- Email: [email protected]
III) redox system in aqueous LiCl solutions at temperatures between 170 K and 300 K
JOURNAL OF
ELSEVIER
Journal of Electroanalytical Chemistry 380 (1995) 279-282
Short communication
Voltammetry in low temperature liquid solutions and frozen media: hexacyanoferrate(II/III) redox system in aqueous LiC1 solutions at temperatures between 170 K and 300 K Kazuko Tanaka, Reita Tamamushi Biophysical Chemistry Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama, 351-01, Japan Received 4 February 1994; in revised form 18 April 1994
Keywords: Low temperature systems; Voltammetry; Hexacyanoferrate(II/III) redox system
1. Introduction Voltammetric studies at low temperatures provide useful information concerning the kinetic and thermodynamic behaviour of redox systems and the transport properties of those species involved in the electrode reaction. In the last 10 years, useful information has been accumulated concerning the electrochemistry of low t e m p e r a t u r e systems involving frozen media [1-7]. The use of microelectrodes combined with a measuring instrument of high performance enables various kinds of voltammetric measurements to be made at low temperatures. In aqueous systems, voltammetric measurements at low temperatures have been carried out mainly in perchloric acid media as they have relatively low freezing points (228 K for H C 1 0 4 - 5 . 5 H 2 0 and 213 K for H C 1 0 4 . H 2 0 ) and the stoichiometric hydrates freeze without changing composition. Our previous study [8] of the cryoscopic and N M R behaviour of concentrated aqueous LiC1 solutions suggests that LiCl is a very useful supporting electrolyte for electrochemical studies of aqueous systems at low temperatures. Concentrated aqueous LiC1 solutions (e.g. 8 - 1 4 mol kg i in molality of LiC1) remain liquid down to a temperature as low as 170 K, and the liquid state of these solutions is stable at least for 2 days. Many studies [9] have been made with the hexac y a n o f e r r a t e ( I I / I I ) redox couple under various conditions, but mostly at temperatures in the vicinity of room temperature. In this p a p e r we report the voltammetric behaviour of the redox couple at a Pt microdisk electrode in aqueous LiC1 solutions of three different molalities (2 mol kg -1, 8 mol kg -1 and 14 mol kg -1) at 0022-0728/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0 0 2 2 - 0 7 2 8 ( 9 4 ) 0 3 5 0 7 - Y
various temperatures between 170 and 300 K. Well-defined voltammograms could be obtained in the frozen media, and the results are discussed from the kinetic and thermodynamic points of view.
2. Experimental Anhydrous LiC1 and K4[Fe(CN)6] were reagent grade (Wako, Japan) and used without further purification. The working electrode was a Pt microdisk electrode prepared from a Pt wire (Nilaco, Japan) with a diameter of 50 /xm; the wire was sealed into a glass tube by melting the glass around the wire. The disk surface of the electrode thus prepared was polished with a piece of fine polishing p a p e r until the surface looked mirror smooth to the eye. The counter-electrode was a Pt wire and the reference electrode was a saturated calomel electrode (SCE) which was kept at room temperature and connected to the cell solution via a salt bridge containing a 14 mol kg-1 LiCI solution. The temperature of the cell solution was regulated by circulating thermostated water at temperatures above 273 K and by using an ice-bath at 273 K. For the measurements below 273 K, the temperature was controlled by adjusting the level of liquid nitrogen in a Dewar bottle. The temperature was monitored by means of an Au(containing 0.07% F e ) - c h r o m e l thermocouple which was placed in contact with the working electrode. Cyclic voltammograms were measured by using a combination of two potentiostats (model 315A and model 972, Fuso Seisakusho, Japan) equipped with a preamplifier (model 971-2, Fuso Seisakusho, Japan).
280
K. Tanaka, R. Tamamushi /Journal of Electroanalytical Chemistry 380 (1995) 279-282
Epa
3. R e s u l t s a n d d i s c u s s i o n
3.1. Voltammetric curves The voltammograms obtained at a Pt microelectrode in a 2 mol kg-1 LiC1 solution at various temperatures are shown in Fig. 1; curve (a) was obtained in the liquid solution, and curves (b)-(d) were recorded in the frozen medium. The electrochemical behaviour of the electrode was normal at temperatures above 170 K, whereas an unusual voltammogram was obtained below 170 K as shown in Fig. l(d). Therefore the following measurements were carried out at temperatures above 170 K. Fig. 2 shows voltammograms observed for 1 mmol kg - I [Fe(CN)6] 4- in aqueous LiCI solutions of different molalities and at different temperatures (scan rate v = 0 . 1 V s-l). The voltammograms (Figs. 2(a) and 2(b)) obtained at room temperature exhibit a shape characteristic of a reversible electrode reaction at a microelectrode. However, the voltammograms (Figs. 2(c) and 2(d)) obtained at lower temperatures generally show anodic and cathodic peaks, which suggests that, particularly in frozen media (Fig. 2(c)), the diffusion of electroactive species will proceed extremely slowly a n d / o r in a very thin liquid layer adjacent to the electrode surface [6].
