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Question: At what pH of HCl solution will hydrogen gas electrode show electrode potential of -0.118 V, \({{H}_...

At what pH of HCl solution will hydrogen gas electrode show electrode potential of -0.118 V, H2{{H}_{2}} gas is bubbled at 298K and 1 atm pressure?
(A)- 2
(B)- 4
(C)- 6
(D)- 8

Explanation

Solution

The Nernst equation is used to determine the pH of the solution, knowing the electrode potential during the reaction and the standard conditions of the hydrogen electrode, having its concentration equal to unity. The concentration and the pH of the solution can be obtained.

Complete step by step solution:
In this reference electrode, it consists of the platinum electrode dipped in the hydrochloric solution and on applying voltage, the hydrogen ions from the solution get reduced on the electrode and release bubbles of hydrogen gas, absorbed on it.
In the standard hydrogen electrode, the reaction at the electrode is as follows:
2H++e−→H22{{H}^{+}}+{{e}^{-}}\to {{H}_{2}}
Using the Nernst equation, we have,
EH+/H2=E∘H+/H2−0.0591nlog⁡[H2][H+]2{{E}_{{{H}^{+}}/{{H}_{2}}}}={{E}^{\circ }}_{{{H}^{+}}/{{H}_{2}}}-\dfrac{0.0591}{n}\log \dfrac{\left[ {{H}_{2}} \right]}{{{\left[ {{H}^{+}} \right]}^{2}}} --------- (a)
During the reduction reaction, with the release of hydrogen bubbles at temperature 298 K and 1 atm pressure, the electrode potential is given to be EH+/H2=−0.118V{{E}_{{{H}^{+}}/{{H}_{2}}}}=-0.118V and the number of electrons transfer during the reaction, n = 2.
So, the concentration of H2{{H}_{2}} gas is unity and the E∘H+/H2=0{{E}^{\circ }}_{{{H}^{+}}/{{H}_{2}}}=0. Then, we have equation (a) as:
EH+/H2=0−0.05912log⁡1[H+]2{{E}_{{{H}^{+}}/{{H}_{2}}}}=0-\dfrac{0.0591}{2}\log \dfrac{1}{{{\left[ {{H}^{+}} \right]}^{2}}}
−0.118=0−0.05912log⁡1[H+]2-0.118=0-\dfrac{0.0591}{2}\log \dfrac{1}{{{\left[ {{H}^{+}} \right]}^{2}}}
−0.118=−0.05912log⁡[H+]  −2-0.118=-\dfrac{0.0591}{2}\log {{\left[ {{H}^{+}} \right]}^{\,\,-2}}
−0.118=−0.05912×(−2)log⁡[H+]-0.118=-\dfrac{0.0591}{2}\times (-2)\log \left[ {{H}^{+}} \right]
−0.118=−0.0591×pH             as pH=−log⁡[H+]-0.118=-0.0591\times pH\,\,\,\,\,\,\,\,\,\,\,\,\,as\,pH=-\log \left[ {{H}^{+}} \right]
Then, pH=2pH=2

Therefore, the pH of HCl solution in the standard electrode potential is option (A)- 2.

Additional information: Even as a reference electrode, the SHE has some limitations as the assembling of the apparatus with such conditions of temperature and pressure for the gas and also unit concentration of the solution. Also, a slight amount of impurity can poison the platinum electrode, varying its voltage.

Note: The standard hydrogen electrode potential is used to determine the potential of the half-cells of other species, acting as the reference electrode for them.