- Email: [email protected]
Electromotive force of concentration cells containing ionic melts
Ekrwoehimico Acra, 1978, Vol. 23. pp. 391.
PergamonFT~SS. Primed
SHORT
in Great Britain
COMMUNICATION
ELECTROMOTIVE FORCE CELLS CONTAINING
OF CONCENTRATION IONIC MELTS
R. HAASE Institut fiir Physikalische
Chemie der Rheinisch-WestISischen Aachen, Germany
Technischen
Hochschule
Aachen,
(Received 16 May 1977)
In the literature, the treatment of concentration cells (with transference) containing ionic melts often lacks rigour and clarity. We will, therefore, take up the subject again. We consider a concentration cell composed of two compartments containing two melts connected to each other by a direct liquid junction[l]. (The use of a diaphragm is unncccssary.) The two melts correspond to two compositions of an ionic melt mixture of the type KN03 + AgNOS or PbCI, + PbBr,. We thus have a two-component ionic melt with three ion constituents. We suppose that the two electrodes are chemically identical and reversible to one ion constituent labeled r. We denote that ion constituent which only occurs in component 1 or 2 by a or 6, respectively, while the ion constituent common to both components is denoted by y. We then have to distinguish between two cases:
of constituent a or B is the relevant quantity. It is a property of the melt alone. Unsatisfactory treatment of the problem is often due to the use of inappropriate or ill-defined transport numbers. Thus, in particular, transport numbers in an external frame of reference are inappropriate since they are not properties of the melt alone. Indeed, the ‘effective transport numbers’, referring to the migration of ions in the melt relative to the fixed parts of the apparatus, depend on the boundary conditions at the electrodes[2], while the “external transport numbers”, referring to the migration of ions relative to a diaphragm, give an alternative description of electroosmosis[3,4]. Combining equations (I), (2), and (3) with relations derived earlier[5,6], we obtain the following formulas for the electromotive force 9 (in differential form) of a concentration cell:
r = p (electrodes reversible to a non-commoh ion constituent), r = y (electrodes reversible to a common ion constituent).
Fd@ = Cr.&
The case r = OLneed not be considered since it is only a question of choice of the components whether we have r = LYor r = 6. An example is a concentration cell containing KNO, f AgNO, with silver electrodes (r = p) or with nitrate electrodes [r = 7). The electromotive force of such a cell has a definite value. Before giving the final formulas, we will make a few remarks about the relevant quantities. The composition of the melt may be described either by the mole fraction _yr or x1 (= 1 - x1) of component 1 or 2 or by the equivalent fraction X, or X, (= 1 - X,) of component 1 or 2. We have the relations x,
= 1 - x, x,/x,
= 2, Y, x,/(2, = r. v=X&B
v, Xr + .z#Vpxs), V#x*1.
= [(to - Xz)/(z. v. X,)1 dpl 0. = Y) (5) where F is the Faraday constant. Equations (4) and (5), based on non-equilibrium thermodynamics, are both rigorous and concise. They tell us how transport numbers or activity coefficients can be computed from measurements on concentration cells. It is interesting to note that in the case r = y the electromotive force vanishes for t, = X1 (fr = X,). Relations given earlier in the literature, as far as they are correctErg 7, 81, are special cases of (4) and (5).
(1) (2)
Here ri or vi is the charge number or dissociation number of ion constituent i (i = a, fi), respectively. The chemical potentials #r and ur (and, hence, the activity coefficients) of the two components are interrelated by the Gibbs-Duhem equation ~1 dfi, + xr dps = 0
qxdl c&z= -CL&, v.X,1 +I (r = 8). (4)
Fd@ = [(a - xtMlrsraX,l]dCrs
REFERENCES 1. J. Richter and E. Amkreutz,
(3)
since temperature and pressure are uniform. In the type of melt discussed here, there is only one independent transport number [2]. It is expedient to use the “internal” or “Hittorf” frame of reference. Here the ion constituent y is the reference substance and thus takes the place of the water in an aqueous electrolyte solution. Hence, the internal transport number ts or ra (= 1 - to)
391
2. Nnntr$ 2711, 280 (1972). R. Haasc, Z. Natur- 28a, 1897 (1973); 29a. 534 (1974). W. Fischer and A. Klemm, 2. N&ur(. 161, 563 (1961). R. Haase, Z. phys. Chem. NF 103, 235 (1976). R. Haase and J. Richter, 2. NaturJ 24x1, 418 (1969). R. Haase, U. Priiser and J. Richter, Ber. Bunsenges. phys. Chem. 81, 577 !1977). 7. A. Klemm, Transport Properties of Molten Salts, in M&en Salt Chetnisny (Edited by M. Blander). Interscience, New York (1964). 8. M. Okada and K. Kawamura, EIecnocAim Acts 15, I (1970); 19, 777 (1974). 2. 3. 4. 5. 6.
