Question

A voltaic cell is set up with copper and hydrogen half-cells. Standard conditions are employed in thecopper half-cell, Cu2+(aq, 1.00 M)|Cu(s). The hydrogen gas pressure is 1 atm, and [H+] in the hydrogen half-cell is the unknown. A value of 0.500 V is recorded for Ecellat 298 K. Determine the pH of the solution.

Answer 1

H2(g) --------> 2H+ (aq) + 2e Anode E° = 0.00V

Cu2+ ( aq) + 2e ------> Cu(s) Cathode E° = 0.34V

Cu2+ (aq) + H2(g) --------> 2H+ (aq) + Cu(s) E°cell = 0.34V -0.00V = 0.34V

Q = [ H+ ] ^2 / pH2 [ Cu2+ ]

Nernst equation is

Ecell = E°cell - (0.0592V/n) logQ

number of electron transfer,n =2

0.500V = 0.34V - (0.0592V/2)log( [ H+ ]^2 )

H2 and Cu2+ terms are omitted because they are in standard condition

- 0.0296V log[ H+]^2 = 0.16V

2pH = 5.41

pH = 2.71