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Electrostatic effect of specifically adsorbed electroinactive ions upon electrode processes
J. Electroanal. Chem., 76 (1977) 51--59 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands
51
ELECTROSTATIC EFFECT OF SPECIFICALLY ADSORBED ELECTROINACTIVE IONS UPON ELECTRODE PROCESSES P A R T IV. C A R B O N T E T R A C H L O R I D E E L E C T R O R E D U C T I O N P R E S E N C E O F C I - , B r - , S C N - , A N D N~-
IN THE
GIOVANNI PEZZATINI and ROLANDO GUIDELLI Institute of Analytical Chemistry, University of Florence, Florence (Italy)
(Received 3rd December 1975; in revised form 6th March 1976)
ABSTRACT The rate constant for CC14 electroreduction on mercury, once corrected for diffuselayer effects according to Frumkin, still depends on the charge density qi due to specifically adsorbed supporting ions. Thus, in the presence of the adsorbed anions Cl--, Br--, SCN-- and N3, the logarithm (I) of the rate constant corrected for diffuse-layer effects decreases linearly with ]qi]- The slopes of the various (D vs. qi plots are in fairly good agreement with the theoretical treatment of ref. 9, which accounts for the electrostatic interactions between the activated complex for the electrode reaction and the neighbouring adsorbed electroinactive ions within the compact layer. An analogous behaviour is observed in the reduction of CBr 4.
INTRODUCTION Organic h a l o g e n c o m p o u n d s are a m o n g t h e first organic s u b s t a n c e s f o r which changes in h a l f - w a v e p o t e n t i a l f o l l o w i n g changes in n a t u r e a n d conc e n t r a t i o n o f s u p p o r t i n g e l e c t r o l y t e h a v e b e e n c o r r e c t l y ascribed t o changes in d o u b l e - l a y e r s t r u c t u r e [ 1 ] . In p a r t i c u l a r , R o g e r s et al. [ 2 - - 4 ] o b s e r v e d t h a t s u p p o r t i n g e l e c t r o l y t e has a m a r k e d e f f e c t u p o n c a r b o n t e t r a c h l o r i d e electror e d u c t i o n a n d qualitatively c o r r e l a t e d half-wave p o t e n t i a l shifts w i t h t h e ads o r p t i v i t y o f s u p p o r t i n g anions and cations. S u b s e q u e n t l y , M a i r a n o v s k i i et al. [5] o b s e r v e d t h a t t h e e f f e c t o f KC1 c o n c e n t r a t i o n u p o n t h e h a l f - w a v e p o t e n tial o f t h e r e d u c t i o n waves o f several iodo-derivatives is in s a t i s f a c t o r y q u a n t i t a tive a g r e e m e n t with t h e p r e d i c t i o n s o f t h e simple F r u m k i n e q u a t i o n . T h e first c a t h o d i c wave o f c a r b o n t e t r a c h l o r i d e in a q u e o u s s o l u t i o n is well d e f i n e d a n d free o f m a x i m a . This t o t a l l y irreversible wave is d u e t o t h e overall e l e c t r o d e r e a c t i o n CC14 + H 2 0 + 2e -) CC13 H + C1- + O H and t u r n s o u t to be p H i n d e p e n d e n t [ 6 , 7 ] . Its limiting c u r r e n t is d i f f u s i o n
(1)
52 controlled [2], as we were able to confirm from its proportionality to the square root oi the height of the mercury head and from the time dependence of the instantaneous limiting current. The half-wave potential of the first wave of CC14 in water falls on the positive side of the electrocapillary maximum, where halide and pseudohalide adsorption is appreciable. We have therefore found it interesting to examine the influence of halide and pseudohalide adsorption upon the reduction rate of CC14, in the framework of a systematic investigation of the effect of ionic specific adsorption upon the kinetics of electrode processes, carried out in this laboratory. EXPERIMENTAL Apparatus and purification of chemicals other than the halogen compounds are described in the first paper of this series [8]. Merck analytical reagent grade CC14 and CBr4 were used without further purification. The CC14 solutions to be electrolyzed were obtained by bubbling into the electrolysis cell containing the supporting electrolyte nitrogen gas previously passed through an immiscible mixture of CC14 and water. All tubing was made out of glass. A t t a i n m e n t of the desired value of the bulk reactant concentration in the cell was detected by continuous recording of the polarographic diffusion limiting current of CC14. An analogous procedure was followed with the other halogen compound. The temperature was (25 -+ 0.1)°C. All potentials are referred to the SCE. Doublelayer data for Cl-, B r - , SCN- and N~ adsorption were kindly provided by Dr. Roger Parsons (cf. ref. 8). RESULTS AND DISCUSSION To account for the effect of double-layer structure upon electrode kinetics in the presence of ionic specific adsorption, one of the authors has recently derived the equation [9] ( R T / F ) In ?4 = const -- a ' E -- (Zox -- a') ~d + Aqi
