Thermal analysis of electrochemical reactions

J. Electroanal. Chem., 145 (1983) 53-65

53

Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

THERMAL ANALYSIS OF ELECTROCHEMICAL REACTIONS INFLUENCE OF ELECTROLYTES ON PELTIER HEAT FOR Cu(0)/Cu(II) AND Ag(0)/Ag(I) REDOX S Y S T E M S

T O R U OZEKI, N O B U A K I OGAWA, K A Z U Y U K I AIKAWA, IWAO WATANABE and SHIGERO IKEDA

Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560 (Japan) (Received 3rd June 1982; in revised form 26th August 1982)

ABSTRACT

The electrochemical Peltier effect is the heat effect observed at an electrode interphase when a reversible electrode reaction proceeds. The values of the molar Peltier heat II for Cu(0)/Cu(II) and Ag(0)/Ag(I) systems are determined by combining controlled current electrolysis and thermometry in aqueous perchlorate solution. The values of II for Ag(0)/0.02 M AgC104, 1 M HCIO4 and Cu(0)/0.02 M Cu(C104)2, 1 M HC104 are determined as - 28 and 12 kJ m o l - I respectively. The dependence of 17 upon the solution composition is theoretically calculated by using ionic entropy and ionic entropy of transport, and is compared with experimental results. The influence of electrochemically inactive supporting ions on YI is ascribed to the ionic heat of transport, and is of the order of several kJ m o l - I . The values of the ionic heat of transport for copper aquo ion and ammonium ion are evaluated.

INTRODUCTION

Ionic entropy is measure of the configuration freedom of an ion, and gives some structural information. Recently, the reaction kinetics has been discussed by using the knowledge of the ionic entropy [1]. The ionic entropy can be derived from the Peltier heat, which is a reversible electrochemical reaction heat and corresponds to the entropy change of the reaction. Lange and Monheim [2] obtained the values of the Peltier heat for several inorganic redox systems by the use of a differential calorimeter. Lange and Hesse [3] suggested that the ionic heat of transport associated with the bulk transport process is involved in the Peltier heat, so that the Peltier heat depends not only upon electroactive ion but also upon the inactive supporting salt. However, the theoretical treatment of the ionic heat of transport in a solution system had to wait for the establishment of irreversible thermodynamics, and was quantitatively carried out by Agar [4]. The ionic heat of transport has often been neglected on deriving the ionic entropy from the electrochemical thermometry of a solution system, because of the lack of the available data on this quantity [5,6]. 0022-0728/83/0000-0000/$03.00

© 1983 Elsevier Sequoia S.A.

54

In this paper, the dependence of the Peltier heat upon the solution composition is studied and the contributions of the ionic entropy and the ionic entropy of transport are determined according to Agar's analysis. In order to measure the Peltier heat, thermometric experiments are carried out using an apparatus having a thermistor in an electrode as a temperature-sensing element. The apparatus is relatively simple and even weak and localized heat can be detected accurately. THEORETICAL

Derivation of molar Peltier heat Lange and Hess [3] suggested the necessity for considering heat of transport to derive the Peltier heat. The heat of transport was introduced first by Eastman [7] in order to interpret the dependence of thermo-electromotive force upon the inactive electrolytes. He suggested that the ionic heat of transport was related to the reversible thermal reactions occuring in the vicinity of an ion as it moved through the solvent. The quantitative derivation of the ionic heat of transport has been developed by Agar [4], and will be briefly described here. As shown in Fig. l, when 1 tool of particle i is transported from the region L to R by a particular force, the entropy of the system in the region R increases by the amount of the ionic entropy s i and that of L decreases by the same amount. The entropy transported across the boundary with the migration of 1 tool of i is defined as the transported entropy ~ . The difference between the transported entropy and the ionic entropy should be equal to the heat supplied from the surroundings to the system. This heat is referred to as the heat of transport Q*, and the corresponding entropy of transport, Si* = Q~/T, is sometimes called Eastman entropy. Thus, = Si "~ Si*

(l)

When the redox reaction of metal (M)/metal ion ( M az,q÷) occurs at an electrode interface M + aq= M~ + + z e-

(2)

the oxidation current of z~F changes the entropy of the electrode system by the

•

A

-Si V

+si

l)

Si Fig. 1. Schematic illustration of the mechanism of the heat of transport accompanied by ion migration.

