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The comparison of half-wave potentials in different solvents
530
JOURNAL
THE COMPARISON SOLVENTS
H_
SCHXEIDER
XXD
ICliax-Plalrck-lnstillrffiir
(Received
July
Dedicated
to Professor
OF
3%
HALF-WAVE
OF
ELECTROANALYTICAL
POTENTIALS
IN
CHEMISTRY
DIFFERENT
STFt.EHLOW
Phystkalische
Chemie,
Gdttingex
/Germany)
15th x966) Dr. >I. VOX
STACKELBERG
on
his 70th birtdsy
The problem of comparing electric potentials in different media cannot be solved without non-thermodynamic assumptions. The difference between the halfwave potentials for a given ion in two solvents is determined by the free enthalpy of transfer for that ion from one solvent into the other- This free enthalpy cannot be measured, since it is impossible to transfer a single ion between two phasesl- With the however, it is possible to estimate the aid of non-thermodynamic assumptions, difference between electrode potentials in different solvents*~a. Although such estimates contain unavoidable errors due to the model involved, they prove to be useful in correlating known experimental data and in predicting, at least qualitatively, the results of experiments as yet unperformedVoltage series in two solvents can be referred to one single reference potential if the free enthalpy of transfer between the two solvents is known for only one ion. A useful non-thermodynamic assumption for this purpose has been proposed by PLESKOV~, According to that author the free enthalpy of solvation of the rubidium ion is taken to be the same in all solvents, i.e., the free enthalpy of transfer is assumed to be zero for all solvent pairs. In a second approximation”, this small quantity has been estimated for a series of solvents_ The Pleskov method seems to be a good approximation_ However, the dete rmination of standard electrode potentials of rubidium in non-aqueous solvents is experimentally difficult. Furthermore, in acidic solvents the technique is unreliable due to corrosion of the amalgam. Another way of solving the problem is by the measurement of Hamrnett acid&y functions, HO. in non-aqueous solutions of dilute strong acids. In this case it is assumed that the free enthalpy of transfer for the indicator base is equal to that of the indicator acid. Since the proton attached to the indicator molecule in the acidic form is on the periphery of the ion, the specific effects of solvation are considerably different in different solvents. Therefore, this approach is a rather poor approximation, except possibly in solvents of high dielectric constant_ The considerable difference in solutions of strong acids in alcohols between Ro- and R-.-H ammett-functions illustrates the difficulties inherent in this method. It has been argued3 that in most to -log LzH+ than W-, the -es NO-Hanim ett-functions are better approximations use of which should be discouraged especially in organic solventsStill another technique for the comparison of voltage series has been proposed, and as which is experimentally as simple -asthe measurement of Hamm ett-functions, reliable as the Pleskov rubidium methodeva. It is assumed, as a first approximation,
HALF-WAVE
that
the
POTESTIALS
free
enthalpy
IS
DIFFERENT
of
solvation
SOLVENTS
of
53=
a suitable
redox
sJ-stem
with
charge
type
o/+ I is independent of the charge. If the charged redox ion is large and the charge distribution is centrosymmetrical, this assumption should be approximately valid. As a second approximation, the small hfference of the free energy of transfer can be estimated. The ferrocene/ferricmium and the analogous cobaltocene/cobalticinium redox couples have been found to be suitable for this purpose. The difference between the standard electrode potentials of these redox systems and the difference between either of them and the standard potential of rubidium have been found to be independent of the solvent n-r all cases for which sufficient experimental data exist. This, of course, is a necessary though not sufficient condition for the reasonableness of the proposed methods for the comparison of voltage series in different solvents. Several applications of the redox method have been published”J*5. The measurement of the cobaltocene/cobalticinium redox potential is especially convenient, since it can be performed by the polarographic technique. Cobalticinium perchlorate is reduced
reversibly at the dropping mercury electrode. In this paper are reported some measurements of half-wave potentials of thallium and cadmium ions referred to the half-wave potential of cobalticinium in a series of different solvents and solvent mixtures_ With these data at hand it is easy to correlate half-wave and standard electrode potentials of other ions in these nonaqueous solvents to the corresponding values in aqueous solution. EXPERIMENT
Cobalticinium
perchlorate
has
been
prepared
according
to
WILKINSON
g.