(2)
with X ~ ( 1 2 / 7 ) l / 2 ( t d / D o x ) l l Z k ; ~ ' - ~ ~ + (Zox --~)(1
--~/d);
A - --47r(Zox -- ~)(fl3`/d)(1 -- lg)/e Here k is the rate constant of the electrode reaction under study at the applied potential E, t d is the drop time of the mercury electrode, Dox and Zox are the diffusion coefficient and the charge of the reactant, @d is the electric potential at the outer Helmholtz plane, and qi is the charge density due to any specifically adsorbed supporting ions. Moreover, ~ i3 the " t r u e " value of the chargetransfer coefficient, ~' is the corresponding directly measurable " a p p a r e n t " value,/3 and d are the distances of the inner and outer Helmholtz planes from the electrode surface, 3' equals (d --fi), and e is the dielectric constant in the
53 compact layer. Finally, the parameter (1 -- ~g) is a complicated function of/3, of d, and of the distance, a, of closest approach between the charge centres of the adsorbed activated complex and of the adsorbed electroinactive ion (cf. refs. 8 and 9). The preceding equation accounts for diffuse-layer effects (the so called ~d-effect) via the --(Zox -- a')~d term, as well as for the effect of the compact layer in the presence of ionic specific adsorption (the qi-effect) via the Aqi term. Equation (2) holds only when the reacting particle is located within the compact layer just prior to charge transfer. In fact, if it is located at the outer Helmholtz plane, A turns out to be zero and eqn. (2) reduces to the well-known Frnmkin equation
(RT/F) In × = const -- a' (E
-- ~d)
-- Zox ~d
(3)
Clearly, the Frumkin equation also holds for the case of a specifically adsorbed activated complex, provided that ionic specific adsorption is absent (qi = 0). Equation (2), with A ¢ 0, was verified for $ 4 0 ~ - [8] and BrO~ [10] reductions on mercury. To estimate the qi-effect, the "apparent" charge-transfer coefficient a' in the presence of ionic specific adsorption must first be determined. This result can be achieved by plotting corrected Tafel plots, namely plots of [(RT/F) In × + Zox~d] vs. (E -- ~d), while keeping qi (and hence the qi-effect, if any) constant [11]. Figure 1 shows these plots for CC14 electroreduction in the presence of CI-, B r - , S C N - , and N~-. Table 1 summarizes the a' values as derived from the slopes of the above plots in accordance with eqn. (2). Once a' is known, the qi-effect can be estimated by plotting either the function (I) = [(RT/F) In X + (Zox -- ~')~d] at constant E, or else the function qJ - [(RT/F) In × + ~'E + (Zox -- ~')~d], against qi. Figures 2 to 5 show both plots for CC14 electroreduction in the presence of Cl-, B r - , S C N - , and N3. These plots exhibit positive and satisfactorily constant slopes from the lowest accessible ]qiJ values. Since both (I) and ~ measure the logarithm of the rate constant for CC14 electroreduction as corrected for diffuse-layer effects only, the dependence of these functions u p o n qi reveals the existence of a definite qi-effect and also proves that this effect is adequately accounted for by a term proportional to qi, such as that, A q i , in eqn. (2). As expected, an increase in the negative value of q~ produces a decrease in the rate constant for CC14 electroreduction in addition to that predicted by the Frumkin equation (3), due to the gradual electrostatic repulsion between the specifically adsorbed halide ions and the negatively charged activated complex. In view of eqn. (2) experimental values of the • function relative to different supporting-electrolyte concentrations should fall on the same line when plotted against qi. Just as in the case of B r O j electroreduction [11], this is actually verified in the presence of S C N - , N~, and C1- ions, b u t n o t in the presence of B r - ion. Equation (2) also states that the slopes of corresponding (I) vs. qi and ~ v s . qi plots should both be equal to A. This is again satisfactorily verified in the presence of S C N - and N y ions b u t not in the presence of B r and C1- ions. In the presence of B r - ions, the whole set of experimental
54 I
J J
J
ol Y _c b_ -prr v
/
Y
20 mV
'oy I -0,4
-0.5
L
I
-0.6
-0.7
-0,8
(E - ~d )/v
Fig. 1. Plots o f (RT/F) In X against ( E - tfld ) at c o n s t a n t qi for t h e e l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CC14 in the p r e s e n c e o f KC1 (curve a, qi = --6 p C c m - - 2 ) , KBr (curve b, qi = - - 1 4 p C c m - - 2 ) , NaSCN (curve c, qi = --14 p C c m - 2 ) , and NaN 3 (curve d, qi = --14 p C c m - - 2 ) . Curves are s h i f t e d along the vertical axis.
