NEET 2023 Chemistry Gibbs Free Energy and Cell Potential Assertion Reason Question

To analyze the statements provided in the question regarding Gibbs Free Energy ($\Delta_rG$) and cell potential ($E_{\text{cell}}$), we need to understand their relationships and properties.

Assertion A:

In equation $\Delta_rG = -nFE_{\text{cell}}$, the value of $\Delta_rG$ depends on $n$.

This assertion is true. In the equation:

$$\Delta_rG = -nFE_{\text{cell}}$$

• $\Delta_rG$ represents the change in Gibbs free energy for a reaction