The Mechanism of the Zinc(ll)-Zinc Amalgam
Electrode Reaction in Alkaline Media
As Studied by Chronocoulometric and
Voltammetric Techniques
DeWitt A. PayneI and Alien J. Bard*
Department o] Chemistry, The University of Texa~ at Austin, Austin, Texas 78712
ABSTRACT
The reduction of zinc (II) and the oxidation of zinc a m a l g a m was studied in
0.18-4.0M KOH solutions. The p r i m a r y electrochemical technique employed
was potential step chronocoulometry with data acquisition on a small digital
computer. The kinetic parameters were obtained by fitting the e x p e r i m e n t a l
c h a r g e - t i m e curves to the complete theoretical equation for a stepwise electron transfer mechanism. The sytem was also studied b y d-c and a-c polarography and linear scan voltammetry. The results of this study were compared to those of previous workers a n d shown to be consistent with a mechanism based on stepwise electron transfer
Zn(OH)42- ~ Zn(OH)~ + 2 O H Zn (OH) 2 + e ~---Zn (OH)=Zn(OH)2- ~- Zn(OH) + OHZ n ( O H ) ~u Hg -t- e ~=~Zn(Hg) -b O H One of the most significant features of the study of
electrochemical kinetics during the last 20 years has
been the evolution of theoretical and e x p e r i m e n t a l
procedures which are useful in uncovering the different stages in the complex series of processes which
comprise an electrode reaction. A n investigation of the
kinetics of an electrochemical reaction would ideally
lead to the elucidation of the n a t u r e of the various
steps and a d e t e r m i n a t i o n of their rate constants, the
identification of the intermediates and products, and
the d e t e r m i n a t i o n of the adsorption isotherm for all
adsorbed species. Usually, because of e x p e r i m e n t a l
and theoretical limitations, only part of the i n f o r m a tion is accessible for a given system. Although characterization of intermediates is of prime importance, direct observation of these m a y not be possible if their
concentrations are too low or their lifetimes are too
short. However, analysis of the c u r r e n t - p o t e n t i a l relationship obtained by several n o n s t e a d y - s t a t e methods
can yield f u r t h e r i n f o r m a t i o n on complex mechanisms
and faster processes.
Of particular interest in this work is the study of
electrode processes involving more t h a n one electron
transfer step (1). Vetter (2-4), H u r d (5), and Mohilner
(6) have calculated the steady-state polarization
curves for a set of two or more consecutive single electron transfer steps. Some reactions for which consecutive electron transfer mechanisms have been proposed
on the basis of steady s t a t e - m e a s u r e m e n t s are T I ( I I I ) /
T I ( I ) (7) and q u i n o n e / h y d r o q u i n o n e (8). The theory
of consecutive electron transfer mechanisms for electrochemical techniques involving potential steps, current steps, and a-c polarography has also been given
(9-15).
The establishment of the mechanisms of a n electrode
reaction often requires acquiring large amounts of accurate e x p e r i m e n t a l data and fitting this data to complicated theoretical equations. Digital data acquisition systems (16-21), especially those based on general
purpose p r o g r a m m a b l e digital computers (20, 21), have
been v e r y useful, p a r t i c u l a r l y for e x p e r i m e n t a l times
in the sub-second region, in obtaining this data. The
data obtained b y these methods can be fitted to the
equations in their complete form, without the necessity
of approximations or linearizations sometimes required
to m a k e the analysis of data tractable. We report here
a study of the z i n c ( I I ) - z i n c a m a l g a m system using
several electrochemical methods and digital data acquisition techniques.
A n u m b e r of studies of the alkaline zinc electrode
reaction have been made. A significant part of this
effort has come from the space program's search for
high e n e r g y - d e n s i t y p r i m a r y and secondary batteries
and the i m p o r t a n t role of silver/zinc and z i n c / a i r
p r i m a r y batteries in this connection. Although studies
of the alkaline zinc electrode reaction often are concerned with reactions at the pure metal electrode, it is
common practice i n batteries to amalgamate the zinc
plates. Hence, we deemed a study of the alkaline
zinc (I) -zinc a m a l g a m electrode reaction justified.
Moreover, the reaction at the a m a l g a m electrode is
easier to u n d e r s t a n d t h a n the reaction at the pure metal
electrode, which m a y be complicated b y the crystallization process and more difficult surface preparation.
A n u m b e r of workers (22-31) have studied the alkaline zinc (II) -zinc amalgam electrode reaction with
somewhat different results. Gerischer (22, 23) determ i n e d reaction orders of hydroxide, zinc, and zincate
b y m e a s u r i n g the change of the charge transfer resistance with concentration and expressed the exchange
current, io, as
io = 2FAk~176
]~
~176[1]
This result led to the reaction m e c h a n i s m in Eq. [2]
a n d [3]
* E l e c t r o c h e m i c a l Society A c t i v e M e m b e r .
1 P r e s e n t a d d r e s s : T e n n e s s e e E a s t m a n C o m p a n y , KingsDort, T e n nessee 37660.
K e y w o r d s : potential step c h r o n o c o u l o m e t r y , electrode r e a c t i o n
kinetics, p o l a r o g r a p h y , digital data acquisition, c o n s e c u t i v e electron
transfer reactions.
fast
Zn(OH)42Zn(OH)2
~ Zn(OH)2
~ 2 OH-
~ 2e ~ Zn (Hg) ~ 2 OH-
[2]
[3]
Farr and Hampson
(24) duplicated Gerischer's results
in ultrapure solutions by faradaic impedance measurements. Matsuda a n d Ayabe (25) studied the reduction
1665
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1666
J. E l e c t r o c h e m . Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
process by d -c p o l a r o g r a p h y and found that the m e c h a nism was the same as that of Gerischer, but t h a t a was
0.42 Behr et al. (26) and Morinaga (27) also obtained
results wh i ch w e r e consistent w i t h the above m e c h a nism. S t r o m b e r g and c o - w o r k e r s (28-31) obtained r esults w h i c h w e r e similar to those of Matsuda and
A y a b e (25) for t h e reduction process but found t h a t
the oxidation process did not fit the m e c h a n ism proposed f r o m the study of the reduction reaction. They
proposed that the reduction and the oxidation i n v o l v e d
two different, totally i r r e v e r s i b l e reactions, each inv o l v i n g a single t w o - e l e c t r o n t r a n s f e r step. T h e i r
m e c h a n i s m for the oxidation reaction was
Zn(Hg) +
Z n ( O H ) + + 2e
[4]
Z n ( O H ) + + 3 OH---> Z n ( O H ) 4 2 -
[5]
OH-
-*
w i t h ~r~ = 0.39 (for [3]) and 1 -- ao = 0.23 (for [4]).
The m e a s u r e m e n t s of Gerischer, Morinaga, and F a r r
and Ham p s o n showed that there was essentially no
dependence of the exchange c u r r e n t on h y d r o x i d e concentration, wh i l e the m e c h a n i s m of P o p o v a and S t r o m berg (31) wo u l d predict a fairly large v a r iat i o n of
exchange c u r r e n t w i t h h y d r o x i d e concentration. The
m e c h a n i s m we propose, based on the results shown
below, involves consecutive o n e - e l e c t r o n t r a n s f e r steps.
Experimental
C h e m i c a l s . - - S t o c k solutions of 4.0M K O H and 4.0M
K F w e r e p r e p a r e d f r o m " B a k e r A n a l y z e d " Reagent
grade K O H and K F obtained f r o m the J. T. B a k e r
Chemical Company. The K O H solution was s t a n d ar d ized by titrating a k n o w n amount of r e a g e n t grade
potassium b i p h t h a l a t e using p h e n o l p h t h a l e i n as an
e n d - p o i n t indicator. A stock solution of 0.05M.zinc (II)
was m a d e by dissolving " B a k e r A n a l y z e d " ZnO in 50
ml of stock K O H solution. The Z n ( I I ) solution was
standardized by ti tr a ti n g w i t h E D T A buffered to pH
10. Purification of e x p e r i m e n t a l solutions w i t h acid
washed activated charcoal ( B a r k e r ' s method) was
tried, but the results w e r e the same w i t h or w i t h o u t
this step, so this p r o c e d u r e was not used regularly.
Solutions w e r e p r e p a r e d by pipeting a k n o w n a m o u n t
of K O H stock solution into a v o l u m e t r i c flask and
then diluting w i t h the stock K F solution, so that all
solutions w e r e at the same ionic strength. Zinc a m a l gam was p r e p a r e d from 99.9% zinc wire and purified
mercury. The zinc wire was a m a l g a m a t e d by dipping
in mercuric chloride solution for a f e w seconds before
it was placed in the m e r c u r y to aid in m o r e rapid
dissolution of t h e zinc. T h e a m a l g a m was stored u n d e r
v a c u u m and r e m o v e d f r o m the storage vessel u n d er
a b l an k et of prepurified helium. U n d e r these conditions, the concentration of zinc in the a m a l g a m w o u l d
r e m a i n stable for m o r e than a week.
