 0.468  " " " ' • " " " »»  • 0,490  "  0.512 0,555 0.575 0.610  " " »*  _ r -J d  0.678 0.723 0,742 0.781 0,789  0,172 0,190 0,214 0.250 0,276 0,296 0,324 0.343 0.361 0.386 0,407 0,427 0.456 a n d  -4=^1.  ft* - d [ H ] / d t = 3/2. x l / 6 0 ( - d [ C r ( V I ) J / d t ) 2  mol-i" 0,098 0.106 0,118 0,131 0.145 0.162 0.184 0.194 0.222 0.258 0.275 0.316 0.326  0.637  «« " '» " »' «» '« •' " " " R a t e  -sec-1  1  0.436x10-6 0.460 " 0.488 »» 0.519 " 0.550 •» 0.583 0.621 "  "  1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2  R  M  0.077 0.082 0.105 0.115 0.137 0.151 0.171 0.201 0.217 0.234 0,269 0,288 0,323  " " " »' " " " " " »» " " R o  =  kxfcu+firH  0.075 0.085 0,098 0,118 0.135 0,148 0,167 0.181 0.196 0,215 0,234 0.251 0,279  -"-i- - " -  1  APPENDIX D- - Table 4 (cont'd.)  (c) c o n t ' d .  ( i i ) 180°C, [ C u J + +  = 0.02 mol,PH  = 10 atm (Fig.10)  k] [Cu - J[K ] = 5.02x10-6 +  mol-i-l-sec"  ;  2  Expt. No. Ac  1 8  ^  180  Ac - 4  Ac °3 1 8  1  R  mol-i"  1  mol-X"-'— s e c "  mol-/"I  0.186 0.187 C188 0.1«V 0.190 0.191 0.192 0.193 0.194 0.195 0.196 0.198 0.199  0.4x10-3 0.8 J » 1.2 V 8 1.6 tt 2.0 t J 2.4 . 8 « 2.8 t 8 3.2 t! 8 ! 3.6 « 8 4.0 8 » 4.4 4.8 t 8 5.2 8 8  1.53x10=6 »« 1.73 1.91 8 0 2.09 9 9 t8 2.27 9 9 2.42 » 8 2.56 2.68 t ? 2.82 J ? 9 9 2.92 3.09 9 t 9 9 3.17 » 9 3.28  0.338 0.339 0.340 0.341 0.342 0.343 0.344 0.345 0.346 0.346 0.347 0.348 0.349  0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2  0.997 1.12 1.22 1.38 1.54 1.68 1.85 2.00 2.08 2.20 2.34 2.51 2.62  0.480 0.481 0.483 0.484 0.486 0.487 0.489 0.490 0.492 0.493 0.495 0.496 0.498  0.4 0.8 1.2 1.6 2.0 2o4 2.8 3.2 3.6 4.0 4o4 4.8 5.2  8 8 8 8  ? »  « J  t8 8 ?  tt 8 8  f  8  9 t 9 »  t  1 ? 9 9 ? 9 » ! 9 8 ! 8  9  8  9  8 5 8 8 8 8  t  8  J  8 8 8 8  J  i  0,620 0,813 b0.932 1.07 1.20 1.32 1.39 1.48 1.57 1.67 1.71 1.75 1.83  9 8 9  9  9 9 9 9 9 9 9 9  9  9  8 8  S  8  9  8  T  8  9  8  1  f  1 8 8 8 8 8 9 9 9 8 9 9 8 9 8 8 8 8 0 8 8 9 8 8 8 8  1  mol-^"  1  0,082 0.098 0.116 0.135 0.157 0.178 0.200 0.221 0.248 0.271 0.314 0,342 . 0,376 0,084 0.097 0,109 0.128 0,151 0.173 0.201 0.230 0,244 0,270 0,302 0,348 0,381 0,068 0.094 0.110 0,131 0.154 0.174 0.189 0.204 0,224 0,246 0,255 0,266 0,287 Continued......  APPENDIX D - Table 4 (cont'd.) (c)  cont'd,  £Cu fj +  ( i i i ) 200°C,  0,02 mol, P H = 10 atm ( F i g , 11) 2  = l&LxHT  Expt, No. 200, Ac - 6  200 Ac - 3  . 