/
,
E-1-
-
Epc
/ ,, t,
IlOpA
0.
E/V:
.5 i
°l
E/vi
/0.5
Fig. 2. Voltammograms of 1 mmol kg 1 [Fe(CN)6]4 at a Pt microdisk electrode in aqueous LiCI solutions: (a) 2 mol kg 1 LiCI,298 K (liquid); (b) 8 tool kg- z LiCI, 298 K (liquid); (c) 2 tool kg- z LiCI, 200 K (frozen); (d) 8 tool kg- 1 LiCI, 200 K (liquid).
3.2. Kinetic considerations An experimental criterion for the reversibility of an electrode reaction is given by the peak separation AEp: A E p = Eva - Epc where
Epa and
(l) Evc are the anodic and cathodic peak
potentials respectively and were determined from the voltammogram by a graphical method as shown in Fig. 2. This method of determining peak potentials is arbitrary and not very accurate but gives sufficiently reliable data for the following qualitative discussion. For the reversible a n d / o r quasi-reversible electrode reaction the peak separation is theoretically represented by the equation [10] AEp = ( 2 R T / n F ) ~
~lOOpA
-lopA ( c
]-50 pA
,t--~
*
I 5 o i
-0.8
I
I
-0.4
I
1
0 [/V
I
t
0.4
I
i
0.8
,,J
Fig. 1. Voltammogramsobserved at a Pt microdisk electrode in a 2 tool kg-1 LiCI solution at (a) 273 K (liquid), (b) 210 K (frozen), (c) 190 K (frozen) and (d) 165 K (frozen). Scan rate v = 0.1 V s i.
(2)
where n is the charge number of the electrode reaction (in the present case n = 1) and R, T and F have their usual meanings. The parameter ~ is a measure of the reversibility and is determined by the standard rate constant and transfer coefficient of the electrode reaction, the diffusion coefficients of the electroactive species and the scan rate of electrode potential. For the totally reversible electrode reaction w = 1.1 and it increases with decreasing reversibility; when ~ is in the region between 1.1 and 6 the electrode reaction will be quasi-reversible, provided that the transfer coefficient is not very different from 0.5 [10]. Parameter w for the electrode reaction of [Fe (CN)6 ]4- was rather variable but was always less than 3 under the present experimental conditions, as shown in Fig. 3, which means that the electrode reaction proceeds with a reasonably high degree of reversibility
K. Tanaka, R. Tamamushi/Journal of Electroanalytical Chemistry 380 (1995) 279-282 I
.
t r o d e p o t e n t i a l of the r e f e r e n c e e l e c t r o d e E ( S C E ) a n d the liquid j u n c t i o n p o t e n t i a l Ej:
I
f ° = E"([Fe(CN)~] 3
[]
1.1 ,~
/[Fe(CN)6] 4 ) - E(SCE) + E i
(+) 0
L--J
281
D
•
o []
f~ E] O ~
0 rq--
--0--
0
0 0 []
0 []
0
0 0 []
U n d e r o u r e x p e r i m e n t a l c o n d i t i o n s E ( S C E ) is k e p t c o n s t a n t i r r e s p e c t i v e of the t e m p e r a t u r e a r o u n d the w o r k i n g e l e c t r o d e , but the liquid j u n c t i o n p o t e n t i a l is difficult to e s t i m a t e owing to the p r e s e n c e of the t h e r m o e l e c t r i c effect [13]. A s s u m i n g that the c o n t r i b u t i o n from Ej can be n e g l e c t e d to a first a p p r o x i m a t i o n , we can d e t e r m i n e an a p p r o x i m a t e value of the s t a n d a r d r e a c t i o n e n t r o p y ArS ° for the e l e c t r o d e r e a c t i o n
[]
1--
i1
I 200
2fi0
300
[Fe(CN)+] 3 + e-~
T/K
Fig. 3. Temperature dependence of the parameter ,..= determined from the voltammograms of 1 mmol kg t [Fe(CN)6]4 measured at a Pt microdisk electrode in 2 tool kg 1 LiCI (©) and 8 mol kg 1 LiCI ([])at u=0.1 V s -1, and i n 2 m o l k g 1 LiClat u - 0 . 5 V s I (e). The arrow indicates the freezing point of a 2 mol kg i LiCI solution.