Al l e x p e r i m e n t s w e r e carried out u n d e r a b l an k et
of nitrogen. C o m m e r c i a l w a t e r - p u m p e d nitrogen was
purified by first bubbling it th r o u g h distilled water,
then t h r o u g h a solution of vanadous chloride standing over saturated zinc amalgam, then passing over
copper strands heated to at least 350~
and finally
t hr o u g h distilled w a t e r again. The copper strands had
previously been exposed to o x y g e n at high t e m p e r a ture and then been reduced by passage of h y d r o g e n
gas at high t e m p e r a t u r e in order to assure an active
surface. The w a t e r used in all e x p e r i m e n t s and in p r e p aration of solutions was deionized w a t e r that had been
f u r t h e r purified by distillation f r o m alkaline potassium
p e r m a n g a n a t e in a Barnstead w a t e r still; its c o n d u c t i v ity was less t h a n 10 -7 ( o h m - c m ) -1. Potassium h y d r o x ide, potassium fluoride dihydrate, and zinc oxide w e r e
re ag en t grade chemicals and w e r e used w i t h o u t f u r ther purification. C o m m e r c i a l m e r c u r y was washed in
5% HNO8 w i t h air bubbling for several days, t h e n
splashed at least tw ic e t h r o u g h a 5% HNO3 scrubbing
tower. A f t e r drying, the m e r c u r y was distilled t w i ce
und er vacuum.
December
1972
A p p a r a t u s . - - A single c o m p a r t m e n t electrolytic cell
m a n u f a c t u r e d by M e t r o h m Ltd. (Model EA664) and
obtained from B r i n k m a n n I n s t r u m e n t s was used for
all experiments. The w o r k i n g electrode was either a
hanging m e r c u r y drop electrode (h.m.d.e.) or a dr opping m e r c u r y electrode (d.m.e.). The a u x i l i a r y or
c o u n t e r e l e c t r o d e was a piece of p l a t i n u m w i r e i m mersed directly in the solution. The reference electrode
was a saturated calomel electrode (SCE) w h i c h was
separated from the solution by a L u g g i n - H a b e r capillary. The tip of the capillary was placed as close as
possible to the w o r k i n g electrode to m i n i m i z e u n c o m pensated resistance. The h a n g i n g m e r c u r y drop electrode was m a n u f a c t u r e d by M e t r o h m Ltd. (Model
E-410). A fresh drop of 0.032 cm 2 theoretical area was
used for each run. The cap i l l ar y tip had to be cut off
at intervals since the strong alkali solution attacked
the glass, and e v e n t u a l l y the tip w o u l d not hold a drop
of the p r o p e r size. Electrical contact to the drop was
made by inserting a p l a t i n u m w i r e into t h e r e s e r v o i r
t h r o u g h the p u m p i n g nipple.
The d.m.e, was constructed f r o m a length of S a r g e n t
6-12 second capillary. The m e r c u r y flow rate of t he
d.m.e, was m e a s u r e d before each e x p e r i m e n t since the
cap i l l ar y did not last long before the tip had to be cut
off, changing the flow rate.
P o t en t i al step c h r o n o c o u l o m e t r y was p e r f o r m e d
w i t h an i n s t r u m e n t p r e v i o u s l y described (32) constructed from P h i l b r i c k solid-state operational a m p l i fiers. A fraction of the v o l t ag e g en er at ed by the c u r r e n t follower could be fed back to the potentiostat for
resistance compensation; the stabilization scheme of
Br o w n et al. (33) was used. A - C and d-c p o l a r o g r a p h y
w e r e p e r f o r m e d using a P r i n c e t o n A p p l i ed Research
Corporation, Princeton, N e w Jersey, Model 170 e l e c t r o chemical instrument. Data from potential step e x p e r i ments were t a k e n using a P D P - 1 2 A c o m p u t e r system
(Digital E q u i p m e n t Corporation, Maynard, Massachusetts). Data for potential sweep e x p e r i m e n t s at sweep
rates below 300 m V / s e c w e r e recorded on a Moseley
2D-2 X - Y recorder. F o r sweep rates above 300 mV/sec,
a T e k t r o n i x Model 564 storage oscilloscope was used
w i t h Type 2A3 (Y axis) and Type 2A63 ( X - a x i s ) p l u g ins. P e r m a n e n t records of oscilloscope data w e r e m a d e
with a Polaroid c a m e r a m o u n t e d on the oscilloscope
using 3000 speed film.
Initial and final potentials for potential step e x p e r i ments and initial potentials for potential sweep e x p er i m en t s w e r e m e a s u r e d w i t h a U n i t e d Systems Corporation Model 204 v o l t m e t e r to an accuracy of • inV.
Two of the relays in the r e l a y register of t h e PDP-12
c o m p u t e r w e r e used to control the potentiostat and
integrator. T i m i n g of data acquisition was controlled
by i n t e r n a l c o m p u t e r cycle counting; the t i m e scale
was calibrated by acquiring data f r o m a function
g e n e r a t o r ( W a v e t e k Model 114).
Data w e r e t a k e n at the same potentials and the same
time scales w i t h and w i t h o u t zinc present. Different
time scales w e r e used at different potentials so that
the charge m e a s u r e d w i t h zinc was significantly l a r g e r
than that without zinc, but at short enough times that
sufficient kinetic i n f o r m a t i o n was still present. The
q u a n t i t y nFADI/2C/~ '/2, w h i ch is the slope of a Q vs. t'/2
plot w h e n t h e potential is stepped far enough so that
the reaction r a t e is controlled by mass transfer, was
ev al u at ed for the reduction of z i n c ( I I ) by stepping
f r o m --1.0 to --1.TV and for the oxidation of zinc
a m a l g a m by stepping f r o m --1.7 to --1.0V an d least
squares analysis on the Q - t'/2 data. Th r ee or four
steps w e r e a v e r a g e d for each potential using a fresh
drop each time.
Th e data acquisition system was checked by r e c or ding a c u r r e n t - t i m e cu r v e w i t h a simple R C d u m m y
cell (R ---- 5 kohm, C ---- 1 ~J) for t h e potential stepped
f r o m 0 to +0.400V. Th e accuracy of m e a s u r e m e n t was
1.2% or better. F u r t h e r details about the apparatus,
procedures, and calibrations are available (34).
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V o l . 119, NO. 12
ZINC(II)-ZINC
AMALGAM ELECTRODE REACTION
Theory
The best m e t h o d of p r o v i n g t h a t a charge t r a n s f e r
reaction consists of m o r e t h a n one electron t r a n s f e r
step is to d e m o n s t r a t e t h e existence of the i n t e r m e d i ate products b y some u n a m b i g u o u s technique (1).
Consider the case
0 -t- n~e ~ Y E1 ~
Y -b n2e ~ R E2 ~
[6]
CRnlCon2
: K = exp
{ n,n2F
-
-
( E i ~ -- E2 ~
RT
}
-
i l (t)
I1
=
Erz/~..z:EI~
n~F
Ji = - - ~
fY~fR c~2
~O
RT
ln(
-- n2---F
~s(t) ----
~2) exp ( x - 2 t )
fR ) ( D y e 8 9
~-Y
DR /
( E - - Er~/~.t) ( i = 1,2)
[18]
[ eJ2-~- e-Jl-~ e (j,-h) ]
[20]
(1~- ej~) (1 -~ eJO
k~ .
.
~i : ~ t e -a~Jl + e ~d')
(i :
1,2)
[21]
Di Y2
Since we are interested h e r e only in t h e case w h e r e
E1~ < ~ Es ~ and because E ~ Erl/2 = (Eri12,1 -~
E r l / s , 2 ) / 2 , some simplifications can be m a d e in these
equations, y i e l d i n g
[~2 exp ( x - S t ) erfc ( x - t '/2)
~1 ( t ) :
2c ~-1 exp (x+st) erfc ( x + t ' / 2 ) ]
~2(t) =
~1X2
[22]
[exp ( x - ~ t ) erfc ( x _ t ~ 2 )
(1 + eJO (;~ + X2)
- - e x p (x+St) erfc
(x+t'/,)]
[23]
The expression for Q (t) is obtained b y i n t e g r a t i n g the
a b o v e equations to o b t a i n Eq. [24] and [25]
f~l(t)dt
erfc
--
(1 + eJ~) (~1 + ~2)
(x-t ~/2) -t-
2X-t'A
~
1
)
~_2
~LI (
Jr - X+ 2
exp (x-2t)
e x p (x+2t)
erfc ( x + t v2) +,-------if-M~2
erfc ( x - t F ~ ) + 2 x~- t v ~
1
[24]
[ xl_2( exp ( X _ ~ )
f C~(t) ----- ( l + e J 0 ( ~ l + X 2 )
1
--
e x p (x+2t)
erfc (x+t~2) + - 2x+t'/"
~'/~
1)]
[25]
Since x+ is m u c h g r e a t e r t h a n x - , the t e r m in the
above equations in x+ can be neglected c o m p a r e d to
t h e t e r m in x - . U n d e r these conditions, then
(t) d t : f ~ 2 ( t )
dt
[26]
and, defining Zr as in Eq. [27]
Zc :
[12]
[13]
[19]
2
K ~---~1~2
then
Dy /
[exp (x+2t)
(1 + eh) (1 -b eJ0 ( x - -- X+)
[11]
RT l n ( f Y ) ( D ~
-- "t~l---'F-
Erl/2,2"-E2 ~
=
[16]
erfc ( x - t ~/,) -- ( x + - - ~2) exp ( x + S t ) erfc (x+tV,)] [17]
f~1
[10]
D2 : D ~ : ~ D ~
fortify az f2
[(x--
(1 + eJl) (x+ + x - )
erfc (x+t'/2) - - e x p ( x - S t ) erfc ( X - t ' / , ) ]
[9]
n i F A C * oDo'A
Do~Dy ~
~l(t) =
X-----:
Pt = 1 - - ai (i = 1,2)
D1 :
= F A C * o D o ' / 2 [ n l ~ l ( t ) -{- n2~2(t)]
i(t)
where
[8]
Hence, for a given total concentration of O and R, C*,
the m a x i m u m a m o u n t of Y is present w h e n CR = Co.
If E~o, is much g r e a t e r t h a n E~~ then solutions containing essentially only Y can be made. If E~o' = E2o',
then K : 1 and for n~ : n2 = 1, the m a x i m u m Cy is
given b y Co : Cy : Cm As the q u a n t i t y E1 o' - - E~ o"
becomes m o r e negative, the m a x i m u m a m o u n t of Y
that can be p r e s e n t decreases rapidly. F o r example,
for nl : n2 = 1, and Co : C~ : C*, if E1 ~ -- E2 ~ =
--0.2V, t h e n Cy ~ 0.03 C*, while if E~ ~ -- E2 ~ :
--0.4V, C y ~ (4 X 10-4) C *.
However, depending upon the values of the r a t e constants for steps [6] and [7], the existence of stepwise
electron t r a n s f e r and t r a n s i e n t f o r m a t i o n of an i n t e r mediate, Y, can be deduced from electrochemical m e a surements [see Ref. (1) and g e n e r a l t r e a t m e n t of
A l b e r y a n d H i t c h m a n (35) ].
Potential step c h r o n o c o u l o m e t r y (33, 34) was chosen
as the p r i n c i p a l electrochemical investigative p r o cedure in this research, because integration of the
c u r r e n t signal removes most of the h i g h - f r e q u e n c y
noise from this signal. Moreover, the i n t e g r a t e d signal
always s t a r t s f r o m zero a n d can a l w a y s be a d j u s t e d
to stay on a given scale, w h i l e in c h r o n o a m p e r o m e t r y
initial d o u b l e - l a y e r c h a r g i n g c u r r e n t m a y be several
orders of m a g n i t u d e l a r g e r t h a n the f a r a d a i c c u r r e n t
so t h a t to obtain sufficient precision in the r e g i o n of
interest, the signal m u s t be allowed to o v e r d r i v e the
amplifiers of the m e a s u r i n g instrument. C h r o n o c o u l o m e t r y can also be used to obtain i n f o r m a t i o n about the
double l a y e r (36, 37). A l t h o u g h the theoretical e q u a tions for stepwise electron t r a n s f e r s in chronocoulome t r y have not been p r e s e n t e d previously, t h e y can be
obtained quite easily b y integration of the a p p r o p r i a t e
equations of c h r o n o a m p e r o m e t r y .
Potentiostatic c u r r e n t - t i m e b e h a v i o r for systems involving a q u a s i - r e v e r s i b l e t w o - s t e p charge t r a n s f e r
was first d e r i v e d b y Hung a n d S m i t h (10) for the
a n a l y t i c a l solution for this case in a - e p o l a r o g r a p h y .
The p a r t i a l differential equations and b o u n d a r y conditions used b y these a u t h o r s in obtaining the f o l l o w ing results a r e given in the A p p e n d i x . F o r t h e reaction
given in Eq. [6] and [7] and following the notation of
H u n g and S m i t h (10), let
~(t)
These authors showed t h a t the c u r r e n t d u r i n g a step
to p o t e n t i a l E is given b y Eq. [16].
[7]
At equilibrium, from the N e r n s t equations for [6] and
[7]
C~ "~+n,
1667
Q(t) :
(n~
-k n2) F A D o ' / 2 C * o~I~2
(1 + e j~) (~.1 -{- X2)
Zc (
2x-t'/2
~
exp ( x - s t ) erfc (x_t~'2) -~ ~'/~
[27]
1
)
[28]
[14]
[15]
F o r t h e case w h e r e R is i n i t i a l l y p r e s e n t but not O and
t h e potential is s t e p p e d in the positive direction, the
expression for Q (t) is the s a m e as t h a t in [28] except
t h a t Z~ is r e p l a c e d b y Z ,
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1668
J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
(nl + n2) FADRV2C*RLlks
Za =
(1 + e -J2) (~.1 -~- ~.2)
,
exp (L2t) erfc (Ltv,) "t- 2~t~
"--'~-/=- 1 )
-
-
,
I
,
0
[30]
2
(e -aJ
~
D e c e m b e r 1972
J
LOG,o(X_)
ko
k
r
[29]
Thus, for a t w o - s t e p electron t r a n s f e r reaction, the
equation for Q ( t ) is identical in f o r m to the e x p r e s sion for Q ( t ) for single-step charge transfer, Eq. [30]
(36, 37)
Q(t) =-~ K(
i
-i- e~J)
2
[31]
D~'=
nF
j -- ~
(E -- E o')
[32]
Za
-4
K = n F A k o ( C * o e -cd -- C*Re~,~)
[33]
To use Eq. [28] or [29] to d e t e r m i n e kinetic p a r a m eters and reaction mechanisms, one steps f r o m a potential w h e r e no appreciable c u r r e n t flows to one
w h e r e a m e a s u r a b l e cathodic or anodic c u r r e n t is obtained and measures the Q vs. t behavior. F r o m this
data K and k are determined. These values a r e d e t e r m i n e d at a n u m b e r of potentials and then the logar i t h m of K and k are plotted vs. the potential. F o r a
single-step charge t r a n s f e r case, th e plot of In K vs. E
is a straight line w i t h a slope e q u a l to - - a n F / R T . The
plot of In ~ vs. E is a c u r v e w h i c h has a m i n i m u m near
E ~ and asymptotically approaches straight lines for E
g r e a t e r t h a n and less t h a n E ~ The slope of the a s y m p tote for E less than E o' is - - a n F / R T , w h i l e for E g r e a t e r
t h a n E o', it is ~nF/RT.
In the case of a t w o - s t e p charge transfer reaction, Z
and x - can be d e t e r m i n e d from Q vs. t (or i vs. t) data
in the same m a n n e r as K and ~ in a one-step reaction.
However, the b e h a v i o r of the plots of In Z and In x vs. E can be m o r e c o m p l e x t h a n in the one-step Case.
It is this difference in b e h a v i o r that can sometimes
allow one to d em o n s t r a t e t h e existence of a t w o - s t e p
mechanism. Th e b e h a v i o r of In x - vs. E and in Z vs. E
can be illustrated by some examples:
(i) If kOl and k% are v e r y large, t h e n the o v e r - a l l
rate of t h e reaction m a y be so fast that the reaction
appears to be Nernstian. In this case, it is not possible
to calculate x - and Z and the reaction is indistinguishable from a one-step m u l t i - e l e c t r o n transfer reaction
(10).
(ii) F o r k~ > > k~ w h e n ( R T / F ) In (k%/kOl) < E
< Erl/22, then 0 In Zc/OE = - - ( 1 + a 2 ) F / R T [see Fig. 1
(Zc,1) ] and in x - has a m i n i m u m n e a r E = 0 ( w h e r e
Erz/2.1 is t a k e n as --0.2V, and E5/2.2 is +0.2V). When
( R T / F ) In (ko2/kol) < E < O, t h e n O l n ( x - ) / O E =
- - ( 1 -t- a 2 ) F / R T [Fig. 1 ( x - 2 ) ] - W h e n 0 < E ~ Eq/2,2
8 l n ( x - ) / S E -- (1 -- a ) F / R T [Fig.1 ( x - . l ) ] and 0 In
Za/OE = ~2F/RT [Fig. 1 (Za,1)]. W h e n Eq/2,1 < E
( R T / F ) In (k%/kOl), then 0 In Zc/OE = - - a x F / R T
[Pig. 1 (Zc,2)], 8 In Z/OE - - ( 2 -- a l ) F / R T [Fig. 1
(Za,2)] and ~ In ( X - ) / O E : - - a z F / R T [Fig. 1 ( X - , 3 ) ] .