values relative to the various supporting-electrolyte concentrations, although quite scattered when plotted against qi, yields an average slope close to that of the corresponding qb vs. qi plot. The discrepancy between the slopes of the q~ vs. qi and qJ vs. qi plots for C1- ion in Fig. 2 is probably ascribable to the scantiness of double-layer data for C1-- adsorption at our disposal, which did not permit us to plot more than three significant ¢p values against qiTABLE 1 E f f e c t o f halide and p s e u d o h a l i d e ions u p o n CCI 4 e l e c t r o r e d u c t i o n Supporting electrolyte
a'
ri/A
103(AxI//Aqi} / V c m 2 pC - 1 Experimental
103(A~/Aqi ) /V c m 2 p C - 1 Experimental
103 [(Acb/Aqi)/a] /V c m 2 //C - 1 Calculated
KCI KBr NaSCN NaN 3
0.39 0.36 0.28 0.30
1.81 1.96 1.74 1.57
--3.0 2.7
1.5 2.0 3.0 2.3
2.5 2.2 2.6 3.0
55
+ 0.02
J
I -
-
-0.16
-0.18
~/v -0.20
-0.04
I -10
I -20 q i/,u C c m -2
Fig. 2. E l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CC14 in the p r e s e n c e o f KC1. (a) 4p vs qi p l o t at E = - - 0 . 5 V; (b) • vs. qi p l o t relative t o 0.1 M (A), 1 M (o), a n d 2.45 M (~) KC1.
The experimental A~/Aqi and AqE/Aqivalues derived from Figs. 2 to 5 are summarized in Table 1. This Table also summarizes the theoretical values o f (A{/Aqi)/o~ = 4~t37(1 - - tg)/(de) as obtained giving/3, d, and e the same values e m p l o y e d in the study of the effect of halide adsorption on $4 O 2 - [8] and BROW- [ 1 0 ] electroreductions, i.e./3 = 3 A, d = 4 A, and e = 1 (electrostatic
I
+0.06
I
I
0 b
-
-0.16
+ 0.04
-
-0.18
+ 0.02
- - 0.20
0.00
- -0.22
-0.02
I -10
I -2O qi/,u. C c m - 2
I -30
- 0,24
Fig. 3. E i e c t r o r e d u c t i o n o f 5 X 10 - 4 M CCI 4 in the p r e s e n c e o f KBr. (a) ffP vs. qi p l o t at E = --0.5 V ; (b) • vs. qi p l o t relative t o 0.2 M (o), 0.5 M (Q), 1 M ( A ) a n d 2 M (®) KBr.
56
1
I
0'08I~
- 0.08
-O.lO
\
~/v
®Iv
~-0.12
0.04
!
"I
!-0.14
0.02
i
i
0.00
~ -©.16
~
1
-0.02 _ _
1
-10
P
-20
-30
qi/,u C cm -2
Fig. 4. E l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CC14 in t h e presence of NaSCN. (a) ~P vs. qi plot at E = - - 0 . 5 V; (b) ~ vs. qi Plot relative t o 2.45 x 10 - 2 M (V), 0 . 1 9 8 M (©), a n d 0.95 M ([]) NaSCN.
c.g.s, unit). Just as in refs. 8 and 10, (1 -- lg) was estimated by setting the distance a of closest approach between the CC14 molecule and the halide or pseudohalide ion equal to the crystal ionic radius, ri, of the supporting anion plus the radius, r(CC14), of the CCI4 molecule. Upon assuming that the tetrahedral CC14 molecule lies on the electrode surface with three chlorine atoms in contact with mercury, r(CC14) was set equal to 1.75 £ + 1.77 sin(180°--109.5 °) A = 3.42 A, where 1.75 A is the Van der Waals radius of a single-bonded chlorine atom [12] and 1.77 h is the length of a C1--C bond. If the true charge-transfer coefficient a is set equal to 0.5, then the experimental Adp/Aqi values are about twice as great as the corresponding calculated ones, with the only exception being the value for the C1- ion. Due to the uncertainties as to the distances fl, d, and a, agreement between experiment and theoretical expectations can be regarded as fairly satisfactory. Naturally, if both electrons involved in the electrode reaction of eqn. (1) are transferred simultaneous ly, then the true transfer coefficient a for the overall electrode reaction is close to unity and hence agreement between experimental and calculated A~p/Aq i values turns out to be much more satisfactory. Further evidence in favour of the above hypothesis as to the a value is provided by the relatively large difference between the apparent charge-transfer coefficient a' in the presence of Na ÷ ions, (~N+ ~ 0.29, and that, aK+ ~ 0.37, in the presence of K ÷ ions. Such !
r
57 J
I
0.08 -
0.06
e/v
ho
0.08
-o.1o
~/v
0.0,4 -0.12
0 . 0 .c
C,
'q
-0.14
O.OC
!_o.16 -0.0~ I
-10
I
-20 qi/u. C c m -2
Fig. 5. E l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CCI 4 in t h e p r e s e n c e of NaN 3. (a) qP vs. qi p l o t at E = - - 0 . 5 V; (b) • vs. qi p l o t relative t o 0 . 0 8 6 M (©), 0.237 M (V), a n d 1 . 1 9 2 M ([3) NaN 3 .