55

following amount: mSs°;s = (s I 4- ZlS e -- SM)

- - z l ( t l s , / z , + t2S2/Z z + t3S3/Z3 + S~)

(3)

where t i and zi are the transference number and the charge including the sign of the ion i, and the subscripts 1, 2 and 3 denote electrochemically, the active ion, the conjugated anion and the supporting electrolyte cation respectively. The quantity in the first parentheses of the equation is the entropy change of the oxidation reaction at the electrode interface and that in the second is the entropy change accompanied by the transport process. The entropies transported across the boundary of the system are summed and expressed as

AS~I= --zl(tl~/Zl 4-t2~/z 2 4- t3~/z 3 4- ~e)

(4)

From the balance of the entropy, the following equation is obtained: ox _ ox ASbd -- bS;y s + H/T

(5)

where II is the heat that the system exchanges with the surroundings, and corresponds to the molar Peltier heat. Substituting eqns. (1), (3) and (4) into (5) gives n

=

-

T(aSox)

-

aQ*

where ASox

= s I 4- Z l S e - - s M

AQ* = zl(X~tiSi *T /zi + S : T )

(6) (7) (8)

Equation (6) is the most basic expression derived by Agar [4] for the electrochemical molar Peltier heat. The term ASox represents the entropies of the species which undergo the redox reaction at the electrode interface (electrodic term), and AQ* represents the entropies of transport of the species which undergo migration in the solution (ionic term). The ionic entropy is obtained from temperature differentiation of chemical potential of ion [8] as follows: s i = s ° - R In a i - R T d ( l n a i ) / d R (9) where a i is the activity of ion i. By using the concentration [i] and activity coefficient fi, eqn. (9) is rewritten s i = s o + siE - R ln[i] - R T d ( l n [ i ] ) / d T

(I0)

where siE is the excess entropy of ion i and is expressed as follows: siE = - R lnfi - R T d ( l n f i ) / d T

(11)

In the solution where ions are regarded to be present as aquo ions, e.g. in most of the perchlorate solutions, [i] = Ci,

d(ln[i])/dT = 0

(12)

56

where c i is an analytical concentration of ion i. Therefore, the entropy is rewritten as follows: (13)

S i = S? -~- S# -- R In c i

Instead of the molar Peltier heat, it is convenient to define the equivalent Peltier heat H. I~ : ~I /z 1 :

1 -~- S e - - S M / Z 1 )

-- T ( s 1 / z

-(EtiS~ii*T+ S~*T)

(14)

where ~* is the equivalent entropy of transport for ion i.

Sl* = S * / z i

(15)

EXPERIMENTAL

Cell assembly and thermistor electrode The cell assembly and procedure used in this work is the same as reported in ref. 9. The final electrochemical plating of the redox electrode was with either copper or silver to form the metal elecetrode.

Measurement device The measurement devices are of conventional design using operational amplifiers. The thermometer circuit shown in Fig. 2 consists of the Wheatstone bridge in principle, and converts the resistance change of the thermistor into output. The output signal is a linear function of the temperature difference between two thermistors, provided the difference is sufficiently small. This system could detect a

+12V

Ik~

reference

A

-15V ika

•

i lIuF

]

sample

+15V ~-

t i

<% ~

~

~

10M~

~/~R2 '

10k~

I

-isv

Fig. 2. Circuit diagram of the thermometer.

57 temperature difference of 0.1 m K at 25°C. The whole system was controlled by a micro-computer as shown in Fig. 3, which offered required binary signals to a digital/analog converter. The output from the converter was fed to a galvanosta. The temperature difference AT and the current I were digitized, accumulated and analysed by the micro-computer system.

63 t'-

,

W C

Z 0

-.-t

BRIDGE

~AT

[

I

]MULT,?EXE 10 Fig. 3. Block diagram of micro-computer system.

