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Determination of standard Gibbs energies of ion partition between water and organic solvents by cyclic voltammetry
J. Electroanal. Chem., 157 (1983) 19-26
19
Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
DETERMINATION OF STANDARD GIBBS ENERGIES OF ION PARTITION BETWEEN WATER AND ORGANIC SOLVENTS BY CYCLIC VOLTAMMETRY PARTI
B. HUNDHAMMER * and THEODROS SOLOMON
Department of Chemistry, Addis Ababa University, P.O. Box 1176, Addis Ababa (Ethiopia) (Received 1lth February 1983)
ABSTRACT Standard Gibbs energies of ion transfer across the water/nitrobenzene and water/I,2 dichloroethane immiscible electrolyte solution interfaces, have been determined using cyclic voltammetry and based on the tetraphenylarsonium tetraphenylborate (TPAsTPB) assumption. The results are compared with those obtained by other methods.
INTRODUCTION
The determination of standard Gibbs energies of ion transfer from water to organic solvents is of considerable interest in the explanation of processes taking place in biological systems, liquid-liquid extraction and in liquid state ion-selective electrodes. The standard Gibbs energies for the transfer of individual ions from one solvent to another can be calculated only if an extrathermodynarnic approach is used. The tetraphenylarsonium-tetraphenylborate assumption (TPAsTPB assumption) [1-3] is one basis for these calculations. According to the experimental method employed for determination of the standard Gibbs energies, Abraham and co-worker [4] proposed to distinguish between standard Gibbs energies of partition (AGp) obtained from the partition of electrolytes between two mutually saturated immiscible solvents [5-8], and standard Gibbs energies of transfer .( AGt°) based on comparison of the solubility of the electrolytes in the pure solvents under study [9,10]. On the other hand, it was shown that standard Gibbs energies of ion partition evaluated from the half-wave potentials of cyclic voltammograms obtained from the ion transfer across the water/nitrobenzene
* Permanent address: Technische Hochschule "C. Schorlemmer", Leuna-Merseburg, Sektion Chemie, 4200 Merseburg, G.D.R.
0022-0728/83/$03.00
© 1983 Elsevier Sequoia S.A.
20
interface are in accordance with those calculated from extraction data if an ion is assigned as an internal standard [1 1]. In this paper the determination of standard Gibbs energies of ion partition by cyclic voltammetry based on the TPAsTPB assumption for the water/nitrobenzene and water/1,2 dichloroethane systems will be discussed. The results are compared with those obtained by other methods [4-9]. THEORY
The partition of an electrolyte M + X - between two mutually saturated immiscible solvents a and fl can be described by the equilibria AG;
M+(a)+X-(a)
AG°
~ M+(I3)+X-(]3) ~ M+X-(/3)
(1)
where AG° represents the standard Gibbs energy of ion association. In order to calculate AGp from the experimentally observed data the activity coefficients in the two solvents and AG° must be known. Provided equilibrium (1) is established between the two solvents the electrochemical potentials/2~ of every ion i is the same in both solvents and a Galvani potential difference A~qo is established across the interface
¢p" - q~# = A%~p= A%ep~++ ( R T / F ) ln( al~M+/a~+) = A~°x-+ ( R T / F )
ln(aPx-/a~-)
(2)
Since the standard Galvani potential difference A~90° or a single ion is related to its standard Gibbs energy of partition AG~.i(a ---, fl) by A~ep° -- AGp,i(ot ~ fl)/7.iF
(3)
the calculation or AG;, i becomes possible if the standard Galvani potential difference can be obtained experimentally. It has been shown [12,13] that the ion transfer across the interface of immiscible electrolytes follows formally the same laws as that describing the electron transfer at the metal- electrolyte solution interface. Thus, the theory of cyclic voltammetry derived for those electrodes can be adopted to describe the voltammetric behaviour of the interface between two immiscible electrolyte solutions. The transfer of ions across the interface studied by cyclic voltammetry is diffusion controlled at low sweep rates. Hence, the current response of the system to a triangular potential signal can be treated like a reversible electron-transfer reaction. It has been shown by Nicholson and Shain [14] that the current-potential relationship for such a system is given by
i = 7.3/2FAcb(Div~)l/2
X (at)
(4)
