Adsorption of Cl− ions on bismuth from ethanol

J. Electroanal. Chem., 70 (1976) 103--115 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

103

A D S O R P T I O N O F C1- I O N S O N B I S M U T H F R O M E T H A N O L

B. DAMASKIN, U. PALM and M. VAARTN6U Laboratory o f Electrochemistry, Tartu State University, Tartu 202400, Estonian S.S.R. (U.S.S.R.) and Chemical Faculty, Moscow State University, Moscow V-234 (U.S.S.R.) (Received 1st September 1975)

ABSTRACT The specific adsorption of el-- ions at the bismuth--ethanol interface has been studied both in the solutions of mixed electrolytes with constant ionic strength and in the binary LiC1 solutions by the method of measuring the potential dependence of differential capacity of bismuth. The charge due to specifically adsorbed anions was calculated from the experimental capacity data. It was found that in the case of specific adsorption of C1-- ions at the bismuth--ethanol interface the conditions of undercharged as well as recharged surface of electrode could be observed experimentally. The analysis of the results obtained by fitting the charge of specifically adsorbed ions to the modified virial isotherm including the diffuse layer correction term suggests that in the conditions of recharge of the bismuth surface cations enter the inner part of the double layer and a considerable ionic association occurs in the inner layer. A procedure has been proposed for calculating the charge due to cations in the inner layer, for determining the actual value of the outer Helmholtz plane potential and for evaluating the real parameters of the adsorption isotherm. The reliability of the results of calculations was verified by comparing the data obtained by the method of mixed electrolytes both considering and neglecting the ionic association in the inner layer with the data of the method of binary electrolyte.

In r e c e n t years c o n s i d e r a b l e progress has been m a d e in the q u a n t i t a t i v e s t u d y o f the specific a d s o r p t i o n o f ions o n ideally polarized e l e c t r o d e s b o t h f r o m a q u e o u s a n d n o n a q u e o u s solutions (see, e.g., reviews 1 and 2). F o r t h e m e r c u r y [ 3 - - 2 3 , 3 1 - - 3 3 ] and for the b i s m u t h [ 2 4 - - 3 0 ] electrodes t h e basic relationships o f the d e p e n d e n c e o f t h e charge due to specifically a d s o r b e d ions (ql) on the bulk c o n c e n t r a t i o n (c) and on the e l e c t r o d e charge (q) have been established in t h e case o f a l m o s t all inorganic ions. The main results have b e e n o b t a i n e d o n the basis o f q u a n t i t a t i v e t r e a t m e n t o f the data o f c a p a c i t y meas u r e m e n t s b o t h in solutions o f single b i n a r y e l e c t r o l y t e s and in c o n s t a n t ionic strength solutions o f m i x e d e l e c t r o l y t e s [ 1 0 , 3 4 ] . However, despite the abundance o f e x p e r i m e n t a l d a t a a b o u t t h e specific a d s o r p t i o n o f ions t h e p r o b l e m s of c h o i c e o f the a d s o r p t i o n i s o t h e r m f o r t h e a d e q u a t e d e s c r i p t i o n o f specific a d s o r p t i o n o f ions on electrodes still r e m a i n u n s e t t l e d [ 9 , 1 4 , 1 5 , 1 7 , 2 7 , 3 0 , 3 5 ] . The main difficulties are c o n n e c t e d with the c h o i c e o f the c o r r e c t c o n c e n t r a tion variable and with t h e a c c o u n t o f the influence o f the diffuse l a y e r o n the a d s o r p t i o n p a r a m e t e r s in the i s o t h e r m e q u a t i o n . The practical i n d e p e n d e n c e

104

of specific adsorption of the ionic strength of the solution of mixed electrolytes has been established for the mercury [22,36] and for the bismuth [27--29,37] electrodes by studying the specific adsorption of cations, the adsorption of which was weak and was not accompanied by the recharge of the electrode surface. On the basis of the experimental data it was established that in this case, i.e. in the case of weak specific adsorption of ions from the solutions of mixed electrolytes with constant ionic strength, the most suitable is to choose the concentration of ions at the outer Helmholtz plane m c exp( - - z F ~ o / R T ) for the concentration variable and to use the isotherm [9,22,27, 35] ln(ql/zmc) + zF~o/RT