over the w h o l e r a n g e of t e m p e r a t u r e a n d even in frozen m e d i a . Such kinetic b e h a v i o u r of the e l e c t r o d e r e a c t i o n suggests a relatively small activation e n e r g y c o m p a r a b l e with t h e most p r o b a b l e e n e r g y ( a b o u t 20 kJ mol t) of h y d r o g e n b o n d s in w a t e r [11] a n d is, at least qualitatively, c o n s i s t e n t with the b e h a v i o u r exp e c t e d f r o m the following kinetic p a r a m e t e r s r e p o r t e d for t h e e l e c t r o d e r e a c t i o n in a 1 mol d m 3 KC1 solution at 20°C [12]: k ° = 0.09 cm s -1
(5)
f r o m the t e m p e r a t u r e d e p e n d e n c e of E ° a c c o r d i n g to the r e l a t i o n
nF(dE°/dT)
= ArS °
(6)
In a d d i t i o n , the effects of t e m p e r a t u r e a n d LiCI conc e n t r a t i o n on t h e s t a n d a r d r e a c t i o n e n t h a l p y A r H ° for t h e e l e c t r o d e r e a c t i o n can b e discussed using the e q u a tion
nFT(dE°/dT)
- nFE° = Ar H ° + nFI£(SCE)
(7)
w h e r e the s e c o n d t e r m on the r i g h t - h a n d side is k e p t c o n s t a n t u n d e r t h e p r e s e n t e x p e r i m e n t a l condition.
500
i
I
!
"~. % ~,,,~,
"%%
U0* = 16.7 kJ mol
w h e r e k ° is the s t a n d a r d r a t e c o n s t a n t a n d U 0 is the activation e n e r g y at t h e s t a n d a r d p o t e n t i a l .
450
3.3. Thermodynamic considerations
4OO
A s s u m i n g a relatively high d e g r e e of reversibility of the e l e c t r o d e r e a c t i o n a n d t h a t the diffusion coefficients of t h e o x i d i z e d and r e d u c e d species are n e a r l y the same, we can e s t i m a t e an a p p r o x i m a t e value of the standard potential E ° from the anodic and cathodic p e a k p o t e n t i a l s using the r e l a t i o n E °= (Ep, + Epc)/2
[Fe(CN)+] 4
"%%
Eo mV
\-
350
300
(3) !
In cases w h e n w e l l - d e f i n e d dc p o l a r o g r a m s could be observed, the log plot analysis of the p o l a r o g r a m s gave the s t a n d a r d p o t e n t i a l s m o r e a c c u r a t e l y than, b u t almost e q u a l to, t h o s e o b t a i n e d from the cyclic v o l t a m m o g r a m s (Fig. 4). T h e s t a n d a r d p o t e n t i a l E ° thus d e t e r m i n e d involves t h r e e c o n t r i b u t i o n s , t h e s t a n d a r d p o t e n t i a l of the w o r k ing e l e c t r o d e E ° ( [ F e ( C N ) 6 ] s - / [ F e ( C N ) 6 ] 4 - ) , the elec-
250 1 0
I
I
200
250
~
"4 I
300
350
T/K
Fig. 4. Temperature dependence of E ° of the [Fe(CN)6]4 /[Fe (CN)6]3 redox system in aqueous LiCI solutions of 14 mol kg + (zx), 8 mol kg t (rn) and 2 mol kg l (© and e) where the solid circles represent E ~ obtained from the log plot analysis of d.c. polarograms. The arrow indicates the freezing point of a 2 mol kg I LiCI solution.
K. Tanaka, R. Tamamushi/Journal of Electroanalytical Chemistry 380 (1995) 279-282
282
Table 1 Thermodynamic quantities of the electrode reaction [Fe(CN)6]3 + e- ~ [Fe(CN)6]4 in aqueous LiCI solutions LiCl molality mol kg ~ 2
8 14
T/K
Ar H° + nFE(SCE) a~
ArS°/J K 1 mol- 1
kJ mol- 1 300-260 b 255-230 c 230-190 c 300--175 b 300-200 b
--67+ 1 --100+2 -- 72+ 1 67 + 1 -- 62 + 1 - -
-- 141 +4 --251+4 -- 134+5 - 114+5 -- 75 + 4
a E(SCE) is the electrode potential of a saturated calomel electrode at room temperature. b Liquid medium. c Frozen medium.