Chemical reagent Copper(II) perchlorate and Ag(I) perchlorate were prepared by the neutralization of corresponding metal carbonate with perchloric acid and were used after several recrystallizations. All the other chemicals used were of reagent grade without further purification.

Experimental operation Controlled-current electrolysis was performed as shown in Fig. 4. Reduction and oxidation current flowed alternatively for 30s each with the same period of zero current between them. The zero current period was placed between the electrolysis because of the slow temperature response. The temperature difference AT was read just before the current I was turned off. In Fig. 3 of ref. 9 is shown the typical plot of AT vs. I for Cu(0)/0.2 M Cu(C104) 2 in 1 M NaC104 aqueous solution. The region

58 0.4' anodic

0.21 \ -

-0.~

-0£

cathodic

~ exother mic

0

!

2

3

4

5

6

7

8

time/ min Fig. 4. The waveform of controlled current electrolysis and the typical temperature response of 0.2 M Cu(C104) 2 + 1 M NaC]O 4 solution (at 25°C).

where the plot is almost linear is betwen _+ 1 mA in this case, and the width of the region is a quasi-linear function of the electroactive ion. The temperature response was measured at 10 different cathodic and anodic currents each from 25 to 250/~A. Each point was obtained by averaging the results of three different measurements. E v a l u a t i o n o f Peltier heat

The observed AT could be converted into t h e heat q generated second at the electrode by using the following relation, under the assumption of linear diffusion of the heat: AT= q/A~

(16)

where X is the thermal conductivity of the solution and A is a cell constant. The following empirical equation gives the value of X for aqueous electrolyte solution

[lO]: X = X o + ~aic i

(17)

where a i is the constant for ion i and is taken from ref. 10. The heat q is expressed in terms of current I as follows: q = ~rI+ R I z

(18)

where ~r is the Peltier coefficient and is positive when exothermic heat is evolved by

59 o x i d a t i o n r e a c t i o n , a n d R is a n a p p a r e n t r e s i s t a n c e . T h e P e l t i e r c o e f f i c i e n t 7r is c o n v e r t e d i n t o t h e m o l a r P e l t i e r h e a t H as f o l l o w s :

I I = zlF~r

(19)

F r o m e q n s . (16) a n d 18) AT=

(~r/A)I + ( R / A ) I 2

(20)

P a r a m e t e r s (~r/A, R / A ) c a n b e e v a l u a t e d b y a l e a s t - s q u a r e s c a l c u l a t i o n a p p l i e d t o t h e e c p e r i m e n t a l p l o t o n X A T vs. I. T h e s o l i d c u r v e i n Fig. 3 o f ref. 9 is t h e r e s u l t o f the least-squares calculation. I n o r d e r t o d e t e r m i n e t h e cell c o n s t a n t A , t h e m e a s u r e m e n t s w e r e c a r r i e d o u t o n s o m e s y s t e m s s u c h as C u ( 0 ) / C u ( I I ) s u l f a t e a n d A g ( 0 ) / A g ( I ) n i t r a t e f o r w h i c h a b s o l u t e 17 v a l u e s a r e k n o w n f r o m c a l o r i m e t r i c a n d / o r t h e r m o e l e c t r i c e x p e r i m e n t s [2]. T h e cell c o n s t a n t A w a s t h e n d e t e r m i n e d b y a l e a s t - s q u a r e s c a l c u l a t i o n t o give t h e b e s t fit t o t h e k n o w n v a l u e s . T h e r e s u l t s a r e g i v e n i n T a b l e 1. DATA ANALYSIS Though the values of ionic entropy and ionic entropy of transport are known for m a n y i o n i c s p e c i e s [4,11], s o m e v a l u e s n e c e s s a r y f o r t h e o r e t i c a l e v a l u a t i o n o f t h e

TABLE 1 Comparison of the molar Peltier heat rI obtained by this work, with those obtained from calorimetry and thermoelectric power measurement at 25°C. Here M is the unit mol dm 3 while m is moles of salt in 1000 g water Molar Peltier heat I I / k J mol- 1 Calorimetry a

