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Calculate the voltage of the cell Fe; Fe+2 ║H+; H2 if the iron half cell is at standard conditions but the H+ ion concentration is 0.001 M.
Solution:
The half-cell reaction for Fe is
and it is an oxidation reaction because iron lost two electrons. From Table of Common Standard Reduction Potentials, E0 = 0.447 V. If you reverse the half-cell reaction, the sign of reduction potential will change. Since Fe+2 is at standard condition, then the concentration is 1 M. The concentration of any whole or pure metal in the half-cell reaction is 1 M.
If the concentration of any metal ion is given, then we can calculate the voltage of half-cell reaction by using Nernst Equation as follows
where n is the number of electrons lost or gained in half-cell reaction. Hence, the voltage for Fe is
The half-cell reaction for H is
and it is a reduction reaction because hydrogen gained two electrons. From Table of Common Standard Reduction Potentials, E0 = 0 V. If you reverse the half-cell reaction, the reduction potential is still the same because it is 0 V. If the concentration of H+ is 0.001M, then the voltage for H by Nernst Equation is
Therefore, the voltage of the cell is