a difference in ~' values, which is also e n c o u n t e r e d in the electroreductions of $ 4 0 2 - [8], $ 2 0 2 - [13] and BROW- [10], can likewise be explained through eqn. (2). In fact, u p o n making the reasonable assumptions that a and/3 remain ! unchanged in passing from Na ÷ to K ÷, from eqn. (2) it follows that aK+ -a N + ~ - - ( Z O x - - 0 ~ ) ( ~ / d 2 ) ( d N a + __ d K +), where dsa+ and dK+ express the compactlayer thickness in the presence of Na ÷ and K ÷ respectively, and d is the geometrical mean between dK+ and dNa +. If we set (dNa+ -- dg÷ ) equal to the difference 2.17 A -- 1.75 A = 0.42 A between the h y d r a t e d radii of Na ÷ and K ÷ as ! t estimated by Monk [14], Zox = 0,/3 = 3 A and d = 4 £ , we obtain ~K+ -- ~Na+ = 0.039 for a = 0.5 and a g÷' -- aN~+' = 0.079 for a = 1. Of the two preceding calcut r lated values of aK÷ -- aS~+, the latter complies better with the experimental value 0.08. It is also interesting to n o t e that, if anything, the experimental r t (aK÷ -- aN+) values for BROW- [10] and SaOs2 - [8] electroreduction are somewhat less than the values calculated via eqn. (2), rather than greater. Like CC14, CBr4 is also reduced in water at potentials positive t o the p o i n t of zero charge. Moreover, the first reduction wave of this halogen c o m p o u n d is i n d e p e n d e n t of pH [6]. Unfortunately, the solubility of CBr4 in water is very small, so that the wave furnished by its saturated solution is appreciably disturbed by the capacitive current. Consequently, the rising p o r t i o n of this wave could n o t be analysed accurately enough to derive reliable values of the apparent charge-transfer coefficient a'. We therefore limited ourselves to a
58 1
I
I
-0.06
(E½-~o)/,, -0.08
-0.10
-0.12
I
-10
I
-20
i
-30
qi/,u C c m -2
Fig. 6. Plots o f (El/2 -- ~fld) against qi for the e l e c t r o r e d u c t i o n o f saturated a q u e o u s solution o f CBr 4 in the presence o f KBr (a) and NaN 3 (b).
measurement of half-wave potentials, which measurement can still be performed to a reasonable degree of accuracy. Taking into account that at the half-wave potential E 1/2 the kinetic parameter × is a constant, eqn. (2) can be written in the form El~2 + [ ( Z o x - - ( ~ ' ) / ( ~ ' ]
~d = A q i / ° ~ ' + c o n s t '
Fortunately enough, in the present case Zo~ equals zero, so that a simple plot of (E 1/2 -- ~d) against qi can allow us to estimate the qi-effect without having to know a'. Figure 6 shows (E1/2 -- ~ ) vs. qi plots for CBr4 reduction in the presence of KBr and of NaNa. In spite of the scattering of experimental points, a definite decrease in (E 1/2 -- ~d) with increasing lqil is apparent. Moreover, the average slopes of the (El/2 -- ~d) vs. qi plots are comparable with those of the qb vs. qi plots in Figs. 2 to 5, relative to CC14 electroreduction. ACKNOWLEDGEMENT
This work was supported by the Italian C.N.R.
REFERENCES 1 2 3 4
E.S. Levin and Z.I. F o d i m a n , Zh. Fiz. Khim., 28 (1954) 601. J.J. L o t h e and L.B. Rogers, J. E l e c t r o c h e m . Soc., 101 (1954) 258. L.E.I. H u m m e l s t e d t and L.B. Rogers, J. E l e c t r o c h e m . Soc., 106 (1959) 248. W.H, R e i n m u t h , L.B. Rogers and L.E.I. H u m m e l s t e d t , J. Amer. Chem. Soc., 81 (1959) 2947.
59 5 S.G. Mairanovskii, V.A. Ponomarenko, N.V. Barashkova and A.D. Snegova, Dokl. Akad. Nauk SSSR, 134 (1960) 387. 6 M. von Stackelberg and W. Stracke, Z. Elektrochem., 53 (1949) 118. 7 I.M. Kolthoff, T.S. Lee, D. Stocesoya and E.P. Parry, Anal. Chem., 22 (1950) 521. 8 M.L. Foresti and R. Guidelli, J. Electroanal. Chem., 53 (1974) 219. 9 R. Guidelli, J. Electroanal. Chem., 53 (1974) 205; see also R. Guidelli and M.L. Foresti, Electrochim. Acta, 18 (1973) 301. 10 M.L. Foresti, D. Cozzi and R. Guidelli, J. Electroanal. Chem., 53 (1974) 235. 11 R. Guidelli and M.L. Foresti, J. Electroanal. Chem., 67 (1976) 231. 12 A. Bondi, J. Phys. Chem., 68 (1964) 441. 13 W.R. Fawcett, J. Electroanal. Chem., 22 (1969) 19. 14 C.B. Monk, Electrolytic Dissociation, Academic Press, New York, 1961, p. 271.