Solvents with relatively high water content and some solvents containing traces of polarographically active impurities were purified by distillation The supporting electrolytes were of anal_y-tical grade and dried before use. The water content of the solutions containing the supporting electrolyte was determined by Karl Fischer titration (except in pyridine, dimethylformamide and acetone) _ Mixtures between water and non-aqueous solvents were prepared by weight. All measurements were performed at 25.0~. The concentrations of the depolarizers (Tlf and Co(C5H5)2+ or Cd5f and Co(CsH5)2+) were 10-5 M. The concentrations of Tlf were smaller in some cases due to limited solubility_ A polaropam was first recorded; if the two waves proved to be well developed, the half-wave potential was determined by a manually operated polarim etric apparatus for the sake of higher accuracy. The drop time, 8, was 4-5 set and the rate of flow of mercury equalled 1.5 mg set-1. A correction to vanishing m-a 0s was not carried out’, although corrections were made for the iR-drop, which was considerable in some solvents. In most measurements the mercury pool was the anode. In some instances its potential was not constant and an aqueous reference electrode, separated by a diaphragm from the non-aqueous solvent, served as the anode_ A siliconized dropping mercury capillary was used. Every measurement was repeated at least once with fresh solutions_ All polarographic waves proved to be reversible within the limit of experimental error. The experimental results obtained are presented in Table I _ Tl+ ions in aqueous solutions do not exhibit a pronounced tendency to form complexes and have been used as pilot io~zs with a half-wave potential which is rather independent of nature and concentration of the supporting electrolyte. When J_ EZectroanaZ.
Chem.,
I?, (1966)
530-534
vr-Propanol
( Ethanol
~etIlRno1
Me4NCl
Tl+ c&J+ Cdz+
10-l Me4NCl
Cda+
5 1 10-1 LiCl 10-l LiCl 5 1 10-3LiCl 10-l LiCI
Cdz+ Cd?+ Cdflk Cdt+ 20.1 20,I
0.5 I.3 ’ 10-e I.2 ’ 10’~
10-LLiCl
5 * 104 LlCl
28.07
Cde+ Cd2+ Cdl+
10-l LiCl 5 1 10-3 LiCl 10-l LiCl
28.07
24.30
24#30
2~.97
Cda+ Cde+
0.5
3 ’ 10-a
0.25 3 * 10’3
085 0.5 0.25 37n15 28.97
10-l LiCl 5 ’ 10-a LiCl
Cda+
’ 5=-n 37u15
5 m10-a LiCl
Cdl+
5Iml7
o-75 0*75 Cda+
5 1 10-2 LiCl 10-I LiCl
Cda+ Cda+
78,48 78.48
I,0
I.0
32.63
CdB+
32.63
0.0
10-l Mc4NCI 5 1 10-a McdNCl
Cdl+
O.OI 0,0
5 1 x0-3 Me$Kl
Tl+ Tl+
IO-~
10-l hIe4WCl 5 1 IO -1 hfedNC1 10-l Mc~INCI 5 * 10-2~e4NCl 10-1 MeANCl 5 * 10-2 MejNCl 5 a 10-1 hfc4NCi
Tl+ Tlf Tl+
5 9 10-2 h~e~NC1
Tl+
Cd2+
48,G 38,8 38.8 38.8
4&G
78 5 7805 61.3 G1.3
O.OI
0.25
0~25 0.25
O,5
0.5
0.15
0.75
‘1.0
1.0
0.03il
0.026
0.05s
0.054
1 347 rt: 3 278 rt 3 zG6 rt: 2
363 z!z 1
415 i
430 Ek I
go2 & 2
512 & I
574 rl- I
578 rt I
325 3 3
336 ct: 3 343 Et 2
353 rt 2
403 I: “,
423 j: 2
659 zk I 602 rl: 6
7’0 rl- 3 70s :I: 1 718 % 1 716rl: I 666 5 z
HALF-\V_%VE
POTEXTIALS
d 0
5d
ci
t
IN
DIFFERENT
SOLVENTS
0” 0
d
6
d
5 d
g
d 0
d
‘;
0
0
I.4
c(
.
e-3.