LOGlo( Z )
--6
i
3
i
2
i
I
POTENTIAL
Fig. 1. Log X Erl/9.1 = - - 0 . 2 V ,
i
o
(2.3RT/F
i
1
I
--3
volts/div.)
and log Z vs. E for case (ii). a l "-- c~ - Erl/2,2
--I-0.2, k ~
=
n2 - - 1, D1 ','= - - D2 V= = 0.00316, fl - 2.03 x 10 - e moles/cm 3, A == 0.032 cm 2.
i
i
--2
[
i
i
2
i
1
i
2.0, k% -- 0.02, nl
=
f2 == 1.0, Co =
]
I
I
i
--1
i
--2
i
--3
0.5,
"-
CR =
0
LOG,olX
I
--2
L O G I o [Zl
6
(iii) F o r ko2 > > ko,, t h e results are t h e m i r r o r
i m a g e of those for case (ii) above.
(iv) The results for ko2 -- k% are shown in Fig. 2.
Therefore, to d e t e r m i n e w h e t h e r a reaction is single
step or multi-step, not only must the o v e r - a l l reaction
be slow enough to b e measurable, but also the r a t e
must be slow enough to be m e a s u r a b l e in the v i c i n i t y
of
Erl/2,1 -~- Erl/2,2
RT
k~
E' ---+
In
,
[34]
2
F
k~
Otherwise, t h e reaction is indistinguishable f r o m a
single-step reaction. For example, for k% > > k%, if the
most positive potential at w h ic h m e a s u r e m e n t s of Z
and x - can be m a d e is less than E' in 38, then O In Za/
i
3
POTENTIAL
i
O
{2.3RT/F
volts/div.]
Fig. 2. Log X - and log Z vs. E from case (iv). The conditions are
the same as in Fig. 1 except k~ -- 0.02.
aE = (2 - - ~ I ) F / R T and a In Zc/aE : - - . I F / R T . U n d e r
these conditions a In Za/aE -- a In Zc/aE -- 2 F / R T and
the results cannot be distinguished f r o m a single-step
reaction w i t h t h e same o v e r - a l l rate and ~ : ~1/2. The
b e h a v i o r of In ( x - ) is s i m i l a r l y indistinguishable.
In o r d er to assign values to both ~i and a2, both
cathodic and anodic plots of In Z and In x - vs. E m u s t
h a v e linear segments w h o se slope is less t h a n nIF/RT.
Downloaded 19 Feb 2009 to 146.6.143.190. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
Then al can be obtained from the slope of the cathodic
plot and a2 can be obtained from the slope of the anodic
plot. (Erl/2,1 -5 Erl/2,2)/2 can be d e t e r m i n e d from the
potential where Za = Zc
Ezafzc :
nlErl/2,1 -5 n2Erl/2,2
-5
~%1 JI- T/'2
RT
(nl -5 n 2 ) F
In
C*o
C*R
[35]
Even here kol, k~ Erl/2,1, a n d Erl/2,2 cannot be assigned
absolute values, since the value of Erl/2.2 -- Erl/2,1 is
not known. We can, however, measure k~" and k2' at
(Erl/e.1 -5 Erl/2,2)/2.
Fornl:n~=
1
kOl
k1' -exp
[ --alF
[
/
k
Erl/2,2
Erl/2,1
[36]
ko2
k2t
[ (I -- a2)F
exp [
-- Erl/2,1
[37]
If we could m e a s u r e the concentration of Y at equilibrium, we could then determine the value of Erl/2,2
-- Erl/2,1. For purposes of calculation it is sufficient to
select a value of E2 -- E~ greater t h a n 0.2V and use that
to calculate k% a n d k~ from the observed k l ' and k2'.
Using the values d e t e r m i n e d above for al, a2, Erl/2,1,
Erl/2.2, nl, n2, k~ and k~ one can calculate Z and x over the whole potential range and see if these values
give a good fit in the n o n l i n e a r portions of the In Z a n d
In x - vs. E plots. If the fit is good, one can say with
confidence that the charge transfer is multi-step.
Clearly, potential step techniques are p a r t i c u l a r l y
useful for distinguishing between single-step and
m u l t i - s t e p electron transfer. Hurd (5) has stated that
unequivocal proof of a two-step consecutive electron
transfer mechanism can only be obtained from steadystate polarization curves if the exchange currents of
the two steps differ by a factor of 100 or more while
still being less t h a n the mass transfer limited current.
Hence, if rate constants are about equal, concentration
ratios would have to be very large in order to achieve
the necessary exchange currents. Large concentration
ratios usually mean large concentrations, high currents,
and problems from solution resistance. Potential step
techniques allow e x a m i n a t i o n of the c u r r e n t - p o t e n t i a l
behavior over a wider range of potentials and larger
rates t h a n is possible with steady-state techniques
since the effects of mass transfer can be accounted for
by proper application of potential step theory.
Results
parameters are u s u a l l y determined by linearization of Eq.
[30] by taking Q values only at times where kt ~/2 > 5,
so that exp (k2t) erfc (kt'/,) is negligible compared to
the other terms in this equation (36). A similar procedure is often followed in chronoamperometric experiments (38, 39) where c u r r e n t values at times corresponding to ~t'/, < 0.1 are used. The difficulty of using
these approximations in practice has been discussed
[see, for example (40, 41)] and is based on the necessity of k n o w i n g the value of ~, the p a r a m e t e r to be
d e t e r m i n e d b y the experiment, before the valid app r o x i m a t i o n zone is established. Moreover, the zone
of the approximation m a y be located where p e r t u r b a tions caused by double layer charging or convection
are important. However, the best use of the data is
made b y fitting the e x p e r i m e n t a l results to the complete theoretical Eq. [30] using a high speed digital
computer, a n d this procedure was followed here.
Because digital data acquisition was employed, the
data were in a p a r t i c u l a r l y convenient form for f u r ther processing on the computer. The procedure folPotential
step
1669
ZINC(II)-ZINC AMALGAM ELECTRODE REACTION
V o l . 119, N o . 12
chronocoulometry.--Kinetic
lowed consisted of guessing initial values of K and
and calculating values of Q for each t using [30], Qcalr
These values are compared to the e x p e r i m e n t a l ones,
Qexp, and the total variance, which is the sum of (Qexp
Qc,lc)~, determined. The values of K and k are
changed u n t i l the variance has been minimized. Details
of this procedure and the method for calculating
exp (y2) erfc (y) are discussed elsewhere (34). P r e l i m i n a r y chronocoulometric m e a s u r e m e n t s showed
that n e i t h e r r e a c t a n t (zincate) or product (zinc in
m e r c u r y ) were adsorbed, so that the n u m b e r of coulombs required to charge the double layer capacitance,
Qdl, was d e t e r m i n e d on a test solution lacking zinc (II)
with a pure m e r c u r y electrode; Qexp was then t a k e n as
Qmeas - Qd], where Qmeas is the measured charge. This
procedure assumes that Qdl is not affected significantly
by the presence of the small a m o u n t s of zinc in solution
or mercury.
The log ~ and log K values at various potentials and
various hydroxide concentrations d e t e r m i n e d by this
procedure are given in Table I. These values were
plotted vs. E and an and/~n were d e t e r m i n e d from the
slopes of the linear parts of the cathodic a n d anodic
branches of the plots at constant hydroxide concentration. The dependence on hydroxide ion c o n c e n t r a t i o n
was determined from plots of log K at constant potential vs. log [ O H - ] . The results are given in Table II.
The diffusion coefficients of zinc (II) and Zn (Hg) were
d e t e r m i n e d by m e a s u r i n g K / ~ w h e n [E -- Erl/2[ was
large. For the reduction process, this gives the value
of n F A C * o D o '/2, while for the oxidation n F A C * R D R I/,.
The effective surface area of the K e m u l a type Metrohm
h.m.d.e, has been shown to be about 90% of the geometrical area (42) yielding a value for our electrode
of 0.0291 cm 2. With this value for A, C*o ---- 2.03 X 10 -8
moles/cm 3 and K r
= 2.82 X 10 -5, we obtain a Do lj~
= 2.47 X 10 -3 cm/secV2. Similarly, with K a / k ---- 2.66
X 10 -5 and D a '/~ ---- 3.98 • 10 -3 cm/sec'/, (43), the
concentration of zinc in the amalgam, C*m was found
to be 1.19 mM. The potentials for the intersection of
Ka and Kc and the concentrations of Z n ( I I ) Z n ( H g ) ,
and O H - can be used to calculate Eq/2 for the over-all
reaction. A plot of Erl/2 vs. log [ O H - ] had a slope of
--0.118V and an intercept of --1.445V vs. SCE.