51
ELECTROSTATIC EFFECT OF SPECIFICALLY ADSORBED ELECTROINACTIVE IONS UPON ELECTRODE PROCESSES P A R T IV. C A R B O N T E T R A C H L O R I D E E L E C T R O R E D U C T I O N P R E S E N C E O F C I - , B r - , S C N - , A N D N~-
IN THE
GIOVANNI PEZZATINI and ROLANDO GUIDELLI Institute of Analytical Chemistry, University of Florence, Florence (Italy)
(Received 3rd December 1975; in revised form 6th March 1976)
ABSTRACT The rate constant for CC14 electroreduction on mercury, once corrected for diffuselayer effects according to Frumkin, still depends on the charge density qi due to specifically adsorbed supporting ions. Thus, in the presence of the adsorbed anions Cl--, Br--, SCN-- and N3, the logarithm (I) of the rate constant corrected for diffuse-layer effects decreases linearly with ]qi]- The slopes of the various (D vs. qi plots are in fairly good agreement with the theoretical treatment of ref. 9, which accounts for the electrostatic interactions between the activated complex for the electrode reaction and the neighbouring adsorbed electroinactive ions within the compact layer. An analogous behaviour is observed in the reduction of CBr 4.
INTRODUCTION Organic h a l o g e n c o m p o u n d s are a m o n g t h e first organic s u b s t a n c e s f o r which changes in h a l f - w a v e p o t e n t i a l f o l l o w i n g changes in n a t u r e a n d conc e n t r a t i o n o f s u p p o r t i n g e l e c t r o l y t e h a v e b e e n c o r r e c t l y ascribed t o changes in d o u b l e - l a y e r s t r u c t u r e [ 1 ] . In p a r t i c u l a r , R o g e r s et al. [ 2 - - 4 ] o b s e r v e d t h a t s u p p o r t i n g e l e c t r o l y t e has a m a r k e d e f f e c t u p o n c a r b o n t e t r a c h l o r i d e electror e d u c t i o n a n d qualitatively c o r r e l a t e d half-wave p o t e n t i a l shifts w i t h t h e ads o r p t i v i t y o f s u p p o r t i n g anions and cations. S u b s e q u e n t l y , M a i r a n o v s k i i et al. [5] o b s e r v e d t h a t t h e e f f e c t o f KC1 c o n c e n t r a t i o n u p o n t h e h a l f - w a v e p o t e n tial o f t h e r e d u c t i o n waves o f several iodo-derivatives is in s a t i s f a c t o r y q u a n t i t a tive a g r e e m e n t with t h e p r e d i c t i o n s o f t h e simple F r u m k i n e q u a t i o n . T h e first c a t h o d i c wave o f c a r b o n t e t r a c h l o r i d e in a q u e o u s s o l u t i o n is well d e f i n e d a n d free o f m a x i m a . This t o t a l l y irreversible wave is d u e t o t h e overall e l e c t r o d e r e a c t i o n CC14 + H 2 0 + 2e -) CC13 H + C1- + O H and t u r n s o u t to be p H i n d e p e n d e n t [ 6 , 7 ] . Its limiting c u r r e n t is d i f f u s i o n
(1)
52 controlled [2], as we were able to confirm from its proportionality to the square root oi the height of the mercury head and from the time dependence of the instantaneous limiting current. The half-wave potential of the first wave of CC14 in water falls on the positive side of the electrocapillary maximum, where halide and pseudohalide adsorption is appreciable. We have therefore found it interesting to examine the influence of halide and pseudohalide adsorption upon the reduction rate of CC14, in the framework of a systematic investigation of the effect of ionic specific adsorption upon the kinetics of electrode processes, carried out in this laboratory. EXPERIMENTAL Apparatus and purification of chemicals other than the halogen compounds are described in the first paper of this series [8]. Merck analytical reagent grade CC14 and CBr4 were used without further purification. The CC14 solutions to be electrolyzed were obtained by bubbling into the electrolysis cell containing the supporting electrolyte nitrogen gas previously passed through an immiscible mixture of CC14 and water. All tubing was made out of glass. A t t a i n m e n t of the desired value of the bulk reactant concentration in the cell was detected by continuous recording of the polarographic diffusion limiting current of CC14. An analogous procedure was followed with the other halogen compound. The temperature was (25 -+ 0.1)°C. All potentials are referred to the SCE. Doublelayer data for Cl-, B r - , SCN- and N~ adsorption were kindly provided by Dr. Roger Parsons (cf. ref. 8). RESULTS AND DISCUSSION To account for the effect of double-layer structure upon electrode kinetics in the presence of ionic specific adsorption, one of the authors has recently derived the equation [9] ( R T / F ) In ?4 = const -- a ' E -- (Zox -- a') ~d + Aqi