T h e a p p r o x i m a t e s t a n d a r d p o t e n t i a l E ° is plotted in Fig. 4 as a f u n c t i o n of t e m p e r a t u r e , and the thermodyn a m i c q u a n t i t i e s derived are s u m m a r i z e d in T a b l e 1. Fig. 4 clearly shows that E ° at t e m p e r a t u r e s higher t h a n a b o u t 250 K changes significantly with varying molality of LiCI. It can be seen from T a b l e 1 that, at room t e m p e r a t u r e , the s t a n d a r d r e a c t i o n e n t h a l p y is almost c o n s t a n t i n d e p e n d e n t of the LiCl molality, whereas the s t a n d a r d reaction e n t r o p y increases with increasing LiC1 molality. T h e r e f o r e the difference in the s t a n d a r d p o t e n t i a l in solutions of different LiC1 molalities at room t e m p e r a t u r e is mainly due to the change in the s t a n d a r d e n t r o p y of reaction. T h e theoretical value of ArS ° at 25°C is estimated to be - 1 7 5 . 3 J K -1 tool - t from the s t a n d a r d m o l a r e n t r o p i e s S o of [Fe(CN)6] 4- a n d [Fe(CN)o] 3- ions [14] by assuming the r e l a t i o n ArS° = S ° ( [ F e ( C N ) 6 ] 4- ) - S ° ( [ F e ( C N ) 6 ] 3- )
(8)
where the c o n t r i b u t i o n of S°(e ) is neglected. T h e Ar S° values given in T a b l e 1 are n o t very different from this theoretical value, a n d the negative sign of ArS ° is also in a g r e e m e n t with the e x p e r i m e n t a l results for the electrochemical Peltier heat of the same redox couple in an a q u e o u s s u l p h a t e solution [15]. I n 8 tool kg -1 a n d 14 mol kg-1 LiC1 solutions, the s t a n d a r d r e a c t i o n e n t h a l p y a n d s t a n d a r d reaction entropy r e m a i n almost u n c h a n g e d over the whole temp e r a t u r e range. I n 2 mol kg-~ LiC1 solution, however, the two t h e r m o d y n a m i c q u a n t i t i e s have different values in different t e m p e r a t u r e regions; Ar H ° a n d Ar S° decrease at t e m p e r a t u r e s below 260 K where the solution freezes, b u t they increase again at t e m p e r a t u r e s below 230 K. T h e change in ArS ° with LiC1 c o n c e n t r a t i o n at room t e m p e r a t u r e a n d the changes i n Ar S° a n d A r H °
with t e m p e r a t u r e in a 2 mol kg-1 LiC1 solution are c o n s i d e r e d to be closely related to the structural change of LiC1 solutions. T h e structure of [Fe(CN)6] 3- and [Fe(CN)6] 4 , typically inert complex ions, is not considered to vary with c h a n g i n g t e m p e r a t u r e a n d LiC1 conc e n t r a t i o n . However, the i n t e r a c t i o n b e t w e e n the complex ions and Li + a n d water molecules will be affected by the c h a n g e in t e m p e r a t u r e a n d LiCI c o n c e n t r a t i o n , which will be reflected in the s t a n d a r d reaction enthalpy a n d s t a n d a r d reaction entropy. It is interesting to note that, in a 2 tool kg l LiC1 solution, Ar H ° a n d arS ° in a stable frozen m e d i u m at t e m p e r a t u r e s below 230 K are almost the same as those in a liquid solution at t e m p e r a t u r e s higher t h a n 260 K (Table 1). F u r t h e r studies of low t e m p e r a t u r e v o l t a m m e t r y in various media may be r e q u i r e d to u n d e r s t a n d such findings.
Acknowledgement W e are grateful to Dr. T. Iizuka for his e n c o u r a g e m e n t t h r o u g h o u t this work.