= In/3

--

2Bql/z

(1)

where m denotes the relative concentration of the surface-active ions in the solution of the mixed electrolytes with ionic strength c; z is the valence number of the surface-active ion, including sign; ~0 is the potential of the outer Helmholtz plane; fi is the constant of adsorption equilibrium; B is the second virial coefficient characterizing repulsive interaction (B < O) of specifically adsorbed ions; the terms R and T have their usual meaning. Considerable difficulties arise using the isotherm (1) for description of specific adsorption in the conditions of recharge of the electrode surface, i.e. in the region [qll ~ IqJ [27,30]. So, in the case of specific adsorption of Cs+ cations from methanol [27] and of C1- anions from ethanol [30] on bismuth, the dependence of the function F 1 = l n ( q l / z m c ) + z F ~ o / R T on ql sharply deviates from linearity in the region of recharge where the sign of ~0 potential changes * Such deviations contradict eqn. (1). The number of systems in which the specific adsorption of ions could be studied experimentally with high accuracy in the conditions Iql I~ Lql and in a wide interval of surface charges q is comparatively limited. Obviously, this is one of the main reasons of the lack of data in the literature about this problem [27,30]. The aim of the present work is to study quantitatively the relationships of the specific adsorption of ions in the conditions of recharge of electrode surface on the example of specific adsorption of C1- anions at the Bi--C2H5OH interface. The preliminary data about this system were obtained in ref. 30. The adsorption of C1- ions was studied both from the solutions of mixed electrolytes with constant ionic strength m c M LiC1 + (1 -- m ) c M LiC104 at the ionic strengths c = 0.01, 0.1 and 0.5 M and from the binary solutions of LiC1. The relative content of LiC1 varied in the limits of m = 2 × 10 -3 -- 1 (in all 15 concentrations) in the solutions of mixed electrolytes with constant ionic strength, and in the solutions of LiC1 alone the concentration interval was c = 3 × 10 -3 -0.5 M (in all 10 concentrations). The investigation of the specific adsorption of chloride ion was carried out by measuring the dependence of the differential capacity C on electrode potential E at 25°C with the aid of the a.c. bridge R-568. The reference electrode * F 1 is t h e s a m e a s f u n c t i o n

F in ref. 27.

105 was an a q u e o u s s a t u r a t e d c a l o m e l e l e c t r o d e s e p a r a t e d f r o m the s o l u t i o n u n d e r s t u d y b y t h e i n t e r m e d i a t e e t h a n o l i c solutions. T h e liquid j u n c t i o n b e t w e e n a q u e o u s a n d e t h a n o l i c s o l u t i o n s was m a d e t h r o u g h s o l u t i o n sealed t a p s a n d was k e p t c o n s t a n t in all m e a s u r e m e n t s . In the case o f the solutions w h e r e c a p a c i t y dispersion w i t h f r e q u e n c y t o o k place ( e x t r e m e l y l o w LiC1 c o n c e n t r a t i o n s a n d the m o s t positive p o t e n t i a l s ) , the values o f C w e r e m e a s u r e d at several d i f f e r e n t f r e q u e n c i e s a n d w e r e t h e n e x t r a p o l a t e d t o zero f r e q u e n c y . T h e e q u i l i b r i u m C,E curves, o b t a i n e d b y e x t r a p o l a t i o n , w e r e u s e d o n l y f o r q u a n t i t a t i v e t r e a t m e n t . T h e p r o c e d u r e o f c a p a c i t y m e a s u r e m e n t s a n d o f preparing b i s m u t h d r o p e l e c t r o d e s w i t h a l m o s t ideally s m o o t h surface was described in detail earlier [ 2 7 ] . T h e e t h a n o l f o r p r e p a r i n g solutions was p u r i f i e d b y m u l t i p l e redistillation o v e r CaO. I t was e s t a b l i s h e d b y a special investigation t h a t t h e c o n c e n t r a t i o n o f residual w a t e r in e t h a n o l used f o r p r e p a r i n g solutions was negligible a n d p r a c t i c a l l y did n o t have a n y e f f e c t on the results o f c a p a c i t y m e a s u r e m e n t s . LiC1 and LiC104 o f high degree o f p u r i t y w e r e additionally p u r i f i e d b y r e c r y s t a l l i z a t i o n f r o m redistilled w a t e r a n d t h e n redistilled a b s o l u t e a l c o h o l a n d were dried in v a c u o . E q u i l i b r i u m d i f f e r e n t i a l c a p a c i t y curves are r e p r e s e n t e d in Figs. 1 a n d 2 f o r