(2)
with X ~ ( 1 2 / 7 ) l / 2 ( t d / D o x ) l l Z k ; ~ ' - ~ ~ + (Zox --~)(1
--~/d);
A - --47r(Zox -- ~)(fl3`/d)(1 -- lg)/e Here k is the rate constant of the electrode reaction under study at the applied potential E, t d is the drop time of the mercury electrode, Dox and Zox are the diffusion coefficient and the charge of the reactant, @d is the electric potential at the outer Helmholtz plane, and qi is the charge density due to any specifically adsorbed supporting ions. Moreover, ~ i3 the " t r u e " value of the chargetransfer coefficient, ~' is the corresponding directly measurable " a p p a r e n t " value,/3 and d are the distances of the inner and outer Helmholtz planes from the electrode surface, 3' equals (d --fi), and e is the dielectric constant in the
53 compact layer. Finally, the parameter (1 -- ~g) is a complicated function of/3, of d, and of the distance, a, of closest approach between the charge centres of the adsorbed activated complex and of the adsorbed electroinactive ion (cf. refs. 8 and 9). The preceding equation accounts for diffuse-layer effects (the so called ~d-effect) via the --(Zox -- a')~d term, as well as for the effect of the compact layer in the presence of ionic specific adsorption (the qi-effect) via the Aqi term. Equation (2) holds only when the reacting particle is located within the compact layer just prior to charge transfer. In fact, if it is located at the outer Helmholtz plane, A turns out to be zero and eqn. (2) reduces to the well-known Frnmkin equation
(RT/F) In × = const -- a' (E
-- ~d)
-- Zox ~d
(3)
Clearly, the Frumkin equation also holds for the case of a specifically adsorbed activated complex, provided that ionic specific adsorption is absent (qi = 0). Equation (2), with A ¢ 0, was verified for $ 4 0 ~ - [8] and BrO~ [10] reductions on mercury. To estimate the qi-effect, the "apparent" charge-transfer coefficient a' in the presence of ionic specific adsorption must first be determined. This result can be achieved by plotting corrected Tafel plots, namely plots of [(RT/F) In × + Zox~d] vs. (E -- ~d), while keeping qi (and hence the qi-effect, if any) constant [11]. Figure 1 shows these plots for CC14 electroreduction in the presence of CI-, B r - , S C N - , and N~-. Table 1 summarizes the a' values as derived from the slopes of the above plots in accordance with eqn. (2). Once a' is known, the qi-effect can be estimated by plotting either the function (I) = [(RT/F) In X + (Zox -- ~')~d] at constant E, or else the function qJ - [(RT/F) In × + ~'E + (Zox -- ~')~d], against qi. Figures 2 to 5 show both plots for CC14 electroreduction in the presence of Cl-, B r - , S C N - , and N3. These plots exhibit positive and satisfactorily constant slopes from the lowest accessible ]qiJ values. Since both (I) and ~ measure the logarithm of the rate constant for CC14 electroreduction as corrected for diffuse-layer effects only, the dependence of these functions u p o n qi reveals the existence of a definite qi-effect and also proves that this effect is adequately accounted for by a term proportional to qi, such as that, A q i , in eqn. (2). As expected, an increase in the negative value of q~ produces a decrease in the rate constant for CC14 electroreduction in addition to that predicted by the Frumkin equation (3), due to the gradual electrostatic repulsion between the specifically adsorbed halide ions and the negatively charged activated complex. In view of eqn. (2) experimental values of the • function relative to different supporting-electrolyte concentrations should fall on the same line when plotted against qi. Just as in the case of B r O j electroreduction [11], this is actually verified in the presence of S C N - , N~, and C1- ions, b u t n o t in the presence of B r - ion. Equation (2) also states that the slopes of corresponding (I) vs. qi and ~ v s . qi plots should both be equal to A. This is again satisfactorily verified in the presence of S C N - and N y ions b u t not in the presence of B r and C1- ions. In the presence of B r - ions, the whole set of experimental
54 I
J J
J
ol Y _c b_ -prr v
/
Y
20 mV
'oy I -0,4
-0.5
L
I
-0.6
-0.7
-0,8
(E - ~d )/v
Fig. 1. Plots o f (RT/F) In X against ( E - tfld ) at c o n s t a n t qi for t h e e l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CC14 in the p r e s e n c e o f KC1 (curve a, qi = --6 p C c m - - 2 ) , KBr (curve b, qi = - - 1 4 p C c m - - 2 ) , NaSCN (curve c, qi = --14 p C c m - 2 ) , and NaN 3 (curve d, qi = --14 p C c m - - 2 ) . Curves are s h i f t e d along the vertical axis.