In eqn. (4) the area A of the interface is expressed in cm 2, the bulk concentration cib in mol dm -3 and the sweep rate v in V s -1. the values for 7rl/2x(at ) vs. ( E - El~2) [or in this particular case, vs. (A~q0 - A~901/2)] are tabulated by Nichol-
21 son and Shain [14]. Following this concept the evaluation of A ~ ° from voltammetric data is straightforward since the relationships
A ~ p = Ayepl/2 - 1.109RT/zF
(5)
and Ay~ ° = Ayqgl/2 - ( R T / 2 z F ) ln(D~/D B) - ( R T / z F )
l n ( y B / 7 ")
(6)
can be employed provided that the experimental AyE scale with an arbitrary reference point, dependent upon the experimental conditions, can be transformed into a potential scale with A~rp = 0 as zero point. In eqns. (5) and (6) Ay~0p is the Galvani potential difference at the current maximum and A~Igl/2 the Galvani potential difference at the half-wave potential. The transformation of the zero point is possible if TPAsTPB is used as the supporting electrolyte in the organic phase and Li2 SO4 or LiF in the aqueous phase. The voltammogram will be limited at negative potentials by the transfer of TPAs + from the organic phase to water, and at the positive side by the transfer of T P B - from the organic phase to water. Here A~E~/2 for TPAs + and T P B - c a n b e estimated by means of eqn. (4) from the initial part of the current-potential curve related to the transfer of these two ions. Since TPAsTPB is the supporting electrolyte in the organic phase, an error is introduced due to the contribution of the ion migration to the observed current. In spite of this, no error will arise in fixing the A y E ' value where Ay~ is zero by (AyE1/2TPAs÷+ AyEI/2TPB_)/2 = AyE'
(7)
since the assumption is justified that the diffusion coefficients and the absolute mobilities of the two ions are equal. In order to avoid errors in solvents with a low permittivity due to ion association, eqn. (6) should be replaced by
ayrv ° = Ayq,~/2 - ( R T / z F ) ln( D~'/E/( Di~1/2 + _.~at~K,D#'/2"~'~,¢ ,, -(RT/zF)
ln((yi~ + V ~ ) / y : )
(81
where a~ is the activity of the anion or the cation of the supporting electrolyte in the organic phase, K a the ion association constant of the transferred ion with the respective ion of the supporting electrolyte, and the subscript ic indicates the ion associate. We have employed eqn. (8) for the calculation of Aycp° from the experimentally observed half-wave potentials. EXPERIMENTAL The measurements were carried out with a four-electrode potentiostat with automatic IR compensation by means of positive feedback [11]. The IR compensation was set to the nearest point before the potentiostat starts oscillating. The potentiostat was set up from operational amplifier modules (McKee-Pedersen In-
22
struments) and a differential amplifier (AM 502, Tektronix). The voltammograms were recorded with an X - Y recorder (PH 8041, Philips). All solutions were prepared from salts of analytical grade (B.D.H. and Fluka) with twice-distilled water. The organic solvents were redistilled. The electrolyte solutions were mutually saturated before use. TPAsTPB and crystal violet tetraphenylborate (CVTPB) [15,16] were employed as supporting electrolytes in the organic phase, Li2SO 4 serving as supporting electrolyte in the aqueous phase. The experiments were carried out at 25 + 0.5°C. RESULTS A N D DISCUSSION
Figure 1 shows the cyclic voltammogram using 1 m M TPAsTPB and l0 m M Li 2SO4 as supporting electrolyte in nitrobenzene and water respectively. The limitation of the applicable potential range is given by the transfer of TPAs + from nitrobenzene to water at the negative side and by the transfer of T P B - in the same direction at positive potentials. Employing Parker's TPAsTPB assumption, two important pieces of information can be obtained from the voltammogram: (1) The actual potential scale AWE can be transformed to a potential scale with A'~0 = 0 as zero point as, shown in Fig. 1. (2) By comparison of the theoretically calculated current by eqn. (4) for, e.g. A ~ c p - AWncpl/2 = 0.150 V with the experimentally observed current the half-wave potentials for the transfer of TPAs + and T P B - can be estimated from the foot of the potential-current curve corresponding to the transfer of these ions. The error due to the contribution of ion migration to the observed current will lead to too low values for the standard Gibbs energies of partition for the two ions but no error is introduced with that uncertainty in the transformation of the
i/~ 2O
IC o
-lO
I TPAs~n)-*TPAs*{w} -o,3
-o~ .
