A galvanic cell is constructed from a half-cell containing a solid copper electr

Question

A galvanic cell is constructed from a half-cell containing a solid copper electrode in a 1.0 M Cu(NO3)2 solution and a half-cell containing a solid aluminum electrode in a 1.0 M Al(NO3)3 solution at standard conditions. The half-cells are linked by an external circuit (a wire) and by a KCl salt bridge.

The balanced overall (net) cell reaction for the spontaneous process is:
(a) Cu(s) + Al3+(aq) ? Cu2+(aq) + Al(s)
(b) 3 Cu(s) + 2 Al3+(aq) ? 3 Cu2+(aq) + 2 Al(s)
(c) 3 Cu2+(aq) + 2 Al(s) ? 3 Cu(s) + 2 Al3+(aq)
(d) Cu2+(aq) + Al(s) ? Cu(s) + Al3+(aq)
(e) A spontaneous reaction is not possible in a galvanic cell.

Explanation / Answer

The standard reduction potential for the reduction of Cu2+ (aq) and Al3+ (aq) ions are

Al3+ (aq) + 3e-   --------------------> Al(s), E0(Red) = - 1.66V

Cu2+ (aq) + 2e-   --------------------> Cu(s), E0(Red) = +0.337V

Since the standard reduction potential value of Cu2+ (aq) is higher than Al3+ (aq), hence Cu2+ (aq) will be reduced to to Cu(s) and Al(s) will be oxidised to Al3+ (aq). Hence

Oxidation Half-cell: Al(s) -------------> Al3+ (aq) + 3e- , E0(oxi) = - ( - 1.66V) = +1.66V --------(1)

Reduction half - cell:Cu2+ (aq) + 2e-   --------------------> Cu(s), E0(Red) = +0.337V --------(2)

Now, in order to balance the over all cell reaction, the the electrons must cancel out. This can be achieved by multiplying equation-(1) by 2 and eqution-2 by 3.

Oxidation Half-cell: 2Al(s) -------------> 2Al3+ (aq) + 6e- , E0(oxi) = - ( - 1.66V) = +1.66V --------(3)

Reduction half - cell:3Cu2+ (aq) + 6e-   --------------------> 3Cu(s), E0(Red) = +0.337V --------(4)

Now 6 e- on opposite side will cancel out and the overall balanced cell reaction can beobtained by adding (3) and (4).Since E0(cell) is positive, the reaction is spontaneous

Over all cell reaction is

2Al(s) 9c+ 3Cu2+ (aq) ---------------> 2Al3+ (aq) +  3Cu(s), E0(cell) = E0(oxi) +E0(Red) = 1.66+0.337 = 1.997V

Hence (c) is the correct answer

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