Question

Consider an electrochemical cell with a zinc electrode immersed in 1.0 M Zn2+ and a nickel electrode immersed in 0.10 M Ni2+. Calculate the concentration of Ni2+ if the cell is allowed to run to equilibrium at 25 degrees C.

Answer 1

At equilibrium Delta G would be 0 now we will calculate the equilibrium constant as follows:

delta G = - RT ln K

0= - RT ln K

Half cell reactions are following:

Ni^2+ + 2e- --> Ni(s) E0: -0.24V
Zn^2+ + 2e- --> Zn(s) E0: -0.76V

here Zn becomes oxidized
therefore,

Zn+ Ni^2+ --> Zn^2+ Ni

E0: -0.24 -(-0.76) = 0.52V

delta Go = -nFEo = -(2)(96,500)(0.52)

= - 100.36 kJ

delta Go = -RT ln K
-100360 = -(8.31)(298 )(ln K)

40.51 = ln K
K = e^40.51 = 3.92x 10^17

Equilibrium constant K = [Product]/ [reactants]

3.92x 10^17= [Zn2+]/ [Ni2+]

[Ni2+]= 1.0/ 3.92x 10^17

[Ni2+]=2.55*10^-18

The concentration of Ni2+ if the cell is allowed to run to equilibrium is 2.55*10^-18