D - C p o l a r o g r a p h y . - - T h e zinc ( I I ) / z i n c a m a l g a m system in alkaline media exhibits a quasi-reversible
polarographic reduction wave. The t r e a t m e n t of the
data follows the t r e a t m e n t of Meites and Israel (44)
and is similar to that of Matsuda and A y a b e (25).
F r o m the Ilkovic equation and the values m = 1.07
mg/sec, t ---- 1.0 sec, i d = 7.64 /~A a n d C*o ---- 2.03 mM,
we find a value of Do w ----2.53 • 10 -3 cm/sec ~/~,in good
a g r e e m e n t with the value obtained from the potential
step experiment. To determine kinetic data, a plot of
l o g [ i / ( i d - - i ) ] VS. E according to the equation for a
totally irreversible reaction (44)
E = E ~ -5
0.059
an
log
1.349kotV,
Do '/2
0.0542
- log .
an
~d -- i
[38]
was m a d e for values of E sufficiently negative as to
m a k e the reverse reaction slow enough to be negligible. Results are given in Table II.
A - C polarography.--Measurement of kinetic parameters by a-c polarography involved phase-sensitive detection of the current, so that the phase angle of the
current as well as its magnitude was measured. F r o m
this data the cotangent of the phase angle, 8, was determined and used to calculate k at different values of E
(45)
Cot (8) ----Ioo/Igoo ---- 1 + (2~) w/~
[39]
The kinetic parameters can be obtained from a plot of
log X vs. E or directly from a plot of cot(0) vs. E by
m e a s u r i n g the potential and m a g n i t u d e of the m a x i m u m value of cot(0) (45)
Downloaded 19 Feb 2009 to 146.6.143.190. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
1670
J. E l e c t r o c h e m . Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
Reduction reaction; Steps from --1.00V vs. SCE to E; solution
contained 2.03 mM zine(II) and KOH; electrode was Hg drop
E
[OH-]
(V vs. SCE)
0.18
--1.36
1.38
1.40
1.42
-- 1 . 4 4
-- 1 . 4 6
Log k
--0.5675
-- 0 . 3 1 8 9
+ 0.0055
0.3193
0.7863
0.7729
1.0177
1.2498
1.4933
-- 0 . 6 8 2 9
-- 0 . 4 7 7 6
--0.1598
+ 0.1881
0.4876
0.8026
- -
- -
- -
--1.48
-----
0.34
1.50
1.62
1.40
1.42
--1.44
-- 1 . 4 6
1.48
1.50
-- 1 . 5 2
- -
- -
-
--1.53
-- 1 . 5 5
1.57
--1.59
-- 1 . 6 1
--1.46
-- 1 . 4 8
-- 1 . 5 0
--1.52
-- 1 . 5 4
--1.56
1.58
1.60
-- 1 . 6 2
1,64
- -
1.76
- -
- -
- -
6.74
9.12
11.20
25.20
25.60
5.14
2.46
15.40
13.50
12.76
38.00
17.10
7.64
6.94
7.84
--3.5614
-- 3 . 3 1 5 3
--3.1080
-- 5 . 3 4 7 1
-- 5 . 0 0 8 2
--4.6555
-- 4 . 3 4 6 6
-- 4 . 0 6 0 7
-- 3 . 7 6 7 0
14.40
3.05
2.65
6.30
-- 0.4673
--0.1595
+0.1403
-- 3.5505
--3.3110
--3.1461
-- 5.8622
--5.4614
-- 5.0589
-- 4.7091
--4.3978
0.4478
0.7000
0.9316
1.1671
1.3156
--0.5434
-- 0 . 6 7 8 8
-- 0 . 4 6 9 8
--0.1748
+ 0.0987
0.3821
0.6573
0.9402
1.0412
1.2536
--4.1129
-- 3 . 8 5 0 4
-- 3.6158
--3.3903
-- 3 . 2 3 1 7
--5.8832
-- 5 . 4 3 2 3
-- 5 . 0 2 8 0
--4.7138
-- 4 . 4 2 5 4
--4.1427
-- 3 . 8 8 5 7
-- 3 . 6 3 6 9
-- 3 , 4 8 3 9
-- 3 . 3 0 6 9
9.58
I0.00
2.88
2.05
2.02
8.95
9.77
16.30
16.20
13.40
11.50
19,80
14.50
7.25
7.29
--0.6991
-
Stand. dev.
• 107
--5.4399
-- 5 . 0 0 4 9
-- 4 . 6 4 0 6
-- 4 . 3 0 9 6
-- 3 . 9 7 8 9
-- 3 . 8 0 1 2
1.0215
1.2627
1.4239
-- 0.5593
--1.54
--1.56
-- 1.43
--1.45
-- 1.47
1.49
--1.51
0.96
Log K
Discussion
The results obtained by the different electrochemical
methods in Table II are in fair agreement with each
other. These results show that the electrode reaction
of zinc in alkaline media is not a simple q u a s i - r e v e r s i ble two-electron transfer. First, the q u a n t i t y an + Bn
is much less t h a n two, w h e n ~ and ~ are calculated
from the appropriate slopes measures well away from
Erl/2. Second, the log K vs. E plots show definite c u r v a ture in the region n e a r E r l / 2 . This c u r v a t u r e cannot
be due to d o u b l e - l a y e r effects, since the rate of change
of potential at the outer Helmholtz p l a n e with electrode potential is n e a r l y constant in the region of i n terest, which is far negative of the potential of zero
charge, and the solution has a high ionic strength. Nor
can it be explained by uncompensated resistance, since
the region of m a x i m u m curvature is in the region
where K was less t h a n 100 ~A, and the uncompensated
resistance was less than 10 ohms, i.e., where the curvature was most pronounced, contributions from I R
effects were at a m i n i m u m . These features correspond
quite closely to a consecutive electron transfer mechanism, however, and the following mechanism appears
to fit the e x p e r i m e n t a l data quite well
9.96
12.20
10.90
6.51
(b)
Oxidation reaction: Steps from --1.700V vs. SCE to E, solution
contained no zinc(II) and KOH, electrode was zinc amalgam
with a
[ Z n ] = 1.2 m M
[OH-]
Stand. dev.
E
(M)
(V vs. SCE)
0.18
--1.38
-- 1 . 3 6
1.32
--1.28
-- 1 . 2 4
Log k
- -
-- 1.20
--1.16
-- 1 . 1 2
-- 1.08
0.34
x 107
Z n ( O H ) 4 2 - ~ Zn(OH)2 + 2 OH-
[42]
--0.2117
-- 0 . 3 6 4 1
-- 0 . 4 5 6 3
--0,1335
--5.8534
-- 5 . 4 8 4 3
-- 5 . 1 2 3 8
--4.7542
4.97
10.20
6.47
6.79
Z n ( O H ) 2 + e ~=~Zn ( O H ) 2 -
[43]
Zn(OH)2- ~ Zn(OH) + OH-
[44]
+ 0.1061
0.3460
0.6573
-- 4 . 4 8 8 0
-- 4 . 2 3 4 8
--3.9680
4.80
3.65
16.3.0
H g + Z n ( O H ) + e~=~Zn(Hg) + O H -
[45]
0.7993
2.42
36.40
10.60
15.60
27.90
68.30
10.30
3.85
3.45
-- 1 . 0 4
-- 1 . 4 2
--1.40
-1.36
--1.32
-- 1 . 2 8
--1.24
1.20
1.5222
-- 0 . 8 2 4 2
--0.8504
-- 0 . 8 1 8 1
--0.1515
-- 0 . 0 1 2 0
+0.3497
0.6166
--1.16
0.8588
--3.7272
3.88
--1,12
1.08
--1.47
1.45
1.41
0.9097
1,2846
--0.3670
-- 0 . 5 1 6 7
-- 0 . 3 8 6 4
--3.6416
-- 3 . 2 8 5 3
--5.8545
-- 5 . 5 9 1 0
-- 5 . 0 5 9 0
8.35
2.79
2.77
4.46
4.33
1.37
--1.33
-- 1 . 2 9
-- 0.0143
+0.2119
-- 4.6425
--4.3768
12.60
5.53
0.4428
0.6871
0.8744
1.0797
1.3468
-- 4 . 1 4 3 1
-- 3 . 8 9 7 5
--3.7023
-- 3 . 4 9 8 7
-- 3 . 2 4 3 4
4.30
2.67
3.59
16.00
2.64
1.0502
- -
0.96
Log K
-- 3 . 7 6 4 1
-- 3.5123
-- 3 . 0 9 7 5
-- 8 . 0 2 4 4
--5.6479
-- 5 . 1 5 9 2
--4.7376
-- 4 . 4 9 6 3
--4.2217
-- 3 . 9 5 9 5
- -
- -
- -
--
-- 1 . 2 5
--1.21
-- 1 . 1 7
1.13
- -
Comparison of this model to the e x p e r i m e n t a l results
is simplified b y using a modification of the notation
of Hung and Smith (10), with O representing Zn (OH)2;
YO, Z n ( O H ) 2 - ; YR, Z n ( O H ) ; and R, Z n ( H g ) . With ]o
= [OH-]2,]vo = 1.0, ]YR = [ O H - l - l , and fR = [ O H - ] ,
the following equations hold for Erl/2.1 and Erl/2,2
10.40
RT
Erl/2,1 :
Erl/2,1
=
RT
2F
In
Do
+ -
Dro
RT
Do
E1~ + - ln--
RT
-
-
2F
Dyo
F
RT
DyR
RT
-F
In - 2F
DR
RT
F
In
]o
[46]
fro
ln[OH-] 2
[47]
ln[OH-] 2
[48]
At constant E -- Er]/2, the hydroxide dependence of
~, is proportional to ft and ~2 to f2, where $1 and f2 are
given by Eq. [49] a n d [50]
(2~D) '/"
[41]
k o [ ( ~ / ~ ) - ~ + (~/~)~]
E1 o' +
Erl/2,2 = E2 o' +
[40]
[E]max = Erl/2 + - ~ l n ( = / ~ )
[cot(0)]max = 1 +
1972
P o t e n t i a l s w e e p v o l t a m m e t r y . - - K i n e t i c parameters
can be obtained from linear potential sweep v o l t a m m e t r y at a stationary electrode by observing the v a r i a tion of Ep or of Ep -- Ep/2 with scan rate, v (46).