~0

C//~Fc~-2

70

70

5O

50

30

50

iO

2~i

~0 i

0.5

ilO-E/v

0.5

1.o -E/v

Fig. 1. Zero frequency capacity of a bismuth electrode in contact with the system 0.01 m M LiC1 + 0.01(1 -- m) M LiC104 in ethanol at the following values of m: (1) 0; (2) 0.01; (3) 0.02; (4) 0.03; (5) 0.05; (6) 0.1; (7) 0.2; (8) 0.3; (9) 0.5; (10) 1. Potentials are with respect to an aqueous saturated calomel electrode. Fig. 2. Zero frequency capacity of a bismuth electrode in contact with LiC1 ethanolic solutions at the following concentrations: (1) 0.003; (2) 0.005; (3) 0.01; (4) 0.02; (5) 0.05; (6) 0.1; (7) 0.2; (8) 0.5 M.

106

the solutions of mixed electrolytes with constant ionic strength c = 0.01 M and for the binary LiC1 solutions at different concentrations. In both cases the increase of LiC1 concentration in the solution is accompanied by a considerable rise of capacity at the anodic branch of C,E curves caused by the specific adsorption of C1- ions on the bismuth electrode in this potential interval. Reproducibility of the capacities at a given E was -+0.1% within a given run and +0.5% from one run to another. As seen in Fig. 1 the cathodic branches of C,E curves corresponding to different LiC1 concentrations in the solutions of mixed electrolytes completely coincide with the capacity curve of an inactive electrolyte LiC104. Consequently, C1- ions do not adsorb specifically on bismuth from ethanol at more negative potentials than --0.80 V. Therefore, in the case of constant ionic strength systems the m e t h o d of back integration of C,E curves can be used for quantitative treatment of capacity data [1,38]. The zero charge potential of bismuth (Eq=o) in ethanol necessary for calculations equals to --0.43 V (in respect of an aqueous saturated calomel electrode) [39]. The capacity values in the cathodic branch of C,E curves rise slightly by the increase of LiC1 concentration in the binary LiC1 solutions (Fig. 2). This p h e n o m e n o n is caused by the corresponding change of the surface charge at a given value of E. The calculation of the charge ql due to specifically adsorbed anions from the solutions of mixed electrolytes with constant ionic strength was carried out by the standard procedure according to Hurwitz [ 34] and Dutkiewicz and Parsons [10]. In the calculations the activities of electrolytes were replaced by their concentrations in the mixture. In other words, it was assumed that the ionic strength of the solution of mixed electrolytes did not change because of different tendencies of LiC1 and LiC104 to association in ethanol by varying the composition of the system under study [40]. The correctness of this assumption was verified experimentally by measuring the dependence of an electrical conductivity of the system rnc M LiC1 + (1 -- m)c M LiC104 upon the composition at different m and c. It was established that at c = 0.01 and 0 . 1 M the electrical conductivity of these systems only slightly (in the limits of some per cent) depended u p o n the composition, but at c = 0.5 M this dependence became more significant. Consequently, the m e t h o d of mixed electrolytes with constant ionic strength turned out to be applicable for the study of specific adsorption of C1- anions from ethanol using C104 as a surface-inactive reference ion. However, the accuracy of this m e t h o d somewhat decreases by increasing ionic strength of solutions. According to ref. 40 the m e t h o d of mixed electrolytes with constant ionic strength must give higher values of the specifically adsorbed charge if the ionic association takes place and the dissociation constant of ion pairs containing the reference ion (in the present case Li ÷ ... C104) exceeds the dissociation constant of ion pairs containing the surface-active ion (Li ÷ ... C1-). If the dissociation constants of these ion pairs are almost the same the m e t h o d of mixed electrolytes yields the total surface charge of specifically adsorbed anions F (1) due to both the unassociated (free) C1- ions (F(cl)_) and the specifically ad-

