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Question: For the EMF of a hydrogen electrode to be zero, the pressure of hydrogen required in neutral pH is: ...

For the EMF of a hydrogen electrode to be zero, the pressure of hydrogen required in neutral pH is:
A. 1×10−7atm1 \times {10^{ - 7}}atm
B. 1×10−14atm1 \times {10^{ - 14}}atm
C. 1.0atm
D. 0.0atm

Explanation

Solution

pH is the power of hydrogen which is considered as the negative logarithm of the hydrogen ion concentration. It helps us in measuring the strength of the acid and bases. The scale ranges from 0 to 14. So the use of litmus paper is done as an indicator to determine whether the substance is acid or base.

Complete step by step answer:
For hydrogen electrode the reaction is as follows:
2H++2e−→H2(g)2{H^ + } + 2{e^ - } \to {H_2}(g)
The two protons will gain two electrons to form hydrogen gas.
Now we have to apply Nernst equation. But before that let us know what a Nernst equation is.
Nernst equation relates the reduction potential of an electrochemical to the standard electrode potential, temperature, and of the chemical species undergoing reduction and oxidation.
According to Nernst equation,
E=Eo−0.05912log⁡pH2[H+]2 E=0 Eo=0 E = {E^o} - \dfrac{{0.0591}}{2}\log \dfrac{{{p_{{H_2}}}}}{{{{[{H^ + }]}^2}}} \\\ E = 0 \\\ {E^o} = 0
Substituting these two values, the above equation looks like:
0=0−0.05912log⁡pH2[H+]20 = 0 - \dfrac{{0.0591}}{2}\log \dfrac{{{p_{{H_2}}}}}{{{{[{H^ + }]}^2}}}
As we know the concentration of hydronium ions is
10−7{10^{ - 7}}. Substituting this value, we get
0=0−0.05912log⁡pH2[10−7]20 = 0 - \dfrac{{0.0591}}{2}\log \dfrac{{{p_{{H_2}}}}}{{{{[{{10}^{ - 7}}]}^2}}}
On solving we get:
log⁡pH2[10−7]2=0\log \dfrac{{{p_{{H_2}}}}}{{{{[{{10}^{ - 7}}]}^2}}} = 0
We can write 0 as log 1. Substituting it in the above equation,
log⁡pH2[10−7]2=log⁡1\log \dfrac{{{p_{{H_2}}}}}{{{{[{{10}^{ - 7}}]}^2}}} = \log 1
On comparing both these equations, we get
pH2=(10−7)2{p_{{H_2}}} = {({10^{ - 7}})^2}
pH2=10−14{p_{{H_2}}} = {10^{ - 14}}
Hence for the EMF of a hydrogen electrode to be zero, the pressure of hydrogen required in neutral pH is 1×10−14atm 1 \times {10^{ - 14}}atm.

So, the correct answer is Option B.

Note: Hydrogen electrode for standard hydrogen electrode has a potential of zero at the temperature of 298 Kelvin. This is the reason it acts as a reference to compare with any other electrode. It is a type of gas electrode. It has many uses. One of the uses is it is used as a reference electrode. It is also used as an indicator electrode when we want to calculate pH values in studies