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8 The Thermodynamics of Electrochemical Systems
HCl
Solution
m ϭ m 1
HCl
Solution
m ϭ m 2
Ag
AgCl
Ag
Pt
H 2 (P 1 )
Pt
H 2 (P 2 )
Figure 8.9 A Double Cell Equivalent to a Concentration Cell.
with hydrogen electrodes. Assuming that the pressure of hydrogen is equal to P ◦ in
both cells, the Nernst equation for the left-hand cell is
E(left cell) 0.2223V −
2RT
F
ln(γ ±,1 m 1 /m
◦ )
and that of the right-hand cell is
E(right cell) −0.2223 V +
2RT
F
ln(γ ±,2 m 2 /m
◦ )
so that the potential difference of the double cell is equal to that of Eq. (8.3-7) without
the liquid junction potential. Another possibility is to build just one cell, like half of
the double cell, and then to measure its potential difference once when filled with a
solution of molality m 1 , and once when filled with a solution of molality m 2 .
Exercise 8.8
Find the potential difference of the concentration cell of Figure 8.8 if in solution 1 the molality is
0.500 mol kg −1 with γ ±,1 equal to 0.757, and in solution 2 the molality is 0.200 mol kg −1 with
γ ±,2 equal to 0.767.
The Temperature Dependence of the Cell Voltage
We have already studied the temperature dependence of ∆G ◦ . From Eqs. (7.6-9) and
(8.2-14), if ∆H ◦ can be assumed to be temperature-independent,
E ◦ (T 2 )
T 2
−
E ◦ (T 1 )
T 1
−
∆H ◦
nF
1
T 2
−
1
T 1
(8.3-8)
8 The Thermodynamics of Electrochemical Systems
HCl
Solution
m ϭ m 1
HCl
Solution
m ϭ m 2
Ag
AgCl
Ag
Pt
H 2 (P 1 )
Pt
H 2 (P 2 )
Figure 8.9 A Double Cell Equivalent to a Concentration Cell.
with hydrogen electrodes. Assuming that the pressure of hydrogen is equal to P ◦ in
both cells, the Nernst equation for the left-hand cell is
E(left cell) 0.2223V −
2RT
F
ln(γ ±,1 m 1 /m
◦ )
and that of the right-hand cell is
E(right cell) −0.2223 V +
2RT
F
ln(γ ±,2 m 2 /m
◦ )
so that the potential difference of the double cell is equal to that of Eq. (8.3-7) without
the liquid junction potential. Another possibility is to build just one cell, like half of
the double cell, and then to measure its potential difference once when filled with a
solution of molality m 1 , and once when filled with a solution of molality m 2 .
Exercise 8.8
Find the potential difference of the concentration cell of Figure 8.8 if in solution 1 the molality is
0.500 mol kg −1 with γ ±,1 equal to 0.757, and in solution 2 the molality is 0.200 mol kg −1 with
γ ±,2 equal to 0.767.
The Temperature Dependence of the Cell Voltage
We have already studied the temperature dependence of ∆G ◦ . From Eqs. (7.6-9) and
(8.2-14), if ∆H ◦ can be assumed to be temperature-independent,
E ◦ (T 2 )
T 2
−
E ◦ (T 1 )
T 1
−
∆H ◦
nF
1
T 2
−
1
T 1
(8.3-8)