200. Ac - 4  [HCIO^D mol-£~l  Dr(vD:J  level  mol-^  6  mol-/"  -d[H ]/dt  0,186 0.187 0.188 0.189 0.190 0.191 0.192 0.193 0.194 0.195 0,196 0.198 0.199  0,4x10-3 8 0 0.8 8 5 1,2 8 5 1.6 J 8 2.0 8 8 2.4 9 9 2.8 9 8 3.2 9 9 3.6 8 9 4.0 0 9 4.4 8 8 4.8 8 8 5.2  0.336 0,338 0.339 0.340 0.342 0.343 0.344 0.345 0.346 0.346 0.347 0,348 0.349  0,4 0.8 1.2 1,6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2  0,480 0.481 0,483 0.484 0,486 0.487 0.489 0.490 0,492 0.493 0.495 0,496 0.498  0.4 0,8 1.2 1.6 2.0 2,4 2.8 3.2 3.6 4.0 4.4 4.8 5.2  8  8  8 8 1 t 9  8  9 8  9 9  8 8 8 8  8 8 8 9  8 8 1 9  T 9  9  9  8 9 9 8  8  9  8  8  8 9  8  8  8 8 0 8 9 8 9 8 9 8 9 8  -sec-1  .4.87x10-6 5.72 7.00 7.66 8,31 8.73 9.02 9.53 9.89 10.3 11,0 11.3 11,3  •  8  8  8 8  9  8  0 9 9 9 8 9 8 8  9  9  9 3 9  8  9  8  8 8  3.44 4.06 4.60 5.11 5.64 6.15 6.60 6,93 7.29 7.45 7.73 7.86 7.90  8 9  2,69 2.97 3.36 3.78 4.18 4.68 5.10 5.40 5.78 6,08 6,43 6,93 7.43  8 9  9 9  1  8  8  8  8  8  8 9  8  8  9 9  9  9  8  9  t ! 9 » »"»  9 8 8  9  8  9  8 8  8  8  8 8  9 0 9  -sec"  1  R  2  molrA  1  8  9 9 8 8 8 8 3 8  mol-/-  1  0.067 0,086 0,118 0.139 0,161 0.178 0,191 0.214 0,233 0,257 0,302 0.3*29 0.330 0,079 0,101 0,116 0,134 0.155 0,176 0,197 0,214 0,233 0,242 0.258 0.268 0,270 0.084 0.096 0,110 0,128 0,150 0-„ 168 0,192 0,208 0,231 0,250 0,273 0,308 0.347  Continued .......  APPENDIX D - T a b l e L (cont'd.)  (c)  ( i i i ) cont'd. 200°C, [ C u 3u+ l k  |cr(VI)] l e v e l  £HC10j  -  mo 1-^-1  mol-/-l  0.480 0.481  0.4x10-3  0.483 0.484 0.486  0.487 0.489 0.490  0.492 0.493 0.495 0.496 0.498  *  [ C u ] = 0.01 M + +  ] = 0.02 mol, P = 10 atm (Fig.11) H " m o l - i ' -sec-1  C "-l L~J  Expt. N o  + +  0.8 " 1.2 " 1.6 " 2.0 ' » 2.4 " 2.8 t . 3.2 " 3.6  4.0  4.4  4.8 5.2  "  " " " "  H  =  1  8  i  x  1  0  6  1  -dfrtj/dt m o > / - l -sec"!  0.91xlO" 1.21 " 1.46 " . 1.68 " 6  1.91 2.13  2.43  " "  "  R mol-i'l  0.054 0.074  0.093 0.110 0.130  0.150 0.178  2.83 3.06 3.16 3.26  " " " "  "  0.211 0.224 0.252 0.266 0.279  3.31  "  0.288  2.72  - 57 APPENDIX E  TABLE 5  S l o p e Measurements o f R a t e ~ l vs [H" ] P l o t s o f 1  F i g u r e s 4* 5 and 6 , and V a l u e s o f S*„  [prlVijJ level  Slope ^  mol-£-l  2  '  „min-mol*"  mol -X° 2  (1)  1.6xl0 3™~*™~" =  2„4  3o2 4.0  8 8  2  -min*"!  160° C 0,927x10=> 1.17 1.40  10o8 x l O ^ 8,54 7.12 " 5.62 0 8  0 9  8 8  S  2  5 0  8 8  1 8  **  (ii)  180 °C  1.6x10=3  2,64x104  3,79x10-5  2,4 3»2 4.0  1 88 1,55 1,28  5,32 6,46 7.84  0 8  0  8  »  8 8  " " 5 5  (iii) 1.6x10-3 2,4 3,2 4.0"  4  0,714xl0 0,546 0,436 0,374  14,0x10 -5 18,3 22.9 26,7  4  8 8  8 8  8 8  8 8  S = Slope"  o  8 8  5 5  1  8 8  200 C  8 8  8 8  8 8  8 5  8 8  - ^[Cu^]^] jk /k 2  [cu ^ + +  = 1  k /k 3  = 1  (Equation  - 58 APPENDIX F E f f e c t of S t i r r i n g V e l o c i t y and  Two  Surface  Area on  Rates.  