values relative to the various supporting-electrolyte concentrations, although quite scattered when plotted against qi, yields an average slope close to that of the corresponding qb vs. qi plot. The discrepancy between the slopes of the q~ vs. qi and qJ vs. qi plots for C1- ion in Fig. 2 is probably ascribable to the scantiness of double-layer data for C1-- adsorption at our disposal, which did not permit us to plot more than three significant ¢p values against qiTABLE 1 E f f e c t o f halide and p s e u d o h a l i d e ions u p o n CCI 4 e l e c t r o r e d u c t i o n Supporting electrolyte
a'
ri/A
103(AxI//Aqi} / V c m 2 pC - 1 Experimental
103(A~/Aqi ) /V c m 2 p C - 1 Experimental
103 [(Acb/Aqi)/a] /V c m 2 //C - 1 Calculated
KCI KBr NaSCN NaN 3
0.39 0.36 0.28 0.30
1.81 1.96 1.74 1.57
--3.0 2.7
1.5 2.0 3.0 2.3
2.5 2.2 2.6 3.0
55
+ 0.02
J
I -
-
-0.16
-0.18
~/v -0.20
-0.04
I -10
I -20 q i/,u C c m -2
Fig. 2. E l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CC14 in the p r e s e n c e o f KC1. (a) 4p vs qi p l o t at E = - - 0 . 5 V; (b) • vs. qi p l o t relative t o 0.1 M (A), 1 M (o), a n d 2.45 M (~) KC1.
The experimental A~/Aqi and AqE/Aqivalues derived from Figs. 2 to 5 are summarized in Table 1. This Table also summarizes the theoretical values o f (A{/Aqi)/o~ = 4~t37(1 - - tg)/(de) as obtained giving/3, d, and e the same values e m p l o y e d in the study of the effect of halide adsorption on $4 O 2 - [8] and BROW- [ 1 0 ] electroreductions, i.e./3 = 3 A, d = 4 A, and e = 1 (electrostatic
I
+0.06
I
I
0 b
-
-0.16
+ 0.04
-
-0.18
+ 0.02
- - 0.20
0.00
- -0.22
-0.02
I -10
I -2O qi/,u. C c m - 2
I -30
- 0,24
Fig. 3. E i e c t r o r e d u c t i o n o f 5 X 10 - 4 M CCI 4 in the p r e s e n c e o f KBr. (a) ffP vs. qi p l o t at E = --0.5 V ; (b) • vs. qi p l o t relative t o 0.2 M (o), 0.5 M (Q), 1 M ( A ) a n d 2 M (®) KBr.
56
1
I
0'08I~
- 0.08
-O.lO
\
~/v
®Iv
~-0.12
0.04
!
"I
!-0.14
0.02
i
i
0.00
~ -©.16
~
1
-0.02 _ _
1
-10
P
-20
-30
qi/,u C cm -2
Fig. 4. E l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CC14 in t h e presence of NaSCN. (a) ~P vs. qi plot at E = - - 0 . 5 V; (b) ~ vs. qi Plot relative t o 2.45 x 10 - 2 M (V), 0 . 1 9 8 M (©), a n d 0.95 M ([]) NaSCN.
c.g.s, unit). Just as in refs. 8 and 10, (1 -- lg) was estimated by setting the distance a of closest approach between the CC14 molecule and the halide or pseudohalide ion equal to the crystal ionic radius, ri, of the supporting anion plus the radius, r(CC14), of the CCI4 molecule. Upon assuming that the tetrahedral CC14 molecule lies on the electrode surface with three chlorine atoms in contact with mercury, r(CC14) was set equal to 1.75 £ + 1.77 sin(180°--109.5 °) A = 3.42 A, where 1.75 A is the Van der Waals radius of a single-bonded chlorine atom [12] and 1.77 h is the length of a C1--C bond. If the true charge-transfer coefficient a is set equal to 0.5, then the experimental Adp/Aqi values are about twice as great as the corresponding calculated ones, with the only exception being the value for the C1- ion. Due to the uncertainties as to the distances fl, d, and a, agreement between experiment and theoretical expectations can be regarded as fairly satisfactory. Naturally, if both electrons involved in the electrode reaction of eqn. (1) are transferred simultaneous ly, then the true transfer coefficient a for the overall electrode reaction is close to unity and hence agreement between experimental and calculated A~p/Aq i values turns out to be much more satisfactory. Further evidence in favour of the above hypothesis as to the a value is provided by the relatively large difference between the apparent charge-transfer coefficient a' in the presence of Na ÷ ions, (~N+ ~ 0.29, and that, aK+ ~ 0.37, in the presence of K ÷ ions. Such !
r
57 J
I
0.08 -
0.06
e/v
ho
0.08
-o.1o
~/v
0.0,4 -0.12
0 . 0 .c
C,
'q
-0.14
O.OC
!_o.16 -0.0~ I
-10
I
-20 qi/u. C c m -2
Fig. 5. E l e c t r o r e d u c t i o n o f 5 X 10 - 4 M CCI 4 in t h e p r e s e n c e of NaN 3. (a) qP vs. qi p l o t at E = - - 0 . 5 V; (b) • vs. qi p l o t relative t o 0 . 0 8 6 M (©), 0.237 M (V), a n d 1 . 1 9 2 M ([3) NaN 3 .