-0,3
-o,2 ,
-0,2
--o,t
I
o
n
o,i
I
0,2
,
,
,
,
- 0,1"
0
0,1
0,2
o,3 o,4 zx(.p/v .
0,3
,
0,4 zxE/V
Fig. 1. Cyclic voltammogram using 1 m M TPAsTPB and 10 m M Li2SO 4 as supporting electrolytes in nitrobenzene and water respectively. Sweep rate 25 mV s - i.
23 I/pA 30' 20' 10' 0 -10 -20 -30 I
-0~
-03
-0,2 -0~
i
0
0,~
0~
0,3
0,~
zx~o/V Fig. 2. Cyclic voltammogram obtained when 0.075 m M C104- is added to the aqueous phase. All other conditions as in Fig. 1.
potential scale, as discussed above. If an ion such as perchlorate is added to the aqueous phase the voltammogram shown in Fig. 2 will be observed. The cathodic current peak is caused by the transfer of C104 from water to nitrobenzene the anodic one is due to the transfer of C104 from nitrobenzene to water. The peak potentials as well as the separation of the peak potentials of the anodic and cathodic current peaks by 59 mV are independent of the sweep rate up to 0.1 V s-1 for all ions investigated. Hence, AWcpl/2, Awq~°, and lastly AG~(w ~ n) for perchlorate can be obtained. This ion can then serve as an internal standard for fixing the zero point if TPAsTPB is replaced by CVTPB or any other supporting electrolyte in the organic phase. The same experiments have been carried out with 1,2-dichloroethane as the organic phase. Tables 1 and 2 compare standard Gibbs energies of ion partition calculated from half-wave potentials with those obtained by other methods. Besides the AGp values, AGt° values are summarized in the tables. The AG~ values determined by cyclic voltammetry are the mean of five independent measurements. Comparison of the values obtained for TPAs + and TPB- by our method with those from partition experiments shows the influence of ion migration which was not taken into account in estimating the AG~ values for the two ions. For the other ions, the AG~ values are determined by the voltammetric method in accordance with the values obtained by other methods. Of particular interest is the comparison of the AGp values with the standard Gibbs energies of transfer. The difference between the two values could be caused by the mixed solvation of the ions, especially in the organic phase of the system [4]. It has been reported [4,8] that, at the least, ions with
24
TABLE
1
C a l c u l a t e d a n d o b s e r v e d AG~ a n d AGt° v a l u e s o f s e l e c t e d i o n s i n t h e n i t r o b e n z e n e / w a t e r the TPAsTPB
system based on
assumption
Ion
AGp/kJ
mol- J "
AGp/kJ
mol- t b
AGt/kJ
mol- t
Calc. c Cs +
15.2
17.2
Bu4N ÷
-23.5
-23.9
Ph4As + l-
- 31.4 18.9
- 36.0 18.9
C I O a-
7.4
Obs. d
17.6
--
-22.6
--
-18.0
-15.9
8.0
10.5
--
23.9 e
30.6
--
NO 3
24.4
SCN -
16.0
--
--
--
10~
6.9
--
--
--
BE 4
11.0
--
--
--
Obtained
by cyclic voltammetry.
b F r o m refs. 5 a n d 6. c F r o m ref. 4. a F r o m ref. 17. e F r o m ref. 18.
a small radius, such as those of chloride, will exist in the organic phase as hydrated entities. This assumption is in accordance with the relatively large difference between the AGp value and the calculated AG° value [4] for NO 3 in the water/ nitrobenzene system. The AGp value for SCN- (16.0 kJ mol -I) found in our experiments is much greater than that of 5.8 kJ mol-I reported by Vanysek [15].
TABLE
2
Calculated
and observed
based on the TPAsTPB Ion
AG~ a n d AGt° v a l u e s o f s e l e c t e d i o n s in t h e 2 - d i c h l o r o e t h a n e / w a t e r assumption
AG~/kJ
mol- t a
AG~/kJ
mol- ] h
AGt°/kJ tool- ] Calc. c
Cs +
24.9
--
Bu4 N+
- 16.4
-21.8
Ph 4 As +
- 32.5
- 35.2
Obs. d
23.0 -22.6 --
23.8 -
17.6
-32.7
I -
26.5
26.4
22.6
25.1
CIO 4
14.9
17.2
14.7
16.8
NO 3 SCN -
30.3 26.5
33.9 --
35.6 --
10 4 B F 4-
14.5 17.9
---
---
'~ O b t a i n e d
by cyclic voltammetry.
