The standard emf for cell, _ Cd _ ( s ) | Cd ⁺²(1 M ) | | Cu ⁺²(1 M ) | Cu _ ( s ) ^ is 0.74 V . If concentration of Cd _ ( aq ) ⁺² and Cu _ ( aq ) ⁺² decreases by 10 times at 298 K . Calculate emf of cell.

Step-by-step solution

The cell is Cd _ ( s ) | Cd ⁺²(1 M ) | | Cu ⁺²(1 M ) | Cu _ ( s ) with E^ _ cell = 0.74 ~V . Oxidation occurs at the anode with Cd _ ( s ) Cd ⁺²_ ( aq ) + 2e⁻ , and reduction at the cathode with Cu ⁺²_ ( aq ) + 2e⁻ Cu _ ( s ) , giving an overall reaction of Cd _ ( s ) + Cu ⁺²_ ( aq ) Cd ⁺²_ ( aq ) + Cu _ ( s ) , where n = 2 . After the concentration of both ions decreases by a factor of 10, [ Cd ⁺²] = 0.1 ~M and [ Cu ⁺²] = 0.1 ~M . The reaction quotient becomes Q = [ Cd ⁺²] [ Cu ⁺²] = 0.1 0.1 = 1 . Using the Nernst