References [1] U. Stimmung and W. Schmicker, J. Electroanal. Chem., 150 (1983) 125. [2] A. Matsunaga, K. Itoh and A. Fujishima, J. Electroanal Chem., 205 (1986) 343. [3] D.K. Gosser and Q. Huang, J. Electroanal. Chem., 267 (1989) 333. [4] A. Borgerding, E. Brost, W. Schmicker, T. Dinan and U. Stimming, Ber. Bunsenges. Phys. Chem., 94 (1990) 607. [5] A.M. Bond and M. Svestka, J. Electroanal. Chem., 301 (1991) 139. [6] A.M. Bond and V.B. Pfund, J. Electroanal Chem., 335 (1992) 281. [7] Z. Borkowska, C. Cappadonia and U. Stimming, Electrochim. Acta, 37 (1992) 565. [8] T. Hasebe, R. Tamamushi and K. Tanaka, J. Chem. Soc. Faraday Trans., 88 (1992) 205. [9] C. Beriet and D. Pletcher, J. Electroanal. Chem., 361 (1993) 93, and references cited therein. [10] H. Matsuda and Y. Ayabe, Z. Elektrochem., 59 (1955) 494. [11] N.N. Greenwood and A. Earnshaw, Chemistry of the Elements, Pergamon, Oxford, 1985, p. 730. [12] J.E.B. Randles and K.W. Somerton, Trans. Faraday Soc., 48 (1952) 937. R. Tamamushi, Kinetic Parameters of Electrode Reactions of Metallic Compounds, Butterworths, London, 1975. [13] R. Haase, Thermodynamics of Irreversible Processes, AddisonWesley, 1969, Ch. 4-25. [14] Revised Nuffield Advanced Science, Book of Data, Longman, 1984, p. 112. [15] R. Tamamushi, J. Electroanal. Chem., 65 (1975) 263.
ELSEVIER
Journal of Electroanalytical Chemistry 380 (1995) 279-282
Short communication
Voltammetry in low temperature liquid solutions and frozen media: hexacyanoferrate(II/III) redox system in aqueous LiC1 solutions at temperatures between 170 K and 300 K Kazuko Tanaka, Reita Tamamushi Biophysical Chemistry Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama, 351-01, Japan Received 4 February 1994; in revised form 18 April 1994
Keywords: Low temperature systems; Voltammetry; Hexacyanoferrate(II/III) redox system
1. Introduction Voltammetric studies at low temperatures provide useful information concerning the kinetic and thermodynamic behaviour of redox systems and the transport properties of those species involved in the electrode reaction. In the last 10 years, useful information has been accumulated concerning the electrochemistry of low t e m p e r a t u r e systems involving frozen media [1-7]. The use of microelectrodes combined with a measuring instrument of high performance enables various kinds of voltammetric measurements to be made at low temperatures. In aqueous systems, voltammetric measurements at low temperatures have been carried out mainly in perchloric acid media as they have relatively low freezing points (228 K for H C 1 0 4 - 5 . 5 H 2 0 and 213 K for H C 1 0 4 . H 2 0 ) and the stoichiometric hydrates freeze without changing composition. Our previous study [8] of the cryoscopic and N M R behaviour of concentrated aqueous LiC1 solutions suggests that LiCl is a very useful supporting electrolyte for electrochemical studies of aqueous systems at low temperatures. Concentrated aqueous LiC1 solutions (e.g. 8 - 1 4 mol kg i in molality of LiC1) remain liquid down to a temperature as low as 170 K, and the liquid state of these solutions is stable at least for 2 days. Many studies [9] have been made with the hexac y a n o f e r r a t e ( I I / I I ) redox couple under various conditions, but mostly at temperatures in the vicinity of room temperature. In this p a p e r we report the voltammetric behaviour of the redox couple at a Pt microdisk electrode in aqueous LiC1 solutions of three different molalities (2 mol kg -1, 8 mol kg -1 and 14 mol kg -1) at 0022-0728/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0 0 2 2 - 0 7 2 8 ( 9 4 ) 0 3 5 0 7 - Y
various temperatures between 170 and 300 K. Well-defined voltammograms could be obtained in the frozen media, and the results are discussed from the kinetic and thermodynamic points of view.
2. Experimental Anhydrous LiC1 and K4[Fe(CN)6] were reagent grade (Wako, Japan) and used without further purification. The working electrode was a Pt microdisk electrode prepared from a Pt wire (Nilaco, Japan) with a diameter of 50 /xm; the wire was sealed into a glass tube by melting the glass around the wire. The disk surface of the electrode thus prepared was polished with a piece of fine polishing p a p e r until the surface looked mirror smooth to the eye. The counter-electrode was a Pt wire and the reference electrode was a saturated calomel electrode (SCE) which was kept at room temperature and connected to the cell solution via a salt bridge containing a 14 mol kg-1 LiCI solution. The temperature of the cell solution was regulated by circulating thermostated water at temperatures above 273 K and by using an ice-bath at 273 K. For the measurements below 273 K, the temperature was controlled by adjusting the level of liquid nitrogen in a Dewar bottle. The temperature was monitored by means of an Au(containing 0.07% F e ) - c h r o m e l thermocouple which was placed in contact with the working electrode. Cyclic voltammograms were measured by using a combination of two potentiostats (model 315A and model 972, Fuso Seisakusho, Japan) equipped with a preamplifier (model 971-2, Fuso Seisakusho, Japan).