b j . C z a p k i e w i c z a n d B. C z a p k i e w i c z - T u t a j , ¢ F r o m ref. 4. a F r o m ref. 9.
t a k e n f r o m r e f . 4.
system
25 This difference cannot be explained by the error arising from the method employed for the estimation of the diffusion coefficients. Samec et al. [11] and Vanysek [15] estimated the diffusion coefficients in nitrobenzene from the diffusion coefficients in water and the ratio of the solvent viscosities, whereas the diffusion coefficients used in our evaluation have been calculated from limiting ion equivalent conductivities in nitrobenzene [19,20]. The differences arising from these two approaches in the AGp values is about 0.3 kJ mol-1 for the tetraalkylammonium ions and up to 2 kJ mol-~ for the other ions. Since no conductivity data were available for 1,2-dichloroethane, the diffusion coefficients have been estimated from the ratio of the solvent viscosities followed by a correction according to the differences observed in nitrobenzene and other solvents. Ion association constants given in ref. 9 have been used to correct for ion association in the water/1,2-dichloroethane system. If the ion association constant for an ion pair was not available, an average value of 10 3 was assumed. The errors introduced in doing so are worth discussing in detail. An examination of eqn. (8) shows that for constant experimental conditions the influence of ion association can be neglected as long as the t e r m acKa(DiBc)1/2 is very small compared to (D~) I/2. For the value of a c about 10 -3 chosen in our experiments up to an association constant of 100, the error by neglecting ion association will not exceed 0.5 kJ m o l - 1, but increases up to about 4 kJ m o l - ~ for K a around 10 4. It has been shown [20] that the ion association constant for tributylammonium iodide is changed from 10 4 in anhydrous nitrobenzene to 2.5 × 10 3 in water-saturated nitrobenzene (0.24% H 2 0 w / w ) . This change will give rise to an error of 3 kJ mol-1. It seems to be justified that in 1,2-dichloroethane the presence of water (0.15% HzO w / w ) will alter the ion association constants in the same way, thus, the resulting error can be estimated be about + 3 kJ tool-1 for cations and anions respectively. In spite of these uncertainties in the determination of standard Gibbs energies of ion partition even in the 1,2-dichloroethane/water system, the voltammetrically obtained AGp values agree fairly well with those obtained from other partition methods [5-7]. This method may be applied for the determination of AGp values in other solvent systems. REFERENCES 1 0 . Popovych,Crit. Rev. Anal. Chem., 1 (1970) 73. 2 A.J. Parker, Chem. Rev., 69 (1969) 1. 3 B.G. Cox, G.R. Hedwig, A.J. Parker and D.W. Watts, Aust. J. Chem., 27 (1974) 477. 4 M.H. Abraham and J. Liszi, J. Inorg. Nucl. Chem., 43 (1981) 143. 5 J. Rais, Collect. Czech. Chem. Commun., 36 (1971) 3253. 6 J. Rais, P. Selucky and M. Kyrs, J. Inorg. Nud. Chem., 38 (1976) 1376. 7 B. Czapkiewicz-Tutajand J. Czapkiewicz,Rocz. Chem., 49 (1975) 1353. 8 M. Grrin and J. Fresco, Anal. Chim. Acta, 97 (1978) 165. 9 M.H. Abraham and A.F. Danil de Namor, J. Chem. Soc., Faraday I, 72 (1976) 955. 10 M.H. Abraham and A.F. Danil de Namor, J. Chem. Sot., Faraday I, 74 (1978) 2101.
26 11 12 13 14 15 16 17 18 19 20
Z. Samec, V. Mare~.ek and J. Weber, J. Electroanal. Chem., 100 (1979) 841. Z. Samec, J. Electroanal. Chem., 99 (1979) 197. J. Koryta, Electrochim. Acta, 24 (1979) 293. R.S. Nicholson and I, Shain, Anal. Chem., 36 (1964) 706. B. Vanysek, J. Electroanal. Chem., 121 (1981) 149. B. Hundhammer, Theodros Solomon and Beniam Alemayehu, J. Electroanal. Chem., 135 (1982) 301 M.H. Abraham, J. Chem. Soc., Perkin II, (1972) 1343. Z. Koczorowski and S. Minc, Electrochim. Acta, 8 (1963) 645. B. Kratochvil and H.L. Yeager, Fortschr. Chem. Forsch., 27 (1972). M. G6rin and J. Fresco, Anal. Claim. Acta, 97 (1978) 155.
19
Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
DETERMINATION OF STANDARD GIBBS ENERGIES OF ION PARTITION BETWEEN WATER AND ORGANIC SOLVENTS BY CYCLIC VOLTAMMETRY PARTI
B. HUNDHAMMER * and THEODROS SOLOMON
Department of Chemistry, Addis Ababa University, P.O. Box 1176, Addis Ababa (Ethiopia) (Received 1lth February 1983)
ABSTRACT Standard Gibbs energies of ion transfer across the water/nitrobenzene and water/I,2 dichloroethane immiscible electrolyte solution interfaces, have been determined using cyclic voltammetry and based on the tetraphenylarsonium tetraphenylborate (TPAsTPB) assumption. The results are compared with those obtained by other methods.
INTRODUCTION
The determination of standard Gibbs energies of ion transfer from water to organic solvents is of considerable interest in the explanation of processes taking place in biological systems, liquid-liquid extraction and in liquid state ion-selective electrodes. The standard Gibbs energies for the transfer of individual ions from one solvent to another can be calculated only if an extrathermodynarnic approach is used. The tetraphenylarsonium-tetraphenylborate assumption (TPAsTPB assumption) [1-3] is one basis for these calculations. According to the experimental method employed for determination of the standard Gibbs energies, Abraham and co-worker [4] proposed to distinguish between standard Gibbs energies of partition (AGp) obtained from the partition of electrolytes between two mutually saturated immiscible solvents [5-8], and standard Gibbs energies of transfer .( AGt°) based on comparison of the solubility of the electrolytes in the pure solvents under study [9,10]. On the other hand, it was shown that standard Gibbs energies of ion partition evaluated from the half-wave potentials of cyclic voltammograms obtained from the ion transfer across the water/nitrobenzene
* Permanent address: Technische Hochschule "C. Schorlemmer", Leuna-Merseburg, Sektion Chemie, 4200 Merseburg, G.D.R.
0022-0728/83/$03.00
© 1983 Elsevier Sequoia S.A.
20
interface are in accordance with those calculated from extraction data if an ion is assigned as an internal standard [1 1]. In this paper the determination of standard Gibbs energies of ion partition by cyclic voltammetry based on the TPAsTPB assumption for the water/nitrobenzene and water/1,2 dichloroethane systems will be discussed. The results are compared with those obtained by other methods [4-9]. THEORY
The partition of an electrolyte M + X - between two mutually saturated immiscible solvents a and fl can be described by the equilibria AG;
M+(a)+X-(a)
AG°
~ M+(I3)+X-(]3) ~ M+X-(/3)
(1)
where AG° represents the standard Gibbs energy of ion association. In order to calculate AGp from the experimentally observed data the activity coefficients in the two solvents and AG° must be known. Provided equilibrium (1) is established between the two solvents the electrochemical potentials/2~ of every ion i is the same in both solvents and a Galvani potential difference A~qo is established across the interface
¢p" - q~# = A%~p= A%ep~++ ( R T / F ) ln( al~M+/a~+) = A~°x-+ ( R T / F )
ln(aPx-/a~-)
(2)
Since the standard Galvani potential difference A~90° or a single ion is related to its standard Gibbs energy of partition AG~.i(a ---, fl) by A~ep° -- AGp,i(ot ~ fl)/7.iF
(3)
the calculation or AG;, i becomes possible if the standard Galvani potential difference can be obtained experimentally. It has been shown [12,13] that the ion transfer across the interface of immiscible electrolytes follows formally the same laws as that describing the electron transfer at the metal- electrolyte solution interface. Thus, the theory of cyclic voltammetry derived for those electrodes can be adopted to describe the voltammetric behaviour of the interface between two immiscible electrolyte solutions. The transfer of ions across the interface studied by cyclic voltammetry is diffusion controlled at low sweep rates. Hence, the current response of the system to a triangular potential signal can be treated like a reversible electron-transfer reaction. It has been shown by Nicholson and Shain [14] that the current-potential relationship for such a system is given by
i = 7.3/2FAcb(Div~)l/2
X (at)
(4)
In eqn. (4) the area A of the interface is expressed in cm 2, the bulk concentration cib in mol dm -3 and the sweep rate v in V s -1. the values for 7rl/2x(at ) vs. ( E - El~2) [or in this particular case, vs. (A~q0 - A~901/2)] are tabulated by Nichol-
21 son and Shain [14]. Following this concept the evaluation of A ~ ° from voltammetric data is straightforward since the relationships
A ~ p = Ayepl/2 - 1.109RT/zF
(5)
and Ay~ ° = Ayqgl/2 - ( R T / 2 z F ) ln(D~/D B) - ( R T / z F )
l n ( y B / 7 ")
(6)
can be employed provided that the experimental AyE scale with an arbitrary reference point, dependent upon the experimental conditions, can be transformed into a potential scale with A~rp = 0 as zero point. In eqns. (5) and (6) Ay~0p is the Galvani potential difference at the current maximum and A~Igl/2 the Galvani potential difference at the half-wave potential. The transformation of the zero point is possible if TPAsTPB is used as the supporting electrolyte in the organic phase and Li2 SO4 or LiF in the aqueous phase. The voltammogram will be limited at negative potentials by the transfer of TPAs + from the organic phase to water, and at the positive side by the transfer of T P B - from the organic phase to water. Here A~E~/2 for TPAs + and T P B - c a n b e estimated by means of eqn. (4) from the initial part of the current-potential curve related to the transfer of these two ions. Since TPAsTPB is the supporting electrolyte in the organic phase, an error is introduced due to the contribution of the ion migration to the observed current. In spite of this, no error will arise in fixing the A y E ' value where Ay~ is zero by (AyE1/2TPAs÷+ AyEI/2TPB_)/2 = AyE'
(7)
since the assumption is justified that the diffusion coefficients and the absolute mobilities of the two ions are equal. In order to avoid errors in solvents with a low permittivity due to ion association, eqn. (6) should be replaced by
ayrv ° = Ayq,~/2 - ( R T / z F ) ln( D~'/E/( Di~1/2 + _.~at~K,D#'/2"~'~,¢ ,, -(RT/zF)
ln((yi~ + V ~ ) / y : )
(81
where a~ is the activity of the anion or the cation of the supporting electrolyte in the organic phase, K a the ion association constant of the transferred ion with the respective ion of the supporting electrolyte, and the subscript ic indicates the ion associate. We have employed eqn. (8) for the calculation of Aycp° from the experimentally observed half-wave potentials. EXPERIMENTAL The measurements were carried out with a four-electrode potentiostat with automatic IR compensation by means of positive feedback [11]. The IR compensation was set to the nearest point before the potentiostat starts oscillating. The potentiostat was set up from operational amplifier modules (McKee-Pedersen In-
22
struments) and a differential amplifier (AM 502, Tektronix). The voltammograms were recorded with an X - Y recorder (PH 8041, Philips). All solutions were prepared from salts of analytical grade (B.D.H. and Fluka) with twice-distilled water. The organic solvents were redistilled. The electrolyte solutions were mutually saturated before use. TPAsTPB and crystal violet tetraphenylborate (CVTPB) [15,16] were employed as supporting electrolytes in the organic phase, Li2SO 4 serving as supporting electrolyte in the aqueous phase. The experiments were carried out at 25 + 0.5°C. RESULTS A N D DISCUSSION
Figure 1 shows the cyclic voltammogram using 1 m M TPAsTPB and l0 m M Li 2SO4 as supporting electrolyte in nitrobenzene and water respectively. The limitation of the applicable potential range is given by the transfer of TPAs + from nitrobenzene to water at the negative side and by the transfer of T P B - in the same direction at positive potentials. Employing Parker's TPAsTPB assumption, two important pieces of information can be obtained from the voltammogram: (1) The actual potential scale AWE can be transformed to a potential scale with A'~0 = 0 as zero point as, shown in Fig. 1. (2) By comparison of the theoretically calculated current by eqn. (4) for, e.g. A ~ c p - AWncpl/2 = 0.150 V with the experimentally observed current the half-wave potentials for the transfer of TPAs + and T P B - can be estimated from the foot of the potential-current curve corresponding to the transfer of these ions. The error due to the contribution of ion migration to the observed current will lead to too low values for the standard Gibbs energies of partition for the two ions but no error is introduced with that uncertainty in the transformation of the
i/~ 2O
IC o
-lO
I TPAs~n)-*TPAs*{w} -o,3
-o~ .
-0,3
-o,2 ,
-0,2
--o,t
I
o
n
o,i
I
0,2
,
,
,
,
- 0,1"
0
0,1
0,2
o,3 o,4 zx(.p/v .
