Question 76: Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : In equation \Delta_{\mathrm{r}} \mathrm{G}=-\mathrm{nFE}_{\text {cell }}, value of \Delta_{\mathrm{r}} \mathrm{G} depends on n.
Reasons R: \mathrm{E}_{\text {cell }} is an intensive property and \Delta_{\mathrm{r}} \mathrm{G} is an extensive property.
In the light of the above statements, choose the correct answer from the options given below :
(1) \mathbf{A} is true but \mathbf{R} is false.
(2) \mathbf{A} is false but \mathbf{R} is true.
(3) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}.
(4) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is NOT the correct explanation of \mathbf{A}.
Answer: Option (3)
Explanation:
The relation between Gibbs free energy change and cell potential is given by
\Delta_{\mathrm{r}} \mathrm{G}=-\mathrm{nFE}_{\text {cell }}.
Here, n is the number of moles of electrons transferred in the electrochemical reaction.
Since \mathrm{E}_{\text {cell }} is an intensive property,
its value does not depend on the amount of substance or number of electrons involved.
Gibbs free energy change \Delta_{\mathrm{r}} \mathrm{G} is an extensive property
and depends on the amount of substance, hence it depends on n.
Therefore, Assertion A is true.
The reason correctly states that \mathrm{E}_{\text {cell }} is intensive and
\Delta_{\mathrm{r}} \mathrm{G} is extensive, which explains why
\Delta_{\mathrm{r}} \mathrm{G} depends on n.
Thus, both Assertion A and Reason R are true and R is the correct explanation of A.