280
K. Tanaka, R. Tamamushi /Journal of Electroanalytical Chemistry 380 (1995) 279-282
Epa
3. R e s u l t s a n d d i s c u s s i o n
3.1. Voltammetric curves The voltammograms obtained at a Pt microelectrode in a 2 mol kg-1 LiC1 solution at various temperatures are shown in Fig. 1; curve (a) was obtained in the liquid solution, and curves (b)-(d) were recorded in the frozen medium. The electrochemical behaviour of the electrode was normal at temperatures above 170 K, whereas an unusual voltammogram was obtained below 170 K as shown in Fig. l(d). Therefore the following measurements were carried out at temperatures above 170 K. Fig. 2 shows voltammograms observed for 1 mmol kg - I [Fe(CN)6] 4- in aqueous LiCI solutions of different molalities and at different temperatures (scan rate v = 0 . 1 V s-l). The voltammograms (Figs. 2(a) and 2(b)) obtained at room temperature exhibit a shape characteristic of a reversible electrode reaction at a microelectrode. However, the voltammograms (Figs. 2(c) and 2(d)) obtained at lower temperatures generally show anodic and cathodic peaks, which suggests that, particularly in frozen media (Fig. 2(c)), the diffusion of electroactive species will proceed extremely slowly a n d / o r in a very thin liquid layer adjacent to the electrode surface [6].
/
,
E-1-
-
Epc
/ ,, t,
IlOpA
0.
E/V:
.5 i
°l
E/vi
/0.5
Fig. 2. Voltammograms of 1 mmol kg 1 [Fe(CN)6]4 at a Pt microdisk electrode in aqueous LiCI solutions: (a) 2 mol kg 1 LiCI,298 K (liquid); (b) 8 tool kg- z LiCI, 298 K (liquid); (c) 2 tool kg- z LiCI, 200 K (frozen); (d) 8 tool kg- 1 LiCI, 200 K (liquid).
3.2. Kinetic considerations An experimental criterion for the reversibility of an electrode reaction is given by the peak separation AEp: A E p = Eva - Epc where
Epa and
(l) Evc are the anodic and cathodic peak
potentials respectively and were determined from the voltammogram by a graphical method as shown in Fig. 2. This method of determining peak potentials is arbitrary and not very accurate but gives sufficiently reliable data for the following qualitative discussion. For the reversible a n d / o r quasi-reversible electrode reaction the peak separation is theoretically represented by the equation [10] AEp = ( 2 R T / n F ) ~
~lOOpA
-lopA ( c
]-50 pA
,t--~
*
I 5 o i
-0.8
I
I
-0.4
I
1
0 [/V
I
t
0.4
I
i
0.8
,,J
Fig. 1. Voltammogramsobserved at a Pt microdisk electrode in a 2 tool kg-1 LiCI solution at (a) 273 K (liquid), (b) 210 K (frozen), (c) 190 K (frozen) and (d) 165 K (frozen). Scan rate v = 0.1 V s i.
(2)
where n is the charge number of the electrode reaction (in the present case n = 1) and R, T and F have their usual meanings. The parameter ~ is a measure of the reversibility and is determined by the standard rate constant and transfer coefficient of the electrode reaction, the diffusion coefficients of the electroactive species and the scan rate of electrode potential. For the totally reversible electrode reaction w = 1.1 and it increases with decreasing reversibility; when ~ is in the region between 1.1 and 6 the electrode reaction will be quasi-reversible, provided that the transfer coefficient is not very different from 0.5 [10]. Parameter w for the electrode reaction of [Fe (CN)6 ]4- was rather variable but was always less than 3 under the present experimental conditions, as shown in Fig. 3, which means that the electrode reaction proceeds with a reasonably high degree of reversibility
K. Tanaka, R. Tamamushi/Journal of Electroanalytical Chemistry 380 (1995) 279-282 I
.