experiments were performed t o t e s t whether at 200°C r a t e s  c o n t r o l l e d by d i f f u s i o n o f hydrogen from t h e  gas-to the  liquid-phase,  whether the t i t a n i u m s u r f a c e i n c o n t a c t w i t h the s o l u t i o n had any  are  and  catalytic  e f f e c t on r a t e s . In the f i r s t normal 620 w i t h one It  rpm t o 410  obtained  rpm,  and t h e  reduced from the  r e s u l t i n g reduction  curve was  compared  under i d e n t i c a l c o n d i t i o n s but at the u s u a l s t i r r i n g  i s e v i d e n t , as seen i n F i g . 18, t h a t the  lowering for  case, the s t i r r i n g v e l o c i t y was  rate.  r e d u c t i o n r a t e s are u n a f f e c t e d  by  o f t h e s t i r r i n g v e l o c i t y except i n i t i a l l y where the time r e q u i r e d  d i s s o l u t i o n of H  i s g r e a t e r f o r the  2  410  rpm  assumed t h a t r e d u c t i o n r a t e s are not d i f f u s i o n  run.  Hence, i t may  c o n t r o l l e d under the  be experi-  mental conditions used. In t h e  second case,  a p p r o x i m a t e l y f i v e grams of f i n e t i t a n i u m  t u r n i n g s , whose s u r f a c e a r e a was  estimated  t o be e q u a l t o t h a t of a l l t i t a n i u m  p a r t s i n c o n t a c t w i t h the s o l u t i o n , were added. shown i n F i g . 19,  and  compared w i t h  s u r f a c e a r e a , i n d i c a t e s t h a t the  decomposition of C r ^ ^ , 1  s t a b i l i t y of C r ^ ^ V I  V I  be due  50% HN0  3  shown In F i g . 19,  p r i o r t o the  a l t h o u g h t h e y had  experiment.  Its eventual  t o the p a s s i v a t i o n of t i t a n i u m by f o r m a t i o n  held  a  place  r e s u l t e d f r o m the o x i d a t i o n o f  s u r f a c e o f t h e t i t a n i u m t u r n i n g s by C r ^ ^ minutes i n  As  the s o l u t i o n was  which soon l e v e l l e d o f f d i d take  i n i t i a l l y . " This decomposition probably  10  curve,  r e f e r r i n g t o t h e normal t i t a n i u m  5 hours at 200°C p r i o r t o hydrogen a d d i t i o n .  slight  r e s u l t i n g reduction  c a t a l y t i c a c t i v i t y of t i t a n i u m i s n e g l i g i b l e .  I n order t o t e s t a l s o the for  one  The  the  been b o i l e d f o r stopping  of a coherent oxide  may film.  F i g . 18.  Comparison o f Cr ^ ' R e d u c t i o n Curves Showing N e g l i g i b l e S t i r r i n g V e l o c i t y E f f e c t on R a t e s . F o r Both Experiments: 200°C; 0.02M C u ( C 1 0 ) | 0.35M HC10 ( i n i t i a l ) ; 10 atm.H . 4  2  4  i  2  1  r  1— Q C r ^ l ) reduction with twice the usual t i t a n i u m surface area i n contact w i t h the s o l u t i o n .  Pre-reduction plot showing some d i s a p p e a r ance of C r ' * I ) ; apparency owing t o r e d u c t i o n by f r e s h t i t a n i u m t u r n i n g s . Note l e v e l l i n g o f curve.  • C r ^ " ^ reduction with the usual titanium surface area i n contact with the s o l u t i o n .  introduced  -Time r e q u i r e d t o heat s o l u t i o n from room temperature t o 200°C.  