0.01 M CuSO 4 0.005 M HzSO 4 0.5 M CuSO 4 0.005 M H2SO 4 0.22 M CuSO 4 0.625 M CuSO4 1.0 M CuSO4 0.005 m AgNO 3 1 m KNO 3 0.01 m AgNO 3 1 m KNO 3 0.05 m AgNO 3 0.1 m AgNO 3

Thermoelectric a power

} )

37.2 41.8 34.3 45.1

This work b

26.3

28.4

37.2

34.7

-33.9 45.6

44.7 37.6 43.9

}

- 17.3

- -

-

17.0

}

- 15.5 - 14.3 - 12.2

- -

-

15.6

- -

-

14.6

-

12.8

-

12.1

Calculated in MKS units from Lange [2]. b The values were obtained by adjusting the cell constant A. See text.

60 m o l a r Peltier h e a t are n o t available, e.g. those of the ionic entropies of t r a n s p o r t for C u 2+ a n d N H ] - a n d of the excess terms for ionic e n t r o p y a n d for ionic e n t r o p y of t r a n s p o r t in the solutions used in the p r e s e n t study. In this section we described h o w the values are d e t e r m i n e d from the e x p e r i m e n tally o b t a i n e d I I values. By c o m b i n i n g eqns. (13) a n d (14) a n d t a k i n g a c c o u n t of ~ t i = 1, the following e q u a t i o n is o b t a i n e d : ~I - R T l n

CM+/Z

1 =

--

T((s°++

s ~ a + ) / z l + s e -- S M / Z 1 )

-TSg, o;- T~*~M,+EM,t..+T(--SL,++ Sg,o;)

(21)

where M + denotes Cu 2+ or A b + a n d M '+ denotes Cu 2+, A g +, H +, N a +, Li + a n d NH~-. The r i g h t - h a n d side of the e q u a t i o n can be d i v i d e d into two parts, i.e. those quantities which c o n t a i n transference n u m b e r s and those which d o not. - R T In CM+/Zl = B M + ~., M.tM,+ ( -- VS~.l.clo4 )

(22)

where B M = - T((s°++ s~a+)/z 1 + s e - SM/Z,)--

T S g , og - T~'~M )

Sm*'c,o, = g~a.+- S~,o;a'*

(23) (24)

T h e value of the l e f t - h a n d side of eqn. (22) is d e t e r m i n e d b y the experiments. T h e transference n u m b e r t i for ion i is calculated f r o m the analytical concentration, a n d the equivalent c o n d u c t i v i t y A i defined at infinite dilution. T h e ionic e n t r o p y of t r a n s p o r t is expressed as S ~ = S *° + S *E

(25)

where S~ ° is the s t a n d a r d e n t r o p y of t r a n s p o r t of which the values for H +, Li ÷, N a ÷ a n d C10 4 are available f r o m ref. 4, a n d Si*z is the excess e n t r o p y of transport. W h i l e the e n t r o p y of t r a n s p o r t for salt is expressed as ff~M,CIO4 _-- Sm,c104 ~-.0 ~.E ~- SM,CIO4

(26)

TABLE 2 The heat of transport for salt, T S~gclo,/kJ equiv- J at 25°C

HC104 NaCIO4 LiCIO4 NH4CIO4 Cu(CIO4) 2 AgC104

This work

By Agar a

12.0 3.7 - 0.5 - 1.2 - 0.9 7.4

12.52 2.81 - 0.18 5.55

" Calculated by using the values of the ionic entropy of transport from Agar [4].

