Question
The reduction potential of hydrogen half-cell will be negative if :
A.
$$p\left( {{H_2}} \right) = 1\,{\text{atm}}\,{\text{and}}\left[ {{H^ + }} \right] = 2.0\,M$$
B.
$$p\left( {{H_2}} \right) = 1\,{\text{atm}}\,{\text{and}}\left[ {{H^ + }} \right] = 1.0\,M$$
C.
$$p\left( {{H_2}} \right) = 2\,{\text{atm}}\,{\text{and}}\left[ {{H^ + }} \right] = 1.0\,M$$
D.
$$p\left( {{H_2}} \right) = 2\,{\text{atm}}\,{\text{and}}\left[ {{H^ + }} \right] = 2.0\,M$$
Answer :
$$p\left( {{H_2}} \right) = 2\,{\text{atm}}\,{\text{and}}\left[ {{H^ + }} \right] = 1.0\,M$$
Solution :
$$\eqalign{
& {H^ + } + {e^ - } \to \frac{1}{2}{H_2};E = {E^o} - \frac{{0.059}}{1}\log \frac{{P_{{H_2}}^{\frac{1}{2}}}}{{\left[ {{H^ + }} \right]}} \cr
& {\text{Now}}\,{\text{if}}\,{P_{{H_2}}} = 2\,{\text{atm}}\,{\text{and}}\,\left[ {{H^ + }} \right] = 1M \cr
& {\text{then}}\,E = 0 - \frac{{0.059}}{1}\log \frac{{{2^{\frac{1}{2}}}}}{1} = - 2 \cr} $$