t r o d e p o t e n t i a l of the r e f e r e n c e e l e c t r o d e E ( S C E ) a n d the liquid j u n c t i o n p o t e n t i a l Ej:
I
f ° = E"([Fe(CN)~] 3
[]
1.1 ,~
/[Fe(CN)6] 4 ) - E(SCE) + E i
(+) 0
L--J
281
D
•
o []
f~ E] O ~
0 rq--
--0--
0
0 0 []
0 []
0
0 0 []
U n d e r o u r e x p e r i m e n t a l c o n d i t i o n s E ( S C E ) is k e p t c o n s t a n t i r r e s p e c t i v e of the t e m p e r a t u r e a r o u n d the w o r k i n g e l e c t r o d e , but the liquid j u n c t i o n p o t e n t i a l is difficult to e s t i m a t e owing to the p r e s e n c e of the t h e r m o e l e c t r i c effect [13]. A s s u m i n g that the c o n t r i b u t i o n from Ej can be n e g l e c t e d to a first a p p r o x i m a t i o n , we can d e t e r m i n e an a p p r o x i m a t e value of the s t a n d a r d r e a c t i o n e n t r o p y ArS ° for the e l e c t r o d e r e a c t i o n
[]
1--
i1
I 200
2fi0
300
[Fe(CN)+] 3 + e-~
T/K
Fig. 3. Temperature dependence of the parameter ,..= determined from the voltammograms of 1 mmol kg t [Fe(CN)6]4 measured at a Pt microdisk electrode in 2 tool kg 1 LiCI (©) and 8 mol kg 1 LiCI ([])at u=0.1 V s -1, and i n 2 m o l k g 1 LiClat u - 0 . 5 V s I (e). The arrow indicates the freezing point of a 2 mol kg i LiCI solution.
over the w h o l e r a n g e of t e m p e r a t u r e a n d even in frozen m e d i a . Such kinetic b e h a v i o u r of the e l e c t r o d e r e a c t i o n suggests a relatively small activation e n e r g y c o m p a r a b l e with t h e most p r o b a b l e e n e r g y ( a b o u t 20 kJ mol t) of h y d r o g e n b o n d s in w a t e r [11] a n d is, at least qualitatively, c o n s i s t e n t with the b e h a v i o u r exp e c t e d f r o m the following kinetic p a r a m e t e r s r e p o r t e d for t h e e l e c t r o d e r e a c t i o n in a 1 mol d m 3 KC1 solution at 20°C [12]: k ° = 0.09 cm s -1
(5)
f r o m the t e m p e r a t u r e d e p e n d e n c e of E ° a c c o r d i n g to the r e l a t i o n
nF(dE°/dT)
= ArS °
(6)
In a d d i t i o n , the effects of t e m p e r a t u r e a n d LiCI conc e n t r a t i o n on t h e s t a n d a r d r e a c t i o n e n t h a l p y A r H ° for t h e e l e c t r o d e r e a c t i o n can b e discussed using the e q u a tion
nFT(dE°/dT)
- nFE° = Ar H ° + nFI£(SCE)
(7)
w h e r e the s e c o n d t e r m on the r i g h t - h a n d side is k e p t c o n s t a n t u n d e r t h e p r e s e n t e x p e r i m e n t a l condition.
500
i
I
!
"~. % ~,,,~,
"%%
U0* = 16.7 kJ mol
w h e r e k ° is the s t a n d a r d r a t e c o n s t a n t a n d U 0 is the activation e n e r g y at t h e s t a n d a r d p o t e n t i a l .
450
3.3. Thermodynamic considerations
4OO
A s s u m i n g a relatively high d e g r e e of reversibility of the e l e c t r o d e r e a c t i o n a n d t h a t the diffusion coefficients of t h e o x i d i z e d and r e d u c e d species are n e a r l y the same, we can e s t i m a t e an a p p r o x i m a t e value of the standard potential E ° from the anodic and cathodic p e a k p o t e n t i a l s using the r e l a t i o n E °= (Ep, + Epc)/2
[Fe(CN)+] 4
"%%
Eo mV
\-
350
300
(3) !
In cases w h e n w e l l - d e f i n e d dc p o l a r o g r a m s could be observed, the log plot analysis of the p o l a r o g r a m s gave the s t a n d a r d p o t e n t i a l s m o r e a c c u r a t e l y than, b u t almost e q u a l to, t h o s e o b t a i n e d from the cyclic v o l t a m m o g r a m s (Fig. 4). T h e s t a n d a r d p o t e n t i a l E ° thus d e t e r m i n e d involves t h r e e c o n t r i b u t i o n s , t h e s t a n d a r d p o t e n t i a l of the w o r k ing e l e c t r o d e E ° ( [ F e ( C N ) 6 ] s - / [ F e ( C N ) 6 ] 4 - ) , the elec-
250 1 0
I
I
200
250
~
"4 I
300
350
T/K
Fig. 4. Temperature dependence of E ° of the [Fe(CN)6]4 /[Fe (CN)6]3 redox system in aqueous LiCI solutions of 14 mol kg + (zx), 8 mol kg t (rn) and 2 mol kg l (© and e) where the solid circles represent E ~ obtained from the log plot analysis of d.c. polarograms. The arrow indicates the freezing point of a 2 mol kg I LiCI solution.