0,3
,
0,4 zxE/V
Fig. 1. Cyclic voltammogram using 1 m M TPAsTPB and 10 m M Li2SO 4 as supporting electrolytes in nitrobenzene and water respectively. Sweep rate 25 mV s - i.
23 I/pA 30' 20' 10' 0 -10 -20 -30 I
-0~
-03
-0,2 -0~
i
0
0,~
0~
0,3
0,~
zx~o/V Fig. 2. Cyclic voltammogram obtained when 0.075 m M C104- is added to the aqueous phase. All other conditions as in Fig. 1.
potential scale, as discussed above. If an ion such as perchlorate is added to the aqueous phase the voltammogram shown in Fig. 2 will be observed. The cathodic current peak is caused by the transfer of C104 from water to nitrobenzene the anodic one is due to the transfer of C104 from nitrobenzene to water. The peak potentials as well as the separation of the peak potentials of the anodic and cathodic current peaks by 59 mV are independent of the sweep rate up to 0.1 V s-1 for all ions investigated. Hence, AWcpl/2, Awq~°, and lastly AG~(w ~ n) for perchlorate can be obtained. This ion can then serve as an internal standard for fixing the zero point if TPAsTPB is replaced by CVTPB or any other supporting electrolyte in the organic phase. The same experiments have been carried out with 1,2-dichloroethane as the organic phase. Tables 1 and 2 compare standard Gibbs energies of ion partition calculated from half-wave potentials with those obtained by other methods. Besides the AGp values, AGt° values are summarized in the tables. The AG~ values determined by cyclic voltammetry are the mean of five independent measurements. Comparison of the values obtained for TPAs + and TPB- by our method with those from partition experiments shows the influence of ion migration which was not taken into account in estimating the AG~ values for the two ions. For the other ions, the AG~ values are determined by the voltammetric method in accordance with the values obtained by other methods. Of particular interest is the comparison of the AGp values with the standard Gibbs energies of transfer. The difference between the two values could be caused by the mixed solvation of the ions, especially in the organic phase of the system [4]. It has been reported [4,8] that, at the least, ions with
24
TABLE
1
C a l c u l a t e d a n d o b s e r v e d AG~ a n d AGt° v a l u e s o f s e l e c t e d i o n s i n t h e n i t r o b e n z e n e / w a t e r the TPAsTPB
system based on
assumption
Ion
AGp/kJ
mol- J "
AGp/kJ
mol- t b
AGt/kJ
mol- t
Calc. c Cs +
15.2
17.2
Bu4N ÷
-23.5
-23.9
Ph4As + l-
- 31.4 18.9
- 36.0 18.9
C I O a-
7.4
Obs. d
17.6
--
-22.6
--
-18.0
-15.9
8.0
10.5
--
23.9 e
30.6
--
NO 3
24.4
SCN -
16.0
--
--
--
10~
6.9
--
--
--
BE 4
11.0
--
--
--
Obtained
by cyclic voltammetry.
b F r o m refs. 5 a n d 6. c F r o m ref. 4. a F r o m ref. 17. e F r o m ref. 18.
a small radius, such as those of chloride, will exist in the organic phase as hydrated entities. This assumption is in accordance with the relatively large difference between the AGp value and the calculated AG° value [4] for NO 3 in the water/ nitrobenzene system. The AGp value for SCN- (16.0 kJ mol -I) found in our experiments is much greater than that of 5.8 kJ mol-I reported by Vanysek [15].
TABLE
2
Calculated
and observed
based on the TPAsTPB Ion
AG~ a n d AGt° v a l u e s o f s e l e c t e d i o n s in t h e 2 - d i c h l o r o e t h a n e / w a t e r assumption
AG~/kJ
mol- t a
AG~/kJ
mol- ] h
AGt°/kJ tool- ] Calc. c
Cs +
24.9
--
Bu4 N+
- 16.4
-21.8
Ph 4 As +
- 32.5
- 35.2
Obs. d
23.0 -22.6 --
23.8 -
17.6
-32.7
I -
26.5
26.4
22.6
25.1
CIO 4
14.9
17.2
14.7
16.8
NO 3 SCN -
30.3 26.5
33.9 --
35.6 --
10 4 B F 4-
14.5 17.9
---
---
'~ O b t a i n e d
by cyclic voltammetry.