61

It is assumed that all of the excess entropies of transport for HC104, LiC104 and NaC104 take the same value since all of these salts are of the 1 : 1 type. By operating the least-squares calculation of eqn. (22) on all the experimental results shown in Figs. 5-8, the individual values B M (M+; Cu 2÷ and Ag ÷) and T S M *°' C I O 4 \tM '+" Cu 2÷, Ag +, H ÷, Na ÷, Li ÷ and NH~-) were obtained, and the values so determined for T S *M'clo4 0 are given in Table 2. The know constants used in the calculation are collected in the Appendix. RESULTS

A series of experimental results are shown in figs. 5-8. The dependence of the molar Peltier heat 1-[ for the Cu(0)/Cu(II) (0.2 M Cu(C104)2) system upon the concentration of various supporting electrolytes is shown in Fig. 5. It is shown that the value of II decreases with the concentration of supporting electrolyte, and that the value of H in various perchlorate supporting electrolytes increases in the order of H + < N a + < Li+< NH~-. The dependence of II upon ln[Cu(II)] in 1 M supporting electrolyte is shown in Fig. 6. The slope of the plot seems to be independent of the kind of supporting electrolytes. The plot shown in Fig. 7 is the dependence of H for the 0.2 M Ag(I) system upon the composition of the supporting electrolyte. The most remarkable difference between the Cu(II) and Ag(I) systems is that the signs of 1-1 are opposite each other. Furthermore, the difference between the curves for NH~and H ÷ for the Ag system is almost half of that for the Cu system. The slope of the plot of II vs. ln[Ag(I)] shown in Fig. 8 is also almost independent of the kind of supporting electrolytes, and equals that for the Cu(II) system shown in Fig. 6. All the curves drawn in Figs. 5-8 are the results of the least-squares calculation described in the preceding section.

40

.0

•

• .

o

.

.

.

.

.

I~

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

'30 ' 0"". 0".. 0""-...

,

.

0

20'

.... "'

o . . . . . . . . 6 . . . . . . . . ~3

I 0.2

c

I

I

I

I

0.4

0.6

0.8

l.O

/

mol

d m -3

Fig. 5. The relation between the molar Peltier heat II and the concentration c of supporting electrolyte in 0.2 M CU(C104) 2. Circles are the experimental 11 values, and curves are the simulated molar Peltier heats by using the ionic quantities: (o, ) NH4C104; ( ~ , . . . . . ) NaC104; ( z x , - - . - ) LiC104; ( O , - . . . . . ) HC104.

62

40,

30"

...•'~) 20"

. •.• "'O"

.... • . . . . ' O " ' • '

-O......... 0

10'

I

I

-2.0

I

-1.5 10g ( C /

I

-0.5

-i.0 tool dm -3 )

Fig. 6. The relation between the molar Peltier heat H and the concentration c of Cu(C104) 2 in 1 M perchlorate supporting electrolyte solution. Circles are the experimental II values, and curves are the simulated molar Peltier heats by using the ionic quantities: (e, ) NHaC104; ( ~ , . . . . . ) NaC104; ( A , - . . - ) LiCIO4; ( O , . . . . . . ) HCIO 4.

-15

-15 O...""

o

".

~ -25

-20

'0 ............ 0 ......

0

0

0

. ..O"'

= -30 ¸

-25 I

I

0.2

0.4 c

/

I

I

I

0.6

0.8

1.0

tool dm -3

-2.0

-1J5 log

( ¢

-]~.0 /

-0~5

tool dm -3 )

Fig. 7. The relation between the molar Peltier heat gl and the concentration c of supporting electrolyte in 0.2 M AgCIO 4. Circles are the experimental 17 values, and curves are the simulated molar Pehier heats by using the ionic quantities: (O, ) NH4C104; ( ~ , . . . . . ) NaClO4; ( A , _ . . _ ) LiCIO4; ( O , . . . . . . ) HCIO,. Fig. 8. The relation between the molar Peltier heat 17 and the concentration c of AgC104 in 1 M perchlorate supporting electrolyte solution. Circles are the experimental 1I values, and curves are the simulated molar Peltier heats by using the ionic quantities: (O, ) NH4C104; ( ~ , . . . . . ) NaC104; (zx,- . . . . ) LiCIO4; ( O , . . . . . . ) HCIO 4.