Kinetic parameters for the cathode reaction were obtained from experiments in a 1.0M KOH solution cont a i n i n g 2.03 mM z i n c ( I I ) at a m e r c u r y electrode while
those for the anodic reaction used a zinc a m a l g a m electrode, [Zn] = 1.2 mM and 1.0M KOH (34). Kinetic
parameters obtained from these m e a s u r e m e n t s are
shown in Table II.
Table I. Potential step chronocoulometry. Results
(a)
December
fl - - fo~lfY0 ~1 =
[OH-]-~176
f2 = [ O H - ] - ~
The results are shown in Table II.
[49]
[50]
Table II. Summary of experimental results by different techniques
~n
Potential
D-C
A-C
step
polarography
polarography
Linear potential
sweep voltammetry
(a) (Ep v s . l o g v )
( b )
( E p
--
Ep/s)
Erl/9
kOclDol/2
kOa/DRll 2
0.82
0.34
0.17
0.30
0.82
0.83
---
0.33
0.18
-.
9.78
1.00
0.33
0.46
0.40
.
( V VS. S C E )
.
0.34
.
DO1~~
( c m / s e c 1/2)
.
-- 1 . 4 4 5
2 . 4 7 • 10 -a
--1.445
.
2.53 • 1 0 -s
.
.
.
.
.
.
.
.
0 log Kc
0 l o g K~.
0 log [OH-]
0 log [OH-]
-- 1 . 8 5
+ 0.83
.
--
.
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Vol.
ZINC (II) -ZINC A M A L G A M ELECTRODE REACTION
119, N o . 12
O
0.18M
KOH
I
!
r
O
~
1671
I
Fig. 3. Log Kc vs. E for reduction reaction. Comparison of experimental data from potential-step
chronocoulometry
([Zn(OH)42-] = 2.03 raM)
with values calculated from consecutive-electron transfer theory.
-4
LOGIo(K)
/
,
-.,o
/A
,/6
POTENTIAL
(volts
,
.,.,o
,
vs. s . c . e . )
This means that for a n y given value of E -- Erl/2, the
hydroxide dependence will be small. I n particular,
w h e n kl is n e a r l y equal to ~2, and the hydroxide concentration is about 1.0M, the hydroxide dependence of
log K and log ~ will be zero. Since the region w h e r e
~1 is equal to ~2 is also the region of c u r v a t u r e of the
log K vs. E plot, the a p p a r e n t ~ measured in this
region will be b e t w e e n the values for the high and
low slope l i n e a r regions; for the Z n ( I I ) / Z n (Hg) reaction an would be equal to about 1.0 in this region.
The m e a s u r e d values of the hydroxide dependence
of log K at constant potential yield the following values for ]1 and f2: fl
[OH-]-~
and ]2
[ O H - ] +0as.
To obtain a q u a n t i t a t i v e comparison between model
and results, we take al = 0.82, a2 ---- 0.66, kol -- 0.228,
ko2 = 0.0209, and use these parameters to calculate
values for log K and log ~ from consecutive electron
transfer theory
----
Erl/2.1
-
-
-
-
=
1.645
RT
- -
~
F
RT
Erl/2,2 -- --1.245 - - - -
F
,
-,.o
ln[OH-] 2
[51]
ln[OH-]2
[52]
m a y show large distortions of the c u r r e n t because of
spherical diffusion inside the drop. Since the theoretical curves in these figures were calculated with p a r a m eters from the potential step experiment, the agreement
must be considered satisfactory.
It is of interest to compare our results with those of
previous studies (Table III). Gerischer (22, 23) and
later F a r r and Hampson (24) d e t e r m i n e d the exchange
c u r r e n t io b y m e a s u r i n g the charge transfer resistance
(RT = R T / n F i o ) at the e q u i l i b r i u m potential of a solution and thus d e t e r m i n i n g the v a r i a t i o n of io with
reactant concentration. F r o m io, one can d e t e r m i n e a
and k o from the relation
io = n F A k ~
The exchange c u r r e n t can also be determined from
consecutive electron transfer theory, either from the
equation derived b y Vetter (2-4) or from the treatm e n t of H u n g and Smith (10)
2.C
~
o
0.18 ~
I
I
I
•
0.96 M K O H
1,E
I
KOH
D 0~4 M KOH
We find that the potential step data fits the theoretical
curves quite well (Fig. 3-6). I n particular, in the plot
of log Ka vs. E w h e r e the c u r v a t u r e is most pronounced,
the fit is excellent.
These same parameters can also be used to calculate
a-c and d-c polarograms using H u n g a n d Smith's e q u a tions (10). In calculating polarograms, the Matsuda
function (47) was used instead of exp (~2t) erfc (kt~/,),
because a d.m.e, is used for polarography and p l a n a r
diffusion no longer occurs. The fit b e t w e e n the theoretical a-c polarographic data (cot 0 vs. E ) and d-c
polarographic data [ l o g ( i / i d -- i) VS. E l and the exp e r i m e n t a l results are shown in Fig. 7 and 8. The
agreement b e t w e e n theory and e x p e r i m e n t for a-c
polarography is not too good, but Delmastro and Smith
(48) pointed out that a m a l g a m formation reactions
[53]
a
(~ 1.76 i
o
D
~
&
KOH
o
O
LOC-Io { )Q
O.C
e
e
-lC
,14o
[~
e
,
-,'~o
'
-&o
P O T E N T I A L (volts vs. s.c,e.)
Fig. 5. Log ~. vs. E for reduction reaction. Comparison of data
from potential-step chronocoulometry with theoretical calculations.
i
i
i
i
I
I
i
I
1.0
-4
E3
Q
O.5
LOGI0 (K)
LOGIo (~)
O 0.18 M KOH
1~4 M KOH
-$
o
D
o.18 M K O H
[3 0 . 3 4 M
KOH
o.96M
KOH
O
O
6
z~
-o.5
I
1.1
I
I
1.2
POTENTIAL
I
I
1,3
i
I \
--1,4
"~i
(volts vs.s.c.e.)
Fig. 4. Log Ka vs. E for oxidation reaction. Comparison of data
from potential-step chronocoulometry ([Zn(Hg)] = 1.2 raM) with
theoretical calculations.
i
-1.1
I
i
-I.2
I
I
-1.3
I
~
1.4
I
P O T E N T I A L (volts vs. s e e )
Fig. 6. Log ;~ vs. E for oxidation reaction. Comparison of data
from potential step chronocoulometry with theoretical calculations.
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1672
D e c e m b e r 1972
J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
50
I
O
I
I
I
I
I
I
I
o
1.2
A
%,,
40
A
o'~
.~
30
0.8
COT(0)
20
10
~
_
LOG10 (R T)
0.4
O
9
I
1.30
I
-1,40
POTENTIAL (volts vs. s,c.e.)
-1.50
Fig. 7. Comparison of Cot(g) vs. E data from a-c polarographic
measurements with theoretical calculations. The solution contained
[Zn(OH)42-] ~- 2.03 mM and [ O H - ] --- 0.18M. The d.m.e, was
mercury with a drop time of 1 sec. ~ ---- 11,0 Hz.