K. Tanaka, R. Tamamushi/Journal of Electroanalytical Chemistry 380 (1995) 279-282
282
Table 1 Thermodynamic quantities of the electrode reaction [Fe(CN)6]3 + e- ~ [Fe(CN)6]4 in aqueous LiCI solutions LiCl molality mol kg ~ 2
8 14
T/K
Ar H° + nFE(SCE) a~
ArS°/J K 1 mol- 1
kJ mol- 1 300-260 b 255-230 c 230-190 c 300--175 b 300-200 b
--67+ 1 --100+2 -- 72+ 1 67 + 1 -- 62 + 1 - -
-- 141 +4 --251+4 -- 134+5 - 114+5 -- 75 + 4
a E(SCE) is the electrode potential of a saturated calomel electrode at room temperature. b Liquid medium. c Frozen medium.
T h e a p p r o x i m a t e s t a n d a r d p o t e n t i a l E ° is plotted in Fig. 4 as a f u n c t i o n of t e m p e r a t u r e , and the thermodyn a m i c q u a n t i t i e s derived are s u m m a r i z e d in T a b l e 1. Fig. 4 clearly shows that E ° at t e m p e r a t u r e s higher t h a n a b o u t 250 K changes significantly with varying molality of LiCI. It can be seen from T a b l e 1 that, at room t e m p e r a t u r e , the s t a n d a r d r e a c t i o n e n t h a l p y is almost c o n s t a n t i n d e p e n d e n t of the LiCl molality, whereas the s t a n d a r d reaction e n t r o p y increases with increasing LiC1 molality. T h e r e f o r e the difference in the s t a n d a r d p o t e n t i a l in solutions of different LiC1 molalities at room t e m p e r a t u r e is mainly due to the change in the s t a n d a r d e n t r o p y of reaction. T h e theoretical value of ArS ° at 25°C is estimated to be - 1 7 5 . 3 J K -1 tool - t from the s t a n d a r d m o l a r e n t r o p i e s S o of [Fe(CN)6] 4- a n d [Fe(CN)o] 3- ions [14] by assuming the r e l a t i o n ArS° = S ° ( [ F e ( C N ) 6 ] 4- ) - S ° ( [ F e ( C N ) 6 ] 3- )
(8)
where the c o n t r i b u t i o n of S°(e ) is neglected. T h e Ar S° values given in T a b l e 1 are n o t very different from this theoretical value, a n d the negative sign of ArS ° is also in a g r e e m e n t with the e x p e r i m e n t a l results for the electrochemical Peltier heat of the same redox couple in an a q u e o u s s u l p h a t e solution [15]. I n 8 tool kg -1 a n d 14 mol kg-1 LiC1 solutions, the s t a n d a r d r e a c t i o n e n t h a l p y a n d s t a n d a r d reaction entropy r e m a i n almost u n c h a n g e d over the whole temp e r a t u r e range. I n 2 mol kg-~ LiC1 solution, however, the two t h e r m o d y n a m i c q u a n t i t i e s have different values in different t e m p e r a t u r e regions; Ar H ° a n d Ar S° decrease at t e m p e r a t u r e s below 260 K where the solution freezes, b u t they increase again at t e m p e r a t u r e s below 230 K. T h e change in ArS ° with LiC1 c o n c e n t r a t i o n at room t e m p e r a t u r e a n d the changes i n Ar S° a n d A r H °
with t e m p e r a t u r e in a 2 mol kg-1 LiC1 solution are c o n s i d e r e d to be closely related to the structural change of LiC1 solutions. T h e structure of [Fe(CN)6] 3- and [Fe(CN)6] 4 , typically inert complex ions, is not considered to vary with c h a n g i n g t e m p e r a t u r e a n d LiC1 conc e n t r a t i o n . However, the i n t e r a c t i o n b e t w e e n the complex ions and Li + a n d water molecules will be affected by the c h a n g e in t e m p e r a t u r e a n d LiCI c o n c e n t r a t i o n , which will be reflected in the s t a n d a r d reaction enthalpy a n d s t a n d a r d reaction entropy. It is interesting to note that, in a 2 tool kg l LiC1 solution, Ar H ° a n d arS ° in a stable frozen m e d i u m at t e m p e r a t u r e s below 230 K are almost the same as those in a liquid solution at t e m p e r a t u r e s higher t h a n 260 K (Table 1). F u r t h e r studies of low t e m p e r a t u r e v o l t a m m e t r y in various media may be r e q u i r e d to u n d e r s t a n d such findings.
Acknowledgement W e are grateful to Dr. T. Iizuka for his e n c o u r a g e m e n t t h r o u g h o u t this work.
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