107 sorbed ion pairs (FLiCl). (i) Thus, in the case of simultaneous adsorption of free ions and ion pairs the method of mixed electrolytes gives the quantity q l = z_ FF (i)" which is not equal to the effective charge of specifically adsorbed ions qi = qi- + q~, where q~ denotes the charge due to Li ÷ cations in the composition of specifically adsorbed ion pairs. The charge due to specifically adsorbed C1- ions was calculated from the C, E curves obtained in binary LiC1 solutions by the method of Grahame and Soderberg [3] which, similarly to the paper 41, was somewhat modified accordingly to constant charge conditions. The Parsons' function for 1,1-electrolytes can be written in the form d}+

= E+ d q - - 2 R T F _

dln a,+

(2)

where E+ is the potential of electrode with respect to an electrode reversible to the cation; F is the surface excess of anions, and a,+ the mean ionic activity. According to eqn. (2) O In

(3)

a,+/q = - - 2 R T F _

So far as 02}+ Olna,+Oq

02}+ 02E+ 0q31na_+andolna,+0q

02E+ OqO Ina_+

the twice differentiation of eqn. (3) with respect to q yields the formula 0 In a,+J q

F

- ~ - .,+

(4)

where

(5)

a_ = O(FP_)/Oq

The left part of eqn. (4) is accessible to experimental determination and does n o t need the knowledge of the E+ values. Thus, it is possible to determine the term a _ by the numerical integration of the formula r eL_-

LOlna±jq dq+~*

2RT.,

(6)

q*

and then the surface excess of anions by the equation q

F F _ = . ; ~_ dq + FF*_

(7)

q*

The integration constants a * and FF*_ refer to the region where no specific adsorption of surface-active anions occurs and they can be calculated by the formulae of diffuse layer theory [42]

108 O~-$ = ~1 +

q* ( 4 A 2 c ~-

+

q2)--I/2

(8)

and FF*_ =q*+!22 (4A2c + q,2)1/2 _Acl/2

(9)

where A = (DR T/2~) 1/2 and D is the mean dielectric constant in the bulk of solution. The surface excess of cations FF+ can be obtained from the difference FF+ = F F _ -- q

(10)

If it is assumed, according to Grahame [42], that the total surface excess of cations is populated only in the diffuse layer (i.e. specific adsorption of C1occurs only in the form of free anions without ion pair formation), then FF+ = q~. Further, on this assumption the charge q2 in the diffuse layer due to the anions can be calculated by the equations of diffuse layer theory, and ql = q~- = - - F F _ -- q~-. Apparently, if the assumption about the absence of specific adsorption of ion pairs is valid, the m e t h o d of mixed electrolytes with constant ionic strength in the condition rn = 1, and the m e t h o d of binary electrolyte at corresponding concentrations of LiC1 must yield coinciding results. The results of calculation of the charge due to the specific adsorption of C1- ions, obtained by two different methods, are shown in Figs. 3 and 4 as the plots of ql against q at different concentrations of C1- in the solution. The Figures demonstrate that at a given q = const, the values of ql referring to the solutions of mixed electrolytes with constant ionic strength are about 30--35% less than those in the binary solutions of LiC1. Thus, for example, at q = 8 pC cm - 2 and m = 1 in the system 0.1 m M LiC1 + 0.1(1 -- m) M LiC104 ql = 10.4 pC cm - 2 , but at the same charge ql = 14.2 pC cm - 2 in the binary solutions of LiC1 (Fig. 4), Besides, the slope of the plots of ql against q, (Oql/Oq)~, is considerably less in the solutions of mixed electrolytes than in the case of binary LiC1 solutions. The discrepancy between the results of two different methods of calculation of the charge of specifically adsorbed C1- ions at the interface Bi--C2H5OH could be related to the invalidity of the condition q~ = FF+ d u e to the entrance of the cations into the inner part of the double layer and to the adsorption of ion pairs Li ÷ ... C1-. As the other possible reason for the discrepancy between the results of two different methods of calculation of the specifically adsorbed charge can be regarded some specific adsorption of the reference ions (C10~-) causing a decrease of the specifically adsorbed charge in the case of the mixed electrolyte [43]. To estimate the role of each of these reasons it is expedient to fit the experimental data, obtained by the m e t h o d of mixed electrolytes, to the adsorption isotherm (1), and, as is usually done, assuming first, that the cations do