I
I
i
d
i)
0 --
1
-2
-1.30
I
I
-1.40
POTENTIAL (volts
I
I
-1.50
s.c.e.)
vs.
Fig. 8. Comparison of log il(i~ - - i) vs. E data from d-c polarogruphy with theoretical calculations. Conditions same as in Fig. 7.
io
=
2FAC* oDo ~/=
).1).2
(1 + eJ,) (~1 + X2)
~1),2
-- 2FAC*RDR v=
I
-'
I
I
-6
LOG10(Zn(Hg))
I
I
-5
(moles/cm 3)
-4
Fig. 9. Log RT VS. log [Zn(Hg)] for different concentrations of
Zn(OH)4 2 - . Comparison of theoretical calculations with experimental data from Farr and Hampson (24). Squares, [Zn(OH)42-]
5.05 x 10 - 6 moles/cm3; triangles, [Zn(OH)42-] ~ 6.8 x 10 - 5
moles/craB; circles, [Zn(OH)42-] ~ 1.834 x 10 - 4 moles/cm 8.
Open symbols are data from this work, solid symbols are from Farr
and Hampson.
I
LOG10
i/(i
--
I
[54]
( 1 2I- e - J ~ ) (;L1 Jr ~ 2 )
Using the kinetic parameters obtained from potential
step m e a s u r e m e n t s to calculate io a n d RT and comparing these results with the data i n Fig. 2 of F a r r and
Hampson (24), we calculate an RT which is larger t h a n
their values b y a factor of 3.5. This difference m a y be
a t t r i b u t e d to differences in the conditions of m e a s u r e m e n t i n the two studies; for example, the ionic strength
of F a r r and Hampson's solutions was 3.0M, while i n the
present work, it was 4.0M. They used NaOH and
NaC104 while KOH and K F were used in the present
work, and the solutions used b y F a r r a n d Hampson
were purified b y circulation over activated charcoal
for at least 28 days. However, w h e n the RT values calculated from potential step data are divided by 3.5,
the values at different Z n ( H g ) a n d O H - concentrations agree fairly well with those of F a r r a n d Hampson
(Fig. 9).
Matsuda and A y a b e (25) studied the reduction process by d-c polarography. Using the t r e a t m e n t for quasireversible polarographic waves they obtained the r e sults shown in Table III, which agree v e r y well with
ours for the reduction process.
Stromberg and Popova (29-31) studied both the oxidation and reduction reactions b y d-c polarography
with a dropping zinc a m a l g a m electrode used to study
the oxidation reaction. Their results do not agree very
well with the results of the present work for the oxidation reaction, although the agreement is fairly good
for the reduction reaction (Table I I I ) . However, their
results still lead to the conclusion that one hydroxide
is involved in the oxidation reaction rate limiting step,
since the oxidation rate shows a dependence on the first
power of the hydroxide concentration. This observation
led Stromberg and Popova to conclude that the oxidation reaction was a two-electron reaction which occurred b y a completely different path t h a n that of the
reduction reaction (Eq. [4] and [5]). However, if they
were correct, then a plot of log K vs. E for a n y one
Table III. Comparison of our results to previous studies
O log /Ce
Present work
F a r r a n d H a m p s o n (24)
M a t s u d a a n d A y a b e (25)
Papaya a n d S t r o m b e r g (31)
aTI,
~Sn
l o g koe
log ko=
Era/=
0,82
1.00
0.84
0.78
0.34
1.00
-0.46
-- :~.37
-- 3.00
--3.3
--3.43
--2.92
~
---3.70
-- 1.445
---1.444
--1.434
l o g [OH-]
log K=
8 l o g [OH-]
-- 1,85
+ 0.83
--1"-.82
--2.3
+ 1,4
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VoL 119, No. 12
ZINC(II)-ZINC
h y d r o x i d e concentration should be l i n e a r over t h e
whole p o t e n t i a l r a n g e (except for c u r v a t u r e due to
double l a y e r effects and distortion due to u n c o m p e n sated resistance); this is not the case. Moreover, this
m e c h a n i s m does not p r e d i c t t h e negligible v a r i a t i o n
of the exchange c u r r e n t w i t h h y d r o x i d e concentration
at e q u i l i b r i u m which s e v e r a l other r e s e a r c h e r s h a v e
r e p o r t e d (22-24, 26, 27). The consecutive electron
t r a n s f e r m e c h a n i s m e x p l a i n s all the o b s e r v e d features.
Recently Despic a n d c o - w o r k e r s (49) d e m o n s t r a t e d
that the C d ( I I ) / C d ( H g ) system in H2SO4 solutions,
long thought to r e p r e s e n t a m e c h a n i s m involving a
simple t w o - e l e c t r o n charge t r a n s f e r step, p r o b a b l y
occurs b y a t w o - s t e p single electron exchange m e c h a nism. The findings h e r e on the Z n ( I I ) / Z n (Hg) system
p a r a l l e l these results and suggest that other electrode
reaction mechanisms p r e v i o u s l y thought to involve
m u l t i p l e electron t r a n s f e r steps b e a r reinvestigation.
Acknowledgment
The support of the National Science F o u n d a t i o n
( N S F G P 6688X) and D e l c o - R e m y Corporation ( u n d e r
A F 33(615)-3487) is g r a t e f u l l y acknowledged. The
P D P - 1 2 A c o m p u t e r was a c q u i r e d u n d e r a g r a n t from
the National Science F o u n d a t i o n ( G P 10360).
M a n u s c r i p t s u b m i t t e d A p r i l 21, 1972; revised m a n u script r e c e i v e d J u n e 1, 1972.
A n y discussion of this p a p e r will a p p e a r in a Discussion Section to be p u b l i s h e d in the J u n e 1973 JOURNAL.
A
C*j
Dj
fJ
Eo!
Erl/2A
n!
ai
;h
koi
F
R
T
t
J, 4, x, ~, K
Za, Zc
Q(t)
i(t)
L I S T O F SYMBOLS
electrode a r e a
b u l k concentration of j t h species
diffusion coefficient of j t h species
a c t i v i t y coefficient of j t h species
f o r m a l r e d o x p o t e n t i a l of ith step (i ---1,2)
r e v e r s i b l e h a l f - w a v e potentials of ith
steps
n u m b e r of electrons t r a n s f e r r e d in ith
charge t r a n s f e r step
charge t r a n s f e r coefficient for ith steps
= 1--al
s t a n d a r d heterogeneous r a t e constants for
ith step
F a r a d a y ' s constant
ideal gas constant
absolute t e m p e r a t u r e
time
d e r i v e d parameters, see Eq. [15]- [21]
d e r i v e d p a r a m e t e r , see Eq. [27] a n d [29]
charge
current
APPENDIX
The equations and b o u n d a r y conditions for the solution of the c u r r e n t - t i m e b e h a v i o r for a q u a s i - r e v e r s i ble t w o - s t e p charge t r a n s f e r are as follows (1O)
0Co
Ot
8Cy
Ot
OCR
Ot
Fort :0,
02Co
= D o Ox2
[1A]
02Cy
Ox2
[2A]
= Dy
: DR ~
02CR
Ox2
[3A]
anyx
F o r t > 0, x -*
F o r t > 0, x -- 0
Do
Co : C*o
[4A]
C~ : C r = O
[5A]
Co ~ C*o
[6A]
CR "~ C:~ ~ 0
[7A]
~Co
ax
:
il (t)
nlFA
1673
AMALGAM ELECTRODE REACTION
[8A]
Dy
aCy
i2 (t)
i, (t)
Ox
n2FA
nlFA
DR
il(t)
nIFAks.1
OCa
--i2(t)
- - - Ox
n2FA
[9A]
[10A]
_ Cox=0 e x p ~ - - ~ l n l F [ E ( t ) -- El~ t
--CYz=0exp {
L
( 1 - aRT
l)nlF
RT
[ E ( t ) -- El ~ }
[IIA]
i2(t)
-- CYz=o exp ~--02~2F
}
n~FAks.2
[. ~
[E (t) -- E2 ~
-- CRx=o exp {
( 1 - RT
a2) n2F [ E ( t ) -- E2 o] }
[12A]
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Electrochemistry," Vol. 5, p. 291ff, J. O'M. Bockris
a n d B. E. Conway, Editors, B u t t e r w o r t h s , W a s h ington (1969).
2. K. J. Vetter, Z. Natur]orsch., 70, 328 (1952).
3. K. J. Vetter, ibid., 8a, 823 (1953).
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6. D. M. Mohilner, J. Phys. Chem., 68, 623 (1964).
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1O. H. L. Hung a n d D. E. Smith, ibid., 11, 237 a n d 425
(1966).
11. J. Plonski, This Journal, 116, 1688 (1969).
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15. J. G. Mason, J. ElectroanaL Chem., 11, 462 (1966).
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Chem., 38, 1130 (1966).
