Page 74 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch06 Elementary Physical Chemistry

Phase and Chemical Equilibria 59

Example 6.6. The reduction potentials for the following reactions are

+2 o
−
Cd +2e → Cd E = −0.40 V
o
Cd + 2OH → Cd(OH) 2 +2e − E = −0.81 V
−
Calculate
(a) The standard cell potential at 298 K for the reaction
+2 −
Cd +2OH → Cd(OH) 2 ;
(b) The equilibrium constant K at 298 K for the reaction in Part (a);
(c) The electrical work produced at constant T and P when the reaction
is in equilibrium.

Solutions

o
−
(a) Cd +2 +2e → Cd E = −0.40 V
o
−
Cd + 2OH → Cd(OH) 2 +2e − E =+0.81 V
Cd 2+ +2OH → Cd(OH) 2 E o =0.41 V
−
cell
o
(b) ∆G = −ν E o ; ν = 2 (mol of electrons)
cell
3
=96.485 × 10 coulomb mol −1 (C mol −1 )
o −1
E = potential difference in volts (1 V = 1 JC )
cell
3
o
∆G = −2 × 96.485 × 10 Cmol −1 × 0.41 JC −1 = −79.12 kJ mol −1
3
K =exp[79.12 × 10 Jmol −1 /(8.3145J K −1 mol −1 × 298 K)]
=7.38 × 10 13
(c) In general, ∆G T,P =∆G o T,P + RT ln K and ∆G T,P ≤ w other.
o
At equilibrium ln K =∆G /RT and ∆G T,P = w other =0. Thus, the
electrical work (a form of w other) is zero.