63 DISCUSSION

As shown in Figs. 5 - 8 the molar Peltier heat is well predicted from the theory. The molar Peltier heat depends upon the concentration of electroactive ion logarithmically. The slopes of the curve in Figs. 6 and 8 are almost equal to the expected value R T ( +_ 10%). The value of I-[ for the copper system is quite different from that of silver, as shown in Figs. 5 and 7. The opposite sign of II is mainly due to the difference of the ASox term, especially of the ionic entropy of electroactive ion, i.e. the value of standard ionic entropy for Ag(I) ion is 51.71 J K - 1 m o l - 7, but that for Cu(II) ion is - 1 4 2 . 9 6 J k 1 m o l - 1 [11]. The dependence of H upon the supporting electrolyte is explained by eqn. (8). In eqn. (8), the value of AQ* is given by transference number and ionic heat of transport for all of the ions present in the solution. The fact that the width between curves for the Ag + system is almost half that for the Cu 2+ system, as shown in Figs. 5 and 7, results from the difference of zj value, i.e. z I = 1 for Ag + andz 1 = 2 for Cu 2+, because the values of the summation in eqn. (8) for both systems are almost the same. The values of ionic entropy of transport for NH4 ~, Cu 2+ were obtained as - 2 . 8 5 and - 1.79 j K - 1 equiv- l respectively, by assuming S~lo, = - 1.02 J K - 1 equiv 1. These values have not yet been published. The ionic entropies of transport for a series of methyl-substituted ammonium ion (NMenH~-4_ u)) from ref. 4 and that for a m m o n i u m ion are plotted in Fig. 9. The plot shows almost constant increase with the substitution of the methyl group. The value of ionic entropy of transport reflects the degree of structural relaxation of the moving ion [7]. The more positive value means that the solvent molecules around the ion have larger entropy if compared with the bulk solvent. Thus, the ionic entropy of transport reflects the lability, i.e. the structure breaking and making during a migration, while the ionic entropy reflects the structure of the central ion and surrounding molecules in a static sense, the order of ionic entropy of transport

30'

.(y ' ~ 20

f 0 f"

,~ 1 0

~J

~f s~ S

o.

-10 NH

j~ iS

I

+ NMeH 3

I

+ NMe2H 2

I

NMe3 H+

I

+ NMe 4

Fig. 9. Plot of the heat of transport for a series of methyl-substituted ammonium ions; (e) is the result of this work, and the others are taken from ref. 4.

64 for cations, H + > A g + > N a + > L i + > Cu2+> NH~- or NMe4+ > NHMe~- > N H a M e ] > N H 3 M e + > NH~- indicates that the entropic wzter decreases in the same order the ion. On the other hand, ionic entropies have the following order: N H 4 ~ > A G + > N a + > L i + > H + > Cu 2+ [11]. Among the ions studied, therefore, NH~- and H + ion occupy the exceptional positions. It has been suggested that NH~ion in aqueous solution locates in the lattice point in place of the water molecule and causes no perturbation to the water framework [12], and that H + ion migration procedds through proton j u m p mechanism, i.e. only the charge and the resultant perturbation move in the solution, but the proton itself does not [13]. Therefore, it is not unusual that the values of the ionic entropy of transport for these ions should occupy the exceptional positions among the ions. From the values of ionic entropy [11] and of B M, the excess entropies for Cu 2+ and Ag + ions are obtained as scZu2+/2 = + 19.1 and s ~ + = +23.0 j K -1 equiv 1. The equivalent excess entropies are almost equal. It seems that the excess entropy is determined mainly by electric interaction. On the other hand, according to the definition of excess entropy (eqn. 11), the value of s~+ can be calculated theoretically if the Debye-Htickel-type interaction operates in the present solutions. l o g fi =

-Az2v/I /( 1 + Bao/I)

(27)

where A =0.5115 mo1-1/2 dm 3/2, B = 0.3291 × 10 l° m -1 mo1-1/2 dm 3/2 and a i is the parameter for the radius of ion i (6 × 10 -1° m for Cu 2÷ and 2.5 × 10 -~° m for Ag ÷) [14,15]. In the present experiments, the ionic strength (l=½Eciz~) of the solution ranges from 0.2 in the case of 0.2 M AgC104 to 2.2 in the case of 0.4 M Cu(C104) 2, 1 M HC104, then the equivalent excess entropy siZ/zi ranges from 5.97 to 7.38 for Cu 2÷ and from 3.19 to 5.84j K -~ equiv -1 for Ag ÷ at 25°C. In the Data Analysis section, Scu2+E or saZ~+ are assumed to be constant notwithstanding the change of ionic strength: The comparison of the Debye-Htickel type siE with that observed shows that the Debye-Htickel theory does not adequately evaluate the excess term, while, the approximation of a constant excess term seems not to give so much error on estimating ionic properties because the variation of s~ is small. The curves in Figs. 5 - 8 are the results of the calculation of eqn. (6) by using the ionic quantities obtained from the above treatment, and they are excellent agreement with the observed molar Peltier heat. Therefore, the individual contribution of ion to the molar Peltier heat can be determined independently in Cu(0)/Cu(II) or Ag(0)/Ag(I) perchlorate systems by the present method, measuring the electrochemical Peltier heat with the thermistor electrode.

65 APPENDIX

Temperature

T = 298 K.

Pressure Constants

P = 1 atm. Gas constant R = 8.31 J K - ~ m o l - 1

Equivalent conductivity: A i / ~ - 1 cm 2 equiv-1 ,. H + 349.81; N a + 50.1; Li + 38.68; NH~- 73.55; Cu 2+ 53.6; Ag + 61.9; C104 67.36. Ionic entropy of transport: S * ° / J K -1 mo1-1 ** (under the assumption that S~ °-= 2.05 J K -1 mol-1). H + 43.05; N a + 10.45; Li + 0.42; Ag + 19.65; NMe4+ 26.54; N H M e f 20.20; N H 2 M e ~- 13.83; N H 3 M e + 10.05; C104 - 1 . 0 2 . Ionic entropy: s ° / J K 1 mol-~ *** (under the assumption that sO+ = - 2 2 . 1 J K l tool 1). N a + 38.04; Li + - 7 . 9 4 ; NH~- 90.7; Cu 2+ - 1 4 2 . 9 6 ; Cu 33.27; Ag + 51.71; Ag 42.66. *oM) +sO M ) ( i n J K - 1 m o l - 1 *** Transported entropy of metallic electron: S=e( M) = S~( e(Cu) - 0.167; e(Ag) - 0.146). REFERENCES 1 N. Sutin, M.J. Weaver and E.L. Yee, Inorg. Chem., 19 (1980) 1096. 2 E. Lange and J. Monheim, Handbuch der Experimental Physik, Vol. XII, Akademische Verlag Gesellschaft, Leipzig, 1933, p. 327. 3 E. Lange and T. Hesse, J. Am. Chem. Soc., 55 (1933) 853. 4 J.N. Agar in P. Delahay (Ed.) Advances in Electrochemistry and Electrochemical Engineering, Vol. 3, Interscience, New York, Londonl 1963, p. 31. 5 G. Milazzo, M. Sotto and C. Devillez, Z. Phys. Chem. N.F., 54 (1967) 1. 6 E.L. Yee, R.J. Cave, K.L. Guyer, P.D. Tyma and M.J. Weaver, J. Am. Chem. Soc., 101 (1979) 1131. 7 E.D. Eastman, J. Am. Chem. Soc., 48 (1926) 1482. 8 J.M. Sherfey, J. Electrochem. Soc., 110 (1963)213. 9 T. Ozeki, I. Watanabe and S. Ikeda, J. Electroanal. Chem., 96 (1979) 117. 10 E. McLaughlin, Chem. Rev., 64 (1964) 389. 11 R.E. Dickerson, Molecular Thermodynamics, W.A. Benjamin, California, 1969, Appendix 4. 12 A.H. Narten, J. Chem. Phys., 49 (1968) 1692. 13 G.M. Barrow, Physical Chemistry, McGraw-Hill, New York, 1966, p. 678. 14 R.A. Robinson and R.H. Stokes, Electrolyte Solutions, Butterworths, London, 1965. 15 J. Kielland, J. Am. Chem. Soc., 59 (1937) 1675.

* Data are taken from Robinson and Stokes [14]. ** Calculated in MKS units from Agar [4]. *** Calculated in MKS units from Dickerson [11].