What is the cathode pH in Co/Co2+(1.00 M)//H1+(x M), H2(1.0 atm)/Pt if E = 0.03 V? Give the pH to 0.01.?

Question

What is the cathode pH in Co/Co2+(1.00 M)//H1+(x M), H2(1.0 atm)/Pt if E = 0.03 V? Give the pH to 0.01.

Answer 1

The related standard reduction potentials are:
2H+(aq) + 2e- ==> H2(g), E° = 0.00V
Co(2+)(aq) + 2e- ==> Co(s), E° = -0.277 V
So the overall reaction is:
Co(s) + 2H+(aq) ==> Co(2+)(aq) + H2(g), E° = 0.277 V.

Using Nernst equation:
E = E° + (0.0591/n)*log([H+]^2/{[Co(2+)]*P(H2)})
Or: 0.03 = 0.277+(0.0591/2)*log([H+]^2)
log([H+]) = (0.03-0.277)/0.0591 = -4.18
pH = -log([H+]) = 4.18