.
u?YS%
o- o- o- o-
J.
EZectroand.
Chem.,
12 (1966)
530-534
H.
534
SCHXEIDER,
H. STREHLOW
the solvent was changed_ however, large changes of the half-wave potential of Tl+ were observed in some cases_ Therefore, in spite of its size, Ti+ would not be a good reference ion, since a reZwcnce ion, e.g., Rb+, should have a small free enthalpy of transfer between different solvents. A.CKNOM7LEDGEMEMT
Theauthorsareiudebtedto
Miss H. WIRTH
forexperimentdt
assistance.
FtEFEREKCES r E. A. GUG-GEIWIEIU, /_ Phys. Chew. 33 (rgzg) 842_ z H.-M. KOEPP, H. WEKDT AND H_ STREHLOW, 2. Elektrochenr.. 64 (1960) _+83in T71e Chmtsi?i-y E&&r&e Potentials in Km++A peous SoZveds, 3 Hi. S~ZEHLOW, SoZvm:s, edited by J_ J_ L_+_GOWSRI. Academic Press, hTe_rvYork, rg66. 4 W. A FLESKOV, Advances ix Chemissfry (IZzrssian), 16 (1947) 254. see ref. 3. 5 H.STREHLOW~DH. WENDT.~. Physik. Chem.X_F_. 30 (1961) I~I_ 6 G. WLLKINSON, J. Am. Cliem. Sot., 74 (1g.p) 614% 7 H. STREHLOWANDM.VONSTACKELBERG.Z. EZektrochen..~4(Ig5o) 51 J_ EEectroanal.
Chena..
12 (1966)
530-534
of .Xon-A
qzreorrs
JOURNAL
THE COMPARISON SOLVENTS
H_
SCHXEIDER
XXD
ICliax-Plalrck-lnstillrffiir
(Received
July
Dedicated
to Professor
OF
3%
HALF-WAVE
OF
ELECTROANALYTICAL
POTENTIALS
IN
CHEMISTRY
DIFFERENT
STFt.EHLOW
Phystkalische
Chemie,
Gdttingex
/Germany)
15th x966) Dr. >I. VOX
STACKELBERG
on
his 70th birtdsy
The problem of comparing electric potentials in different media cannot be solved without non-thermodynamic assumptions. The difference between the halfwave potentials for a given ion in two solvents is determined by the free enthalpy of transfer for that ion from one solvent into the other- This free enthalpy cannot be measured, since it is impossible to transfer a single ion between two phasesl- With the however, it is possible to estimate the aid of non-thermodynamic assumptions, difference between electrode potentials in different solvents*~a. Although such estimates contain unavoidable errors due to the model involved, they prove to be useful in correlating known experimental data and in predicting, at least qualitatively, the results of experiments as yet unperformedVoltage series in two solvents can be referred to one single reference potential if the free enthalpy of transfer between the two solvents is known for only one ion. A useful non-thermodynamic assumption for this purpose has been proposed by PLESKOV~, According to that author the free enthalpy of solvation of the rubidium ion is taken to be the same in all solvents, i.e., the free enthalpy of transfer is assumed to be zero for all solvent pairs. In a second approximation”, this small quantity has been estimated for a series of solvents_ The Pleskov method seems to be a good approximation_ However, the dete rmination of standard electrode potentials of rubidium in non-aqueous solvents is experimentally difficult. Furthermore, in acidic solvents the technique is unreliable due to corrosion of the amalgam. Another way of solving the problem is by the measurement of Hamrnett acid&y functions, HO. in non-aqueous solutions of dilute strong acids. In this case it is assumed that the free enthalpy of transfer for the indicator base is equal to that of the indicator acid. Since the proton attached to the indicator molecule in the acidic form is on the periphery of the ion, the specific effects of solvation are considerably different in different solvents. Therefore, this approach is a rather poor approximation, except possibly in solvents of high dielectric constant_ The considerable difference in solutions of strong acids in alcohols between Ro- and R-.-H ammett-functions illustrates the difficulties inherent in this method. It has been argued3 that in most to -log LzH+ than W-, the -es NO-Hanim ett-functions are better approximations use of which should be discouraged especially in organic solventsStill another technique for the comparison of voltage series has been proposed, and as which is experimentally as simple -asthe measurement of Hamm ett-functions, reliable as the Pleskov rubidium methodeva. It is assumed, as a first approximation,