109

/a /s -q~/.Ccm-~

10

67

t0

1

5

5

0

I

I

3

6

I q/~Cc~ ~

-5

0

5

6

c~/~.C~m-2

Fig. 3. Plot of charge due to specifically adsorbed Cl-- against charge on the bismuth electrode in the ethanolie solutions of the system 6.1 m M LiC1 + 0.1(1 -- m) M LiClO 4 at the following values of m: (1) 0.005; (2) 0.01; (3) 0.02; (4) 0.03; (5) 0.05; (6) 0.1; (7) 0.2; (8) 0.3; (9) 0.5; (10) 1. Fig. 4. Plot of charge due to specifically adsorbed C1-- against charge of the bismuth electrode in contact with ethanolic solutions of LiC1 at the following concentrations: (1) 0.003; (2) 0.005; (3) 0.01;(4) 0.02; (5) 0.05; (6) 0.1;(7) 0.2; (8) 0.5 M.

not enter the inner layer, i.e. q l = ql- This assumption is necessary for the calculation of the outer Helmholtz plane potential ~0, since 2 R T s i n h _ 1( q + q l 1

I~O = - - ~

\ 2ncl/2 ]

(11)

The results of this calculation are given in Fig. 5. As can be seen from Fig. 5, the shape of the curves depends significantly upon the ionic strength of the solution under study. If at c = 0.5 M the plots of F1 against ql in Fig. 5 in the first approximation may be represented by the straight lines over the entire range of electrode charges studied, then at c = 0.1 and 0.01 M sharp deviations occur in the region of the recharge of the electrode surface, i.e. in the region [qll ~ Iql. The amplitude of these deviations significantly increases with the decrease of the ionic strength of solution and with the increase of q. It is characteristic of the systems of mixed electrolytes that in Fig. 5 at Iqll < Iql the curves corresponding at a given q = const, to different ionic strengths c merge, within experimental error, into one c o m m o n line the parameters of which

110 b e c o m e i n d e p e n d e n t o f the ionic s t r e n g t h o f t h e s o l u t i o n . C o n s e q u e n t l y , similarly t o t h e specific a d s o r p t i o n o f cations, t h e a d s o r p t i o n i s o t h e r m (1) c o r r e c t l y describes t h e i n f l u e n c e o f ionic s t r e n g t h o f s o l u t i o n o n a d s o r p t i o n p a r a m e t e r s also in t h e case o f specific a d s o r p t i o n o f a n i o n s o n t h e " u n d e r c h a r g e d " e l e c t r o d e surface [ 2 2 , 2 7 , 3 7 ] . S h a r p d e v i a t i o n s f r o m l i n e a r i t y in t h e region o f r e c h a r g e o f t h e e l e c t r o d e surface can f o r m a l l y be r e g a r d e d as a result of s t r o n g l y e l e v a t e d values o f ql a n d t h e r e f o r e t h e y c a n n o t be r e l a t e d t o t h e specific a d s o r p t i o n o f t h e r e f e r e n c e ions (C10~-) resulting, o n the c o n t r a r y , in t h e decrease o f ql values [ 4 3 ] . I t is also easy t o see t h a t t h e s h a p e o f t h e curves in Fig. 5 c a n n o t b e caused b y t h e c h a n g e o f t h e degree o f ionic a s s o c i a t i o n w i t h v a r i a t i o n o f t h e c o m p o s i tion o f t h e s y s t e m , i.e. b y t h e c h a n g e o f e f f e c t i v e ionic s t r e n g t h w i t h t h e increase o f LiC1 c o n c e n t r a t i o n in t h e m i x t u r e . A c t u a l l y , if t h e a n o m a l o u s s h a p e of t h e i s o t h e r m s in Fig. 5 w e r e c a u s e d b y t h e b u l k a s s o c i a t i o n o f t h e ions t h e n a c c o r d i n g t o the law o f mass a c t i o n , c o r r e s p o n d i n g e f f e c t s s h o u l d b e t h e s t r o n g e s t in t h e s y s t e m w h e r e c = 0.5 M a n d t h e l o w e s t in t h e s y s t e m w i t h e l e c t r o l y t e c o n c e n t r a t i o n c = 0.01 M, w h i c h c o n t r a d i c t s t h e e x p e r i m e n t a l d a t a in Fig. 5. F u r t h e r m o r e , in t h a case o f c o n s i d e r a b l e d i f f e r e n c e o f t h e associa-

