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Question: The potential of hydrogen electrode having a solution of \(pH = 4\) at \(298K\) is, A)\( - 0.177V\...

The potential of hydrogen electrode having a solution of pH=4pH = 4 at 298K298K is,
A)−0.177V - 0.177V
B) −0.236V - 0.236V
C) 0.177V0.177V
D) 0.236V0.236V

Explanation

Solution

We know the Hermann Nernst equation is commonly accustomed to calculate the cell potential of a chemical science cell at any given temperature, pressure, and chemical concentration.
Ecell=E0−[RT/nF]lnQ{E_{cell}} = {E_0}-\left[ {RT/nF} \right]lnQ
Where,
Ecell{E_{cell}} = cell potential of the cell
The cell potential below customary conditions is E0{E_0}
R is the universal gas constant
T is temperature
n is amount of electrons transferred within the chemical reaction
Q is the reaction quotient

Complete answer:
We can calculate the [H+][H^+] by using the formula, pH=−log⁡[H+]pH = - \log \left[ {{H^ + }} \right]
Given,
pH=4pH = 4
Thus, ⇒[H+]=10−4 \Rightarrow \left[ {{H^ + }} \right] = {10^{ - 4}}
The reaction which occurs at electrode is,
H++e−→12H2{H^ + } + {e^ - } \to \dfrac{1}{2}{H_2}
Where,
Ecell{E_{cell}}=0, n=1 and [H2]=1 atm
Ecell= - 0.0591log⁡[H2][H+]{E_{cell}} = {\text{ - }}\dfrac{{0.059}}{1}\log \dfrac{{\left[ {{H_2}} \right]}}{{\left[ {{H^ + }} \right]}}
Now we can substitute the known values we get,
⇒Ecell= - 0.0591log⁡110−4\Rightarrow {E_{cell}} = {\text{ - }}\dfrac{{0.059}}{1}\log \dfrac{1}{{{{10}^{ - 4}}}}
Ecell= - 0.059(−log⁡10−4){E_{cell}} = {\text{ - 0}}{\text{.059}}\left( { - \log {{10}^{ - 4}}} \right)
On simplifying we get,
⇒Ecell=0.059(−4)=−0.236V\Rightarrow {E_{cell}} = {\text{0}}{\text{.059}}\left( { - 4} \right) = - 0.236V
Thus the correct option is B.

Note: We can see the limitations of Nernst Equation:
The activity of an ion in an exceedingly} very dilute solution is on the point of eternity and can, therefore, be expressed in terms of the ion concentration. However, for solutions having very high concentrations, the ion concentration isn't up to the particle activity. So as to use the Nernst equation in such cases, experimental livements should be conducted to get actuality activity of the ion. Another defect of this equation is that it can't be accustomed to measure cell potential once there's current flowing through the electrode. This can be as a result of the flow of current that affects the activity of the ions on the surface of the electrode. Also, further factors adore resistive loss and over potential must be thought-about when there is a current flowing through the electrode.