Question

Calculate the pH at which the potential of the hydrogen electrode will be $0.059V$ .

Answer 1

The pH of a solution is defined as the negative of the logarithm of the concentration of hydrogen ion to the base 10. The Nernst equation can be applied on each and every electrolytic cell provided their standard electrode potential is known.

Complete answer:
For the reduction of the hydrogen ions to produce hydrogen gas, the following reaction takes place in the standard hydrogen electrode.
${H^ + } + {e^ - } \to \dfrac{1}{2}{H_2}(g)$
Applying Nernst equation, we have:
${E_{cell}} = E_{cell}^o - \dfrac{{0.059}}{1}\log \dfrac{{product}}{{reactant}}$ …. (i)
We already know that the standard electrode potential of a hydrogen electrode is equal to zero.
Thus, $E_{cell}^o = 0$
In the given question, the electrode potential of hydrogen is equal to $0.059V$.
Thus, ${E_{cell}} = 0.059V$
Now, substituting these values in equation (i), we have:
$0.059 = 0 - 0.059\log \dfrac{1}{{{H^ + }}}$
We know that, $pH = - {\log _{10}}{H^ + } \\\ pH = {\log _{10}}\dfrac{1}{{{H^ + }}} \\\$
Applying this, we have the final equation as:
$0.059 = - 0.059pH \\\ pH = - 1 \\\$
Thus, the pH at which the potential of hydrogen electrode will be $0.059V$ is -1.

Note:
The pH of any solution varies from 0 to 14 on the universal pH scale. So, technically a pH of -1 is not possible. But, theoretically, this pH is attainable under certain conditions of electrode potential and temperature. In the relation between electrode potential and pH, if one of the values is known, the other can be calculated easily.