bi(q,]/zmc) ~0

1o

8 +

\ (

~6

I

5

l

~o %/~Cc~-2

I

s

I

to -~l/-,cc~ ~

Fig. 5. Plot of the function l n ( q l / z m c ) + z F ~ o / R T against the charge of specifically adsorbed C1-- ions in the ethanolic solutions of the system mc M LiC1 + (1 -- m) c M LiC104 at the following concentrations c: (©) 0.01 M; (e) 0.1 M; (x) 0.5 M. The charge on the bismuth electrode is given near each curve in pC c m - 2 . Fig. 6. Plot of the function l n ( q T / z m c ) against the charge of specifically adsorbed C1-ions in the ethanolic solutions of the system 0.1 m M LiC1 + 0.1(1 -- m) M LiC104. Numbers by each line indicate the charge on the electrode in pC cm -2.

111 tion constants of Li + ... C1- and Li + ... C10 4 ion pairs it is unrealistic to expect the merging of F1, ql curves into a c o m m o n line in the conditions Iqll < [qL Consequently, we can conclude that sharp deviations from linearity in Fig. 5 at c < 0.5 M, as well as discrepancies between the results of two methods of calculation of ql values, are probably related to the increasing association of specifically adsorbed anions with cations in the inner layer in the region of recharge of the electrode surface. As a result, the distribution of the potential drop across the inner layer and the value of the outer Helmholtz plane potential change. Therefore, as a result of incorrect assumptions FF÷ = q~ and q~- = ql, the equations of the diffuse layer theory lead to distorted values of ~0 potential [27,30]. Insofar as the influence of the diffuse layer on the specific adsorption of ions and on the parameters of the isotherm (1) is the strongest at low ionic strengths, the distortions of ~0 values caused by the ionic association in the inner layer are the most considerable in the solutions with low total concentration of electrolytes (Fig. 5). It is obvious that the p h e n o m e n o n of ionic association in the inner layer takes place also at q < 0, however, in this case the effect of recharge of the electrode surface is absent and the corresponding anomalies are weakly expressed. For separating the components of the charge q~-, q + l , q2 and q2÷ we assume that in the first approximation the isotherm (1) describes adequately the specific adsorption of anions (i.e. q T / z - ) also in the region of recharge of electrode surface, but, unlike the systems in refs. 9, 13--15, and 37, it is necessary to consider in the calculations of ~0 values the entrance of the cations into the inner layer. In this case the isotherm (1) involves the term q~- instead of ql and the terms In/3, B and ~0 become u n k n o w n in eqn. (1). The following procedure can be proposed for determination of these terms and of the charge of cations drawn into the inner layer by the specifically adsorbed anions. As can be seen in Fig. 6, the total charge due to the specific adsorption of C1- ions at the bismuth--ethanol interface can be fitted to the simple virial isotherm l n ( q l / z _ m c ) = In/3 v -- 2 B v q l / z _

(12)

where the adsorption equilibrium constant/3v has, however, a formal character, as far as the plots F v = l n ( q l / z _ rnc) against q~- at q = const, do n o t coincide with each other at different c (Fig. 7). If the diffuse layer correction is introduced into the term fly according to the formula ln/3=ln/3 v+