PergamonFT~SS. Primed
SHORT
in Great Britain
COMMUNICATION
ELECTROMOTIVE FORCE CELLS CONTAINING
OF CONCENTRATION IONIC MELTS
R. HAASE Institut fiir Physikalische
Chemie der Rheinisch-WestISischen Aachen, Germany
Technischen
Hochschule
Aachen,
(Received 16 May 1977)
In the literature, the treatment of concentration cells (with transference) containing ionic melts often lacks rigour and clarity. We will, therefore, take up the subject again. We consider a concentration cell composed of two compartments containing two melts connected to each other by a direct liquid junction[l]. (The use of a diaphragm is unncccssary.) The two melts correspond to two compositions of an ionic melt mixture of the type KN03 + AgNOS or PbCI, + PbBr,. We thus have a two-component ionic melt with three ion constituents. We suppose that the two electrodes are chemically identical and reversible to one ion constituent labeled r. We denote that ion constituent which only occurs in component 1 or 2 by a or 6, respectively, while the ion constituent common to both components is denoted by y. We then have to distinguish between two cases:
of constituent a or B is the relevant quantity. It is a property of the melt alone. Unsatisfactory treatment of the problem is often due to the use of inappropriate or ill-defined transport numbers. Thus, in particular, transport numbers in an external frame of reference are inappropriate since they are not properties of the melt alone. Indeed, the ‘effective transport numbers’, referring to the migration of ions in the melt relative to the fixed parts of the apparatus, depend on the boundary conditions at the electrodes[2], while the “external transport numbers”, referring to the migration of ions relative to a diaphragm, give an alternative description of electroosmosis[3,4]. Combining equations (I), (2), and (3) with relations derived earlier[5,6], we obtain the following formulas for the electromotive force 9 (in differential form) of a concentration cell:
r = p (electrodes reversible to a non-commoh ion constituent), r = y (electrodes reversible to a common ion constituent).
Fd@ = Cr.&
The case r = OLneed not be considered since it is only a question of choice of the components whether we have r = LYor r = 6. An example is a concentration cell containing KNO, f AgNO, with silver electrodes (r = p) or with nitrate electrodes [r = 7). The electromotive force of such a cell has a definite value. Before giving the final formulas, we will make a few remarks about the relevant quantities. The composition of the melt may be described either by the mole fraction _yr or x1 (= 1 - x1) of component 1 or 2 or by the equivalent fraction X, or X, (= 1 - X,) of component 1 or 2. We have the relations x,
= 1 - x, x,/x,
= 2, Y, x,/(2, = r. v=X&B
v, Xr + .z#Vpxs), V#x*1.
= [(to - Xz)/(z. v. X,)1 dpl 0. = Y) (5) where F is the Faraday constant. Equations (4) and (5), based on non-equilibrium thermodynamics, are both rigorous and concise. They tell us how transport numbers or activity coefficients can be computed from measurements on concentration cells. It is interesting to note that in the case r = y the electromotive force vanishes for t, = X1 (fr = X,). Relations given earlier in the literature, as far as they are correctErg 7, 81, are special cases of (4) and (5).
(1) (2)
Here ri or vi is the charge number or dissociation number of ion constituent i (i = a, fi), respectively. The chemical potentials #r and ur (and, hence, the activity coefficients) of the two components are interrelated by the Gibbs-Duhem equation ~1 dfi, + xr dps = 0
qxdl c&z= -CL&, v.X,1 +I (r = 8). (4)
Fd@ = [(a - xtMlrsraX,l]dCrs
REFERENCES 1. J. Richter and E. Amkreutz,
(3)
since temperature and pressure are uniform. In the type of melt discussed here, there is only one independent transport number [2]. It is expedient to use the “internal” or “Hittorf” frame of reference. Here the ion constituent y is the reference substance and thus takes the place of the water in an aqueous electrolyte solution. Hence, the internal transport number ts or ra (= 1 - to)
391
2. Nnntr$ 2711, 280 (1972). R. Haasc, Z. Natur- 28a, 1897 (1973); 29a. 534 (1974). W. Fischer and A. Klemm, 2. N&ur(. 161, 563 (1961). R. Haase, Z. phys. Chem. NF 103, 235 (1976). R. Haase and J. Richter, 2. NaturJ 24x1, 418 (1969). R. Haase, U. Priiser and J. Richter, Ber. Bunsenges. phys. Chem. 81, 577 !1977). 7. A. Klemm, Transport Properties of Molten Salts, in M&en Salt Chetnisny (Edited by M. Blander). Interscience, New York (1964). 8. M. Okada and K. Kawamura, EIecnocAim Acts 15, I (1970); 19, 777 (1974). 2. 3. 4. 5. 6.