HALF-WAVE
that
the
POTESTIALS
free
enthalpy
IS
DIFFERENT
of
solvation
SOLVENTS
of
53=
a suitable
redox
sJ-stem
with
charge
type
o/+ I is independent of the charge. If the charged redox ion is large and the charge distribution is centrosymmetrical, this assumption should be approximately valid. As a second approximation, the small hfference of the free energy of transfer can be estimated. The ferrocene/ferricmium and the analogous cobaltocene/cobalticinium redox couples have been found to be suitable for this purpose. The difference between the standard electrode potentials of these redox systems and the difference between either of them and the standard potential of rubidium have been found to be independent of the solvent n-r all cases for which sufficient experimental data exist. This, of course, is a necessary though not sufficient condition for the reasonableness of the proposed methods for the comparison of voltage series in different solvents. Several applications of the redox method have been published”J*5. The measurement of the cobaltocene/cobalticinium redox potential is especially convenient, since it can be performed by the polarographic technique. Cobalticinium perchlorate is reduced
reversibly at the dropping mercury electrode. In this paper are reported some measurements of half-wave potentials of thallium and cadmium ions referred to the half-wave potential of cobalticinium in a series of different solvents and solvent mixtures_ With these data at hand it is easy to correlate half-wave and standard electrode potentials of other ions in these nonaqueous solvents to the corresponding values in aqueous solution. EXPERIMENT
Cobalticinium
perchlorate
has
been
prepared
according
to
WILKINSON
g.
Solvents with relatively high water content and some solvents containing traces of polarographically active impurities were purified by distillation The supporting electrolytes were of anal_y-tical grade and dried before use. The water content of the solutions containing the supporting electrolyte was determined by Karl Fischer titration (except in pyridine, dimethylformamide and acetone) _ Mixtures between water and non-aqueous solvents were prepared by weight. All measurements were performed at 25.0~. The concentrations of the depolarizers (Tlf and Co(C5H5)2+ or Cd5f and Co(CsH5)2+) were 10-5 M. The concentrations of Tlf were smaller in some cases due to limited solubility_ A polaropam was first recorded; if the two waves proved to be well developed, the half-wave potential was determined by a manually operated polarim etric apparatus for the sake of higher accuracy. The drop time, 8, was 4-5 set and the rate of flow of mercury equalled 1.5 mg set-1. A correction to vanishing m-a 0s was not carried out’, although corrections were made for the iR-drop, which was considerable in some solvents. In most measurements the mercury pool was the anode. In some instances its potential was not constant and an aqueous reference electrode, separated by a diaphragm from the non-aqueous solvent, served as the anode_ A siliconized dropping mercury capillary was used. Every measurement was repeated at least once with fresh solutions_ All polarographic waves proved to be reversible within the limit of experimental error. The experimental results obtained are presented in Table I _ Tl+ ions in aqueous solutions do not exhibit a pronounced tendency to form complexes and have been used as pilot io~zs with a half-wave potential which is rather independent of nature and concentration of the supporting electrolyte. When J_ EZectroanaZ.