RT

=ln/3v+2Z-

sinh -1

q

(13)

then at a given q = const, practically one and the same value of in 13 characterizing the energy of the specific adsorption of C1- anions at the bismuth electrode is obtained (Figs. 7, 8). This result shows that at q~ -- 0 also the cations are n o t drawn into the inner part (q~ = 0) and, consequently, q = --q2. There: fore, in the conditions q~- -+ 0 the actual second virial coefficient B can be

112

! "12.I \ \

{5

5

\\\

_%"., \

to

5 I

I

5

6 -q7#cc,¢ 2

I

I

I

5

6

I

~/~Cc,.-~

Fig. 7. Plot of the functions F v (1--3) and F 1 (4) against the charge due to specifically adsorbed C1-- at q = 5 pC cm - 2 in the ethanolic solutions of the system mc M LiC1 + (1 -- rn) c M LiC104 at the following concentrations c: (©) 0.01 M; (e) 0.1 M; (x) 0.5 M. Fig. 8. Plot of In fiv(1--3) and In/3 (4) against the charge of the bismuth electrode in the ethanolic solutions of the system rnc M LiC1 + (1 -- m) c M LiC104 at the following concentrations: (o) 0.01 M; (e) 0.1 M; (x) 0.5 M. In the formula In 13 = a + bq parameters have the following value: a = 3.6; b = 0.68 cm 2 tIC- I . calculated b y the f o r m u l a [ 2 7 , 3 7 ] B =Bv -- [4A2c

+ q2]-1/2

(14)

It is w o r t h n o t i n g t h a t also t h e values o f B calculated b y the relationship (14) at q = const, are a l m o s t i n d e p e n d e n t o f the values o f c. The actual p l o t o f F1 against qT can be o b t a i n e d if a straight line with the slope c o r r e c t e d according to eqn. (14) is d r a w n f r o m the p o i n t o n the o r d i n a t e axis c o r r e s p o n d i n g t o the real In fi term. N o w , on the basis o f the d i f f e r e n c e (Fv - - F1) the real values o f @0 p o t e n t i a l can be calculated at d i f f e r e n t q~- considering eqns. (1) and (12). F u r t h e r , the actual diffuse layer charge can be c a l c u l a t e d b y t h e diffuse layer t h e o r y [42] q2 = - - 2 A c l / 2 s i n h ( @ o F / 2 R T )

(15)

Because --q = qi- + q~ + q2

(16)

the dependence of q~ on qi- can be determined at different q and c since the values of q, q~- and q2 are known.

113 4-

~ ~Ccm-~

~Ccm -~

[3

,% ~m

/, 3

6

[]

[3

-q?/~Cc~-2

5

6

-~:/~,cc~~

Fig. 9. Plot o f charge due t o Li + ions in t h e i n n e r layer against charge o f specifically ads o r b e d CI-- in t h e e t h a n o l i c s o l u t i o n s o f t h e s y s t e m 0.01 m M LiCI + 0.01 (1 - - m ) M LiCIO 4 at t h e f o l l o w i n g charges o n t h e b i s m u t h e l e c t r o d e in p C cm--2: (+) 1 ; ( $ ) 2; (x) 3; (o) 4; (*) 5; (A) 6; (..) 7; (D) 8. Fig. 10. Plot o f charge d u e t o Li + ions in t h e i n n e r layer against charge o f specifically ads o r b e d C1-- in t h e e t h a n o l i c s o l u t i o n s o f t h e s y s t e m 0.1 m M LiCl + 0.1 (1 - - m ) M LiC10 4 at t h e f o l l o w i n g charges o n t h e b i s m u t h e l e c t r o d e i n / / C cm--2: (~) 0 ; (+) 1 ; ( e ) 2 ; (x) 3 ;

(©) 4;(*) 5;(A) 6;(") 7;([]) 8.