a difference in ~' values, which is also e n c o u n t e r e d in the electroreductions of $ 4 0 2 - [8], $ 2 0 2 - [13] and BROW- [10], can likewise be explained through eqn. (2). In fact, u p o n making the reasonable assumptions that a and/3 remain ! unchanged in passing from Na ÷ to K ÷, from eqn. (2) it follows that aK+ -a N + ~ - - ( Z O x - - 0 ~ ) ( ~ / d 2 ) ( d N a + __ d K +), where dsa+ and dK+ express the compactlayer thickness in the presence of Na ÷ and K ÷ respectively, and d is the geometrical mean between dK+ and dNa +. If we set (dNa+ -- dg÷ ) equal to the difference 2.17 A -- 1.75 A = 0.42 A between the h y d r a t e d radii of Na ÷ and K ÷ as ! t estimated by Monk [14], Zox = 0,/3 = 3 A and d = 4 £ , we obtain ~K+ -- ~Na+ = 0.039 for a = 0.5 and a g÷' -- aN~+' = 0.079 for a = 1. Of the two preceding calcut r lated values of aK÷ -- aS~+, the latter complies better with the experimental value 0.08. It is also interesting to n o t e that, if anything, the experimental r t (aK÷ -- aN+) values for BROW- [10] and SaOs2 - [8] electroreduction are somewhat less than the values calculated via eqn. (2), rather than greater. Like CC14, CBr4 is also reduced in water at potentials positive t o the p o i n t of zero charge. Moreover, the first reduction wave of this halogen c o m p o u n d is i n d e p e n d e n t of pH [6]. Unfortunately, the solubility of CBr4 in water is very small, so that the wave furnished by its saturated solution is appreciably disturbed by the capacitive current. Consequently, the rising p o r t i o n of this wave could n o t be analysed accurately enough to derive reliable values of the apparent charge-transfer coefficient a'. We therefore limited ourselves to a
58 1
I
I
-0.06
(E½-~o)/,, -0.08
-0.10
-0.12
I
-10
I
-20
i
-30
qi/,u C c m -2
Fig. 6. Plots o f (El/2 -- ~fld) against qi for the e l e c t r o r e d u c t i o n o f saturated a q u e o u s solution o f CBr 4 in the presence o f KBr (a) and NaN 3 (b).
measurement of half-wave potentials, which measurement can still be performed to a reasonable degree of accuracy. Taking into account that at the half-wave potential E 1/2 the kinetic parameter × is a constant, eqn. (2) can be written in the form El~2 + [ ( Z o x - - ( ~ ' ) / ( ~ ' ]
~d = A q i / ° ~ ' + c o n s t '
Fortunately enough, in the present case Zo~ equals zero, so that a simple plot of (E 1/2 -- ~d) against qi can allow us to estimate the qi-effect without having to know a'. Figure 6 shows (E1/2 -- ~ ) vs. qi plots for CBr4 reduction in the presence of KBr and of NaNa. In spite of the scattering of experimental points, a definite decrease in (E 1/2 -- ~d) with increasing lqil is apparent. Moreover, the average slopes of the (El/2 -- ~d) vs. qi plots are comparable with those of the qb vs. qi plots in Figs. 2 to 5, relative to CC14 electroreduction. ACKNOWLEDGEMENT
This work was supported by the Italian C.N.R.
REFERENCES 1 2 3 4
E.S. Levin and Z.I. F o d i m a n , Zh. Fiz. Khim., 28 (1954) 601. J.J. L o t h e and L.B. Rogers, J. E l e c t r o c h e m . Soc., 101 (1954) 258. L.E.I. H u m m e l s t e d t and L.B. Rogers, J. E l e c t r o c h e m . Soc., 106 (1959) 248. W.H, R e i n m u t h , L.B. Rogers and L.E.I. H u m m e l s t e d t , J. Amer. Chem. Soc., 81 (1959) 2947.
59 5 S.G. Mairanovskii, V.A. Ponomarenko, N.V. Barashkova and A.D. Snegova, Dokl. Akad. Nauk SSSR, 134 (1960) 387. 6 M. von Stackelberg and W. Stracke, Z. Elektrochem., 53 (1949) 118. 7 I.M. Kolthoff, T.S. Lee, D. Stocesoya and E.P. Parry, Anal. Chem., 22 (1950) 521. 8 M.L. Foresti and R. Guidelli, J. Electroanal. Chem., 53 (1974) 219. 9 R. Guidelli, J. Electroanal. Chem., 53 (1974) 205; see also R. Guidelli and M.L. Foresti, Electrochim. Acta, 18 (1973) 301. 10 M.L. Foresti, D. Cozzi and R. Guidelli, J. Electroanal. Chem., 53 (1974) 235. 11 R. Guidelli and M.L. Foresti, J. Electroanal. Chem., 67 (1976) 231. 12 A. Bondi, J. Phys. Chem., 68 (1964) 441. 13 W.R. Fawcett, J. Electroanal. Chem., 22 (1969) 19. 14 C.B. Monk, Electrolytic Dissociation, Academic Press, New York, 1961, p. 271.