Chem.,
I?, (1966)
530-534
vr-Propanol
( Ethanol
~etIlRno1
Me4NCl
Tl+ c&J+ Cdz+
10-l Me4NCl
Cda+
5 1 10-1 LiCl 10-l LiCl 5 1 10-3LiCl 10-l LiCI
Cdz+ Cd?+ Cdflk Cdt+ 20.1 20,I
0.5 I.3 ’ 10-e I.2 ’ 10’~
10-LLiCl
5 * 104 LlCl
28.07
Cde+ Cd2+ Cdl+
10-l LiCl 5 1 10-3 LiCl 10-l LiCl
28.07
24.30
24#30
2~.97
Cda+ Cde+
0.5
3 ’ 10-a
0.25 3 * 10’3
085 0.5 0.25 37n15 28.97
10-l LiCl 5 ’ 10-a LiCl
Cda+
’ 5=-n 37u15
5 m10-a LiCl
Cdl+
5Iml7
o-75 0*75 Cda+
5 1 10-2 LiCl 10-I LiCl
Cda+ Cda+
78,48 78.48
I,0
I.0
32.63
CdB+
32.63
0.0
10-l Mc4NCI 5 1 10-a McdNCl
Cdl+
O.OI 0,0
5 1 x0-3 Me$Kl
Tl+ Tl+
IO-~
10-l hIe4WCl 5 1 IO -1 hfedNC1 10-l Mc~INCI 5 * 10-2~e4NCl 10-1 MeANCl 5 * 10-2 MejNCl 5 a 10-1 hfc4NCi
Tl+ Tlf Tl+
5 9 10-2 h~e~NC1
Tl+
Cd2+
48,G 38,8 38.8 38.8
4&G
78 5 7805 61.3 G1.3
O.OI
0.25
0~25 0.25
O,5
0.5
0.15
0.75
‘1.0
1.0
0.03il
0.026
0.05s
0.054
1 347 rt: 3 278 rt 3 zG6 rt: 2
363 z!z 1
415 i
430 Ek I
go2 & 2
512 & I
574 rl- I
578 rt I
325 3 3
336 ct: 3 343 Et 2
353 rt 2
403 I: “,
423 j: 2
659 zk I 602 rl: 6
7’0 rl- 3 70s :I: 1 718 % 1 716rl: I 666 5 z
HALF-\V_%VE
POTEXTIALS
d 0
5d
ci
t
IN
DIFFERENT
SOLVENTS
0” 0
d
6
d
5 d
g
d 0
d
‘;
0
0
I.4
c(
.
e-3.
.
u?YS%
o- o- o- o-
J.
EZectroand.
Chem.,
12 (1966)
530-534
H.
534
SCHXEIDER,
H. STREHLOW
the solvent was changed_ however, large changes of the half-wave potential of Tl+ were observed in some cases_ Therefore, in spite of its size, Ti+ would not be a good reference ion, since a reZwcnce ion, e.g., Rb+, should have a small free enthalpy of transfer between different solvents. A.CKNOM7LEDGEMEMT
Theauthorsareiudebtedto
Miss H. WIRTH
forexperimentdt
assistance.
FtEFEREKCES r E. A. GUG-GEIWIEIU, /_ Phys. Chew. 33 (rgzg) 842_ z H.-M. KOEPP, H. WEKDT AND H_ STREHLOW, 2. Elektrochenr.. 64 (1960) _+83in T71e Chmtsi?i-y E&&r&e Potentials in Km++A peous SoZveds, 3 Hi. S~ZEHLOW, SoZvm:s, edited by J_ J_ L_+_GOWSRI. Academic Press, hTe_rvYork, rg66. 4 W. A FLESKOV, Advances ix Chemissfry (IZzrssian), 16 (1947) 254. see ref. 3. 5 H.STREHLOW~DH. WENDT.~. Physik. Chem.X_F_. 30 (1961) I~I_ 6 G. WLLKINSON, J. Am. Cliem. Sot., 74 (1g.p) 614% 7 H. STREHLOWANDM.VONSTACKELBERG.Z. EZektrochen..~4(Ig5o) 51 J_ EEectroanal.
Chena..
12 (1966)
530-534
of .Xon-A
qzreorrs