8.2 Electrochemical Cells
359
E X A M P L E 8.1
Find the potential difference of our cell at 298.15 K if the hydrogen pressure is equal to
744 torr and if m 0.500 mol kg −1 . The value of E ◦ is 0.2223 V, and at this molality the
mean ionic activity, coefficient is equal to 0.757.
Solution
E 0.2223 V −
(8.3145 J K −1 mol −1 )(298.15 K)
(2)(96485 C mol −1 )
ln
(0.757) 4 (0.500) 4
(744 torr)/(750 torr)
0.2223 V − (−0.0498 V) 0.2721 V
Our discussion of the Nernst equation applies to a particular cell. Consider now a
general cell without liquid junction. The chemical reaction equation can be written:
0
c
i1
v i F i + ne
− (R) − ne
− (L)
(8.2-18)
where n is the number of electrons in the reaction equation. The Nernst equation for a
general cell is
E E ◦ −
RT
nF
ln(Q) (general Nernst equation)
(8.2-19)
where
Q
c
i1
a
v i
i
(8.2-20)
The activity quotient Q does not include the activity of the electron.
E X A M P L E 8.2
Write the cell symbol, the cell reaction equation, and the Nernst equation for the cell with the
half-reactions
2Hg(l) + 2Cl − − → Hg 2 Cl 2 (s) + 2e −
Cl 2 (g) + 2e − − → 2Cl −
Solution
The cell symbol is
Pt|Hg(l)|Hg 2 Cl 2 (s)|HCl|Cl 2 (g)|Pt
The cell reaction equation is
2Hg(l) + Cl 2 (g) + 2Cl − − → Hg 2 Cl 2 (s) + 2Cl −
If we omit the chloride ion from both sides, this is the same as
2Hg(l) + Cl 2 (g) − → Hg 2 Cl 2 (s)