Note change o f time -1  1  2  2  Hours  scale 10 Time  F i g . 19. Comparison o f Cr E f f e c t ' o n Rates. 10 atm. H . 2  Minutes  Reduction Curves S h o w i n g ' N e g l i g i b l e T i t a n i u m S u r f a c e Area F o r Both. Experiments: 200 C; 0.02M C u ( C 1 0 j ; 0.35M H C 1 0 ( i n i t i a l ) ; 6  2  4  APPENDIX G  The o r d e r o f dependence of r a t e s on G u of  t h e magnitude of the  K + K' * '[H 3 + K + K°  o r Cr  + +  (VI)  change i n t h e n u m e r i c a l v a l u e o f the  is a function expression  ( E q u a t i o n 18(b)', with a change i n e i t h e r K o r K°  9  respective-  5  +  ly  w h i l e the o t h e r terms of the e x p r e s s i o n are h e l d c o n s t a n t .  s  t a b l e shows "that dependence o f r a t e s on e i t h e r C u  + +  or C r ^ - ^  The  subsequent  i s shifted  toward h i g h e r o r d e r whenever the magnitude of t h e above change, expressed i n percent, i s large, TABLE 6 (a)  Order o f C u  + +  Dependence of Rates R e l a t e d t o  K + K" Percent Change of  J*H+] + K + K°  E  &*]  |Gr(VI)j  3 u + 4  1)  With Changing K (i„e,  200°C,  a t  Ratios  Percent I n c r e a s e in Ratio  K + K  fH 1+ K + K' +  4x10-3 4x10-3  0,1 0,1  0,0075 0,04  Observations  Observations 0,01 0,08  first  4x10-3 xlO-3  order i n C u , 0,31 0.44  1.6x10-3 1,6x10-3  0.5 0,5  +  0.16 0.36  toward second  K« = k a / k . i l g r C ^ ' J .  and  (compare w i t h T a b l e  +  k  = i  1  /k  3  = 0.02  L2%  order i n Cu '  K = k /k_ |Ju tl 2  Curve A, F i g . ,16  +  Rates a p p r o x i m a t e l y f i r s t  O b s e r v a t i o n s Rates s h i f t  ±  0,69 0.75  Rates a p p r o x i m a t e l y  0.50,5  0.01 0,08  ,  + s  1 |  order i n C u  Curve B, F i g , 16, 125%  + +  , Curve C  For s i m p l i c i t y k ^ / k g 2)  9  ,Fig„ 16,  =  0,40  - 62 APPENDIX G - Table 6 (cont'd.) (b) Order of C r ( ) Dependence of Rates Related to Percent VI  Change of fcH ^ + K + K* With Changing K« (i.e.,[Cr( )J) 4  [Cu 1 m-^-I  JJH+j m-Jt  0.08 0.08  0.5 0.5  ++  Observation: 0.01 0.01  Qcr( )] m-l' VI  1  0.5 0.5  at 200°C.  VI  1  1.6x10-3 4.0x10-3  Ratio:  1^2  K + K' + K + K'  0.36 0.44  Percent Increase i n Ratio  I f  .  Rates approximately'zero order i n C r ^ ^ Curve A, F i g . 15. 1.6x10-3 4.0x10-3  0.16 0.31  I *  ' V  V  Observation: Rates approaching f i r s t order i n C r ^ ^ Curve E, F i g . 15. 1  0.02 0.02  0.05 0.05  1.6x10-3 4,0x10-3  0.72 I 0.83 \  -.c^  Observation: ' Rates approximately zero order i n C r ^ ) Curve A, Fig,-3 1  0.02 0.02  1.50 1.50  Observation:  1.6x10-3 4.0x10-3  0.08 I 0.14 J  7  5  /  3  Rates approaching f i r s t order i n Cr.(VI) Curve F, F i g , 3. Kyxj  

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