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Question: Emf of hydrogen electrode in terms of pH (at \[1atm\] pressure). A.\[{E_{{H_2}}} = \dfrac{{RT}}{F}...

Emf of hydrogen electrode in terms of pH (at 1atm1atm pressure).
A.EH2=RTF×pH{E_{{H_2}}} = \dfrac{{RT}}{F} \times pH
B.EH2=RTF1pH{E_{{H_2}}} = \dfrac{{RT}}{F}\dfrac{1}{{pH}}
C.EH2=2.303RTFpH{E_{{H_2}}} = \dfrac{{2.303RT}}{F}pH
D.EH2=−0.0591pH{E_{{H_2}}} = - 0.0591pH

Explanation

Solution

For solving this question we need to understand Nernst equation. Nernst equation is an equation which we use in electrochemistry, it gives the relation between reduction potential of reaction and standard electrode potential, temperature and concentration of elements undergoing reduction and oxidation. Reaction can be a half-cell reaction or full cell reaction.

Complete answer:
Nernst equation is given as
E=E∘−RTnFln⁡QE = {E^ \circ } - \dfrac{{RT}}{{nF}}\ln Q
Where E is the Emf, n is the number of electrons absorbed or transferred in the reaction, F is the faraday constant (96500C/mol96500C/mol), T is the temperature and R is the gas constant (8.314J/K8.314J/K). Nernst equation at standard temperature (298K)(298K)can be further simplified by putting all known values. We get the equation
E=E∘−0.0591nlog⁡QE = {E^ \circ } - \dfrac{{0.0591}}{n}\log Q
We are calculating Emf of the Hydrogen electrode. Hydrogen electrode is a type of redox half-cell. Let’s see the reaction involved
2{H^ + } + 2{e^\\_} \to {H_2}
Hydrogen ions absorb two electrons to give Hydrogen gas. So, the value of n will be two and Standard electrode potential of hydrogen is zero. Nernst equation for the above equation is given as
EH2=0−0.05912log⁡1[H+]2{E_{{H_2}}} = 0 - \dfrac{{0.0591}}{2}\log \dfrac{1}{{{{[{H^ + }]}^2}}}
On further simplifying the equation we get
EH2=−0.05912×−2log⁡[H+]{E_{{H_2}}} = - \dfrac{{0.0591}}{2} \times - 2\log [{H^ + }]
We know that negative log of Hydrogen ions gives the pH, we get
EH2=−0.0591pH{E_{{H_2}}} = - 0.0591pH
We get the Emf of the hydrogen electrode in terms of pH.

So, option (D) is the correct answer.

Note:
While simplifying Nernst equation by putting values of Gas constant, Faraday constant and temperature we also convert natural log to log base 1010. n is the number of electrons transferred from a balanced reaction. Q is the ratio of concentration of product ions to concentration of reactant ions.