Figures 9 and 10 illustrate the results of these calculations for the systems of mixed electrolytes with constant ionic strength c = 0.01 and 0.1 M. As can be seen from these Figures within possible experimental errors the values of q~ significantly rise with the increase of the charge due to specifically adsorbed C1- ions and almost do n o t depend on the electrode charge and the ionic strength of the solution. As a consequence, it is possible that a certain distribution between specifically adsorbed free anions and ion pairs (for the present system it is a function of qi- and approaches 1 : 1 at high qi- values) is energetically favourable. It is also possible that the peculiar ionic triplets consisting of two specifically adsorbed C1- ions and of a Li ÷ cation exist in the inner layer. To verify the results obtained by the above mentioned methods the quantity q2 and then the total surface excess of anions F F _ were calculated by the use of the actual values of q2(q~ > O) F F _ = - - ( q l + q2)

(17)

where the values of qi- were f o u n d by the m e t h o d of mixed electrolytes with constant ionic strength at m = 1. In Figs. 11 and 12 the results of the calculations are compared with the values of F F _ , obtained in 0.1 and 0.01 M LiC1 solutions by the m e t h o d of binary electrolyte. In these Figures also the plots of F F _ against q, calculated by the data of the m e t h o d of mixed electrolytes are represented, but without considering entrance of the cations into the inner part of the electrical double layer {i.e. assuming q~ = 0). As can be seen in

114

uCcm-2

/

FL/~Ccm-2

/

t0

5

I

5

I

6 ,~/~cc~ ~

I

0

5

I

6 q/~Ccm

Fig. 11. Charge due to surface excess of C1-- ions as a function of electrode charge in 0.01 M LiC1 ethanolic solution calculated in different ways: (o) by the method of binary electrolyte; (o) by the method of mixed electrolytes assuming q~ = 0; (x) by the method of mixed electrolytes assuming q~ > 0. Fig. 12. Charge due to surface excess of C1-- ions as a function of electrode charge in 0.1 M LiC1 ethanolic solution calculated in different ways: (o) by the method of binary electrolyte; (o) by the method of mixed electrolytes assuming q~ = 0; (x) by the method of mixed electrolytes assuming q~ > 0. Figs. 11 and 12, f o r b o t h solutions the calculation o f quantities F F _ f r o m the e x p e r i m e n t a l data o b t a i n e d b y t h e m e t h o d o f m i x e d e l e c t r o l y t e s [ 1 0 , 3 4 ] and considering the ionic association in the inner layer (q~ > 0) yields a l m o s t the same results as b y t h e m e t h o d o f b i n a r y e l e c t r o l y t e . Especially g o o d a g r e e m e n t b e t w e e n t w o sets o f d a t a is observed in t h e s o l u t i o n with 0.01 M LiC1 c o n c e n t r a t i o n (Fig. 11). S o m e d i s c r e p a n c y b e t w e e n the results o b t a i n e d by t w o d i f f e r e n t m e t h o d s occurs in the s o l u t i o n with 0.1 M LiC1 c o n c e n t r a tion, which m a y be due to a higher degree o f ionic association in t h e bulk o f solution. H o w e v e r , in b o t h solutions the values o f F F _ calculated b y t w o diff e r e n t m e t h o d s w i t h o u t considering the ionic association in the i n n e r layer (q~ = 0) differ essentially (Figs. 11 and 12). These results c o n f i r m t h e conclusion t h a t in the case o f specific a d s o r p t i o n o f C1- ions at the b i s m u t h - - e t h a n o l i n t e r f a c e Li ÷ cations e n t e r the inner p a r t o f t h e electrical d o u b l e layer. T h e p r o c e d u r e p r o p o s e d in the p r e s e n t w o r k f o r evaluation o f charge q~ due to the cations in t h e i n n e r l a y e r seems to b e valid. In conclusion, it should be n o t e d t h a t an ionic association in the inner layer a p p a r e n t l y occurs also in o t h e r systems, especially in n o n a q u e o u s solutions with relatively low dielectric c o n s t a n t . In this c o n n e c t i o n it w o u l d be o f interest t o revise earlier e x p e r i m e n t a l d a t a f r o m the p o s i t i o n o f c o n c e p t i o n s develo p e d in the p r e s e n t w o r k .

115 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

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