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(1966).
18. G. L. Booman, ibid., 38, 1144 (1966).
19. M. W. Breiter, This Journal, 112, 845 (1965).
20. G. Lauer, R. Abel, and F. C. Anson, Anal. Chem.,
39, 765 (1967).
21. G. L a u e r and R. A. Osteryoung, ibid., 40, 30A
(1968).
22. H. Gerischer, Z. Physik. Chem. (Leipzig), 262, 302
(1953).
23. H. Gerischer, Anal. Chem., 31, 33 (1959).
24. J. P. G. F a r r and N. A. Hampson, J. Electroanal.
Chem., 18, 407 (1968).
25. H. M a t s u d a and Y. A y a b e , Z. Elektrochem., 63,
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26. B. Behr, J. Dojlido, a n d J. Malyszko, Roezniki
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27. K. Morinaga, J. Chem. Soc. Japan, 79, 204 (1958).
28. A. G. S t r o m b e r g and L. F. Trushina, Elektrokhimiya, 2, 1363 (1966).
29. A. G. S t r o m b e r g and L. N. Popova, Isv. Tomsk
Politekhn. Inst., 167, 91 (1967).
30. A. G. S t r o m b e r g and L. N. Popova, Elektrokhimiya,
4, 39 (1968).
31. A. G. S t r o m b e r g and L. N. Popova, ibid., 4, 1147
(I968).
32. F. C. Anson and I:). A. Payne, J. Electroanal. Chem.,
13, 35 (1967).
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34. D. A. Payne, Ph.D. dissertation, The U n i v e r s i t y of
Texas at A u s t i n (1970).
35. J. A l b e r y and M. Hitchman, "Ring-Disc Electrodes," pp. 38-41, O x f o r d U n i v e r s i t y Press
(1971).
36. J. H. Christie, G. Lauer, and R. A. Osteryoung, J.
ElectroanaL Chem., 7, 60 (1964).
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Anson, Anal. Chem., 35, 1979 (1963).
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(Frankfurt), 3, 16 (1955).
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J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
39. H. Gerischer and W. Vielstich, ibid., 4, 10 (1955).
40. K. B. Oldham and R. A. Osteryoung, J. Electroanal.
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Acta, 16, 525 (1971).
42. K a t s u m i K a n z a k i Niki, Ph.D. dissertation, pp. 16
and 80, The University of Texas at A u s t i n
(1966).
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December 1972
45. D. E. Smith in "Electroanalytical Chemistry," Vol.
1, p. 26ff, A. J. Bard, Editor, Marcel Dekker, New
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47. H. Matsuda, Z. Elektrochem., 59, 494 (1955).
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169 (1966).
49. A. R. Despic', D. R. Jovanovic', and S. P. Bingulac,
Electrochim. Acta, 15, 459 (1970).
The Kinetics of the p-Toluquinhydrone Electrode
F. Kornfeil*
Electronics Technology and Devices Laboratory,
United States A r m y Electronics Command, Fort Monmouth, New Jersey 07703
ABSTRACT
The reaction m e c h a n i s m of the redox system p - t o l u q u i n o n e / t o l u h y d r o q u i none ( t o l u q u i n h y d r o n e electrode) on smooth p l a t i n u m was elucidated with the
aid of the electrochemical reaction order method. It was found that in the pH
r a n g e 0.1-3.2 the reaction proceeds according to the scheme Q % H + ~=~ HQ +,
HQ + + e - ~ HQ, HQ -~ H + ~ H2Q +, H2Q + + e - ~=~ H2Q. This m e c h a n i s m
is identical with the H e l l e sequence determined b y Vetter for the benzoquinone electrode. The relatively fast rate of the c h a r g e - t r a n s f e r steps, however,
necessitated m e a s u r e m e n t s of the electrode polarization in the nonsteady state.
A method is described to d e t e r m i n e the i n d i v i d u a l exchange c u r r e n t densities
in m o d e r a t e l y fast consecutive c h a r g e - t r a n s f e r reactions.
The reaction mechanism of the redox couple pb e n z o q u i n o n e / h y d r o q u i n o n e ( q u i n h y d r o n e electrode)
was first elucidated b y Vetter (1) who i n t e r p r e t e d the
steady-state overpotential on smooth p l a t i n u m with
the aid of the electrochemical reaction order method.
He showed that, in the over-all electrode reaction
H2Q ~:~ Q -}- 2H + -}- 2 e - , the electrons are exchanged
in two different c h a r g e - t r a n s f e r steps. Hale a n d P a r sons (2), using the Koutecky method on dropping
mercury, and Eggins a n d Chambers (3), employing
cyclic v o l t a m m e t r y on polished p l a t i n u m electrodes,
arrived at essentially similar conclusions in more
recent studies of the reduction of b e n z o q u i n o n e and
other p-quinones. The consecutive c h a r g e - t r a n s f e r
mechanism is, however, challenged by Loshkarev and
Tomilov who account for their e x p e r i m e n t a l results
obtained on Pt (4, 5) a n d other metals (6) by postulating that both electrons are transferred s i m u l t a n e ously i n a single c h a r g e - t r a n s f e r step.
The present paper describes an investigation of the
kinetics of the redox system m e t h y l - p - b e n z o q u i n o n e /
m e t h y l - h y d r o q u i n o n e ( t o l u q u i n h y d r o n e electrode).
The aim of this study has been (i) to clarify the situation with respect to the reaction mechanism and (it)
to ascertain what effect, if any, the addition of the
CH~-group to the benzene ring m a y have on the
kinetic parameters of the q u i n h y d r o n e electrode
reaction.
Experimental Procedure
All m e a s u r e m e n t s of the overpotential were made
at the same constant t e m p e r a t u r e (25 ~ • 0.5~
in
solutions of equal ionic strength ~/2zcjnj: ---- 1.0. The
excess of supporting electrolyte accomplished, as usual,
the suppression of the ~-potential to negligible values,
m i n i m a l tranference n u m b e r s tj, and the v i r t u a l constancy of the activity coefficients of all reacting species
Sj, t h e r e b y m a k i n g the substitution of cj for aj possible.
Electrolyte solutions.--Both the t o l u q u i n o n e and the
t o l u h y d r o q u i n o n e used were obtained from E a s t m a n
* Electrochemical Society A c t i v e M e m b e r .
K e y w o r d s : t o l u q u i n h y d r o n e electrode, reaction m e c h a n i s m , exc h a n g e current densities, electrochemical reaction order.
Kodak "practical grade" reagents. The t o l u q u i n o n e
was purified b y s u b l i m a t i o n u n d e r atmospheric pressure and the sublimate collected as c a n a r y - y e l l o w
needles (mp 68.0~
The toluhydroquinone, however,
required repeated recrystallization from benzene and
had to be subsequently twice sublimed in vacuo before
s n o w - w h i t e crystals could be obtained (mp 126.5~
All other reagents used in the electrolyte solutions
were of C.P. quality and were used without f u r t h e r
purification. Triply distilled w a t e r served as the
solvent. The t o l u q u i n o n e and t o l u h y d r o q u i n o n e concentrations varied from 10 -2 to 10 -4 molar.
Because of the k n o w n v u l n e r a b i l i t y of aqueous
solutions of t o l u q u i n h y d r o n e to photodecomposition (7)
the toluquinone and t o l u h y d r o q u i n o n e were dissolved
in the electrolyte immediately before the start of each
experiment. No decomposition could be detected within
a 6-hr period, provided that the solutions were kept
free of dissolved oxygen. Purified argon was, therefore,
b u b b l e d t h r o u g h the electrolyte at the start of each
series and also, i n t e r m i t t e n t l y , b e t w e e n i n d i v i d u a l
m e a s u r e m e n t s w i t h i n a series of determinations of the
overpotential. This procedure insured sufficient stability during the 2-3 hr n o r m a l l y required for establishing the anodic and cathodic c u r r e n t densitypotential relation at a given concentration.
Reierence electrodes.--The values of all electrode
potentials 9 are referred to the SHE and were measured
against a Ag/AgC1/KCI(1M) electrode (co = 40.2387
V). Highly stable reference electrodes were prepared
b y the electrolytic formation of AgC1 on t h e r m a l l y
reduced spheres (r ~ 0.2 cm) of Ag20 (8) attached to
small Pt spirals. The scatter of potential differences
among these electrodes n e v e r exceeded 0.05 inV.
Electrolysis celI.--A P y r e x cell as shown i n Fig. 1
was used in all the polarization m e a s u r e m e n t s described
in this paper. The w o r k i n g electrode, a smooth P t wire
(r ,~ 0.25 m m ) , was sealed into a glass tube leaving
2.55 cm exposed to the electrolyte solution, and was
located along the axis of a cylindrical P t counterelectrode through which a small hole had been drilled
to accommodate the H a b e r - L u g g i n capillary of the
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