b j . C z a p k i e w i c z a n d B. C z a p k i e w i c z - T u t a j , ¢ F r o m ref. 4. a F r o m ref. 9.
t a k e n f r o m r e f . 4.
system
25 This difference cannot be explained by the error arising from the method employed for the estimation of the diffusion coefficients. Samec et al. [11] and Vanysek [15] estimated the diffusion coefficients in nitrobenzene from the diffusion coefficients in water and the ratio of the solvent viscosities, whereas the diffusion coefficients used in our evaluation have been calculated from limiting ion equivalent conductivities in nitrobenzene [19,20]. The differences arising from these two approaches in the AGp values is about 0.3 kJ mol-1 for the tetraalkylammonium ions and up to 2 kJ mol-~ for the other ions. Since no conductivity data were available for 1,2-dichloroethane, the diffusion coefficients have been estimated from the ratio of the solvent viscosities followed by a correction according to the differences observed in nitrobenzene and other solvents. Ion association constants given in ref. 9 have been used to correct for ion association in the water/1,2-dichloroethane system. If the ion association constant for an ion pair was not available, an average value of 10 3 was assumed. The errors introduced in doing so are worth discussing in detail. An examination of eqn. (8) shows that for constant experimental conditions the influence of ion association can be neglected as long as the t e r m acKa(DiBc)1/2 is very small compared to (D~) I/2. For the value of a c about 10 -3 chosen in our experiments up to an association constant of 100, the error by neglecting ion association will not exceed 0.5 kJ m o l - 1, but increases up to about 4 kJ m o l - ~ for K a around 10 4. It has been shown [20] that the ion association constant for tributylammonium iodide is changed from 10 4 in anhydrous nitrobenzene to 2.5 × 10 3 in water-saturated nitrobenzene (0.24% H 2 0 w / w ) . This change will give rise to an error of 3 kJ mol-1. It seems to be justified that in 1,2-dichloroethane the presence of water (0.15% HzO w / w ) will alter the ion association constants in the same way, thus, the resulting error can be estimated be about + 3 kJ tool-1 for cations and anions respectively. In spite of these uncertainties in the determination of standard Gibbs energies of ion partition even in the 1,2-dichloroethane/water system, the voltammetrically obtained AGp values agree fairly well with those obtained from other partition methods [5-7]. This method may be applied for the determination of AGp values in other solvent systems. REFERENCES 1 0 . Popovych,Crit. Rev. Anal. Chem., 1 (1970) 73. 2 A.J. Parker, Chem. Rev., 69 (1969) 1. 3 B.G. Cox, G.R. Hedwig, A.J. Parker and D.W. Watts, Aust. J. Chem., 27 (1974) 477. 4 M.H. Abraham and J. Liszi, J. Inorg. Nucl. Chem., 43 (1981) 143. 5 J. Rais, Collect. Czech. Chem. Commun., 36 (1971) 3253. 6 J. Rais, P. Selucky and M. Kyrs, J. Inorg. Nud. Chem., 38 (1976) 1376. 7 B. Czapkiewicz-Tutajand J. Czapkiewicz,Rocz. Chem., 49 (1975) 1353. 8 M. Grrin and J. Fresco, Anal. Chim. Acta, 97 (1978) 165. 9 M.H. Abraham and A.F. Danil de Namor, J. Chem. Soc., Faraday I, 72 (1976) 955. 10 M.H. Abraham and A.F. Danil de Namor, J. Chem. Sot., Faraday I, 74 (1978) 2101.
26 11 12 13 14 15 16 17 18 19 20
Z. Samec, V. Mare~.ek and J. Weber, J. Electroanal. Chem., 100 (1979) 841. Z. Samec, J. Electroanal. Chem., 99 (1979) 197. J. Koryta, Electrochim. Acta, 24 (1979) 293. R.S. Nicholson and I, Shain, Anal. Chem., 36 (1964) 706. B. Vanysek, J. Electroanal. Chem., 121 (1981) 149. B. Hundhammer, Theodros Solomon and Beniam Alemayehu, J. Electroanal. Chem., 135 (1982) 301 M.H. Abraham, J. Chem. Soc., Perkin II, (1972) 1343. Z. Koczorowski and S. Minc, Electrochim. Acta, 8 (1963) 645. B. Kratochvil and H.L. Yeager, Fortschr. Chem. Forsch., 27 (1972). M. G6rin and J. Fresco, Anal. Claim. Acta, 97 (1978) 155.