Question

Determine the overall reaction and its standard cell potential at 25 °C for the reaction involving the galvanic cell made from a half-cell consisting of a silver electrode in 1 M silver nitrate solution and a half-cell consisting of azinc electrode in 1 M zinc nitrate. Is the reaction spontaneous at standard conditions?

Short answer

The overall reaction is \(3Cu(s) + 2A{u^{3 + }}(aq) \to 3C{u^{2 + }}(aq) + 2Au(s)\)

The standard cell potential at \({25{\circ }}{\rm{C}}\) is \( + 1.16\;{\rm{V}}\)

The standard cell potential is positive, so the reaction is spontaneous.

Step-by-step solution

Define standard cell potential

• The shorthand notation of a cell reaction indicates phase boundary by a single vertical line (|) and salt bridge is denotes by a double vertical line . In this notation on the left side of salt bridge oxidation reaction which occurred at anode and on the right side of salt bridge; reduction reaction which occurred at cathode.
• The electrodes are written on the extreme corners; anode on extreme left and cathode on extreme right. The reactants in each half-cell are always first, followed by the products.
• If the standard cell potential is positive, then the reaction isspontaneousand if the standard cell potential is negative, then the reaction isnon-spontaneous

Determine the standard cell potential

The cell reaction that involves silver electrode in \(1{\rm{M}}\) silver nitrate and zinc electrode in \(1{\rm{M}}\) zinc nitrate.

Therefore, the cell notation is as follows:

\(Zn(s)\left| {{Z^{2 + }} || (1M)A{g^ + }(1M)} \right|Ag(s)\)

In the given reaction zinc is oxidized at anode and silver is reduced at cathode.

Anode reaction:

\({\rm{Zn}}(s) \to {\rm{Z}}{{\rm{n}}^{2 + }}(aq) + 2{e^ - }\quad {E^o} = - 0.7618\;{\rm{V}}\)

Cathode reaction:

\(A{g^ + }(aq) + {e^ - } \to Ag(s)\quad {E^o} = + 0.7996\;{\rm{V}}\)

Because the reduction potential of Silver is more than that of Zinc so Ag half-cell acts as cathode Zinc half-cell acts as anode.

The overall or net cell reaction is as follows:

\(2\left( {A{g^ + }(aq) + {e^ - } \to Ag(s)} \right)\)

\(\frac{{1\left( {{\rm{Zn}}(s) \to {\rm{Z}}{{\rm{n}}^{2 + }}(aq) + 2{e^ - }} \right)}}{{{\rm{Zn}}(s) + 2A{g^ + }(aq) \to 2Ag(s) + {\rm{Z}}{{\rm{n}}^{2 + }}(aq)}}\)

Now calculate the standard cell potential at \({25\circ }{\rm{C}}\), using the following expression: