Question

The potential of hydrogen electrode at $25^\circ {\text{C}}$ will be: $({{\text{P}}_{{{\text{H}}_2}}} = 1{\text{ atm, concentration of }}{{\text{H}}^ + }{\text{ = 0}}{\text{.1M)}}$A.) 0.00 VB.) -0.059 VC.) 0.118 VD.) 0.059 V

Hint: We know that Nernst equation is used to get the value of electrode potential. It relates, cell potential, temperature, reaction quotient and standard cell potential to each other.

We have been given the temperature to be ${\text{25}}^\circ {\text{C}}$ i.e. ${\text{25}}^\circ {\text{C + 273 = 298K}}$. Also, ${{\text{P}}_{{{\text{H}}_2}}} = 1{\text{ atm}}$and ${\text{[}}{{\text{H}}^ + }{\text{] = 0}}{\text{.1M}}$.

Reaction occurring on hydrogen electrode is –
${\text{2}}{{\text{H}}^ + }{\text{ + 2}}{{\text{e}}^ - }{\text{ }} \to {\text{ }}{{\text{H}}_2}$.
At ${\text{25}}^\circ {\text{C}}$, Nernst equation is given as - ${{\text{E}}_{{\text{cell }}}}{\text{ = }}{{\text{E}}^0}{\text{ - }}\dfrac{{0.059}}{2}{\text{log}}\dfrac{{{{\text{P}}_{{{\text{H}}_2}}}}}{{[{{\text{H}}^ + }]}}$

Substituting given values in above equation we get,
${{\text{E}}_{{\text{cell }}}}{\text{ = 0 - 0}}{\text{.059 log}}\dfrac{1}{{(0.1)}}$
(standard electrode potential of hydrogen electrode is taken as 0. Hence, ${{\text{E}}^0}{\text{ = 0}}$.)
$\begin{gathered} {{\text{E}}_{{\text{cell }}}}{\text{ = 0}}{\text{-0.059 log {10}}} \\ {\text{ = - 0}}{\text{.059 V}} \\ \end{gathered}$

Hence, the potential of hydrogen electrode at is ${\text{ - 0}}{\text{.059 V}}$.

So, option B is correct.

The potential difference between the metal and solution is known as electrode potential. It is a measure of tendency of an electrode in a half cell to gain or lose electrons. Whereas, standard electrode potential is the measure of electrode potential at equilibrium conditions. In other words, the electrode potential of a given electrode measured at STP is called a standard electrode potential. It is represented by ${{\text{E}}^0}_{{\text{cell}}}$.
Note: At STP, ${\text{Temperature = 298 K}}$, ${\text{Pressure = 1 atm}}$ and ${\text{Concentration = 1}}{\text{ M}}$. Standard hydrogen electrode is used as a reference or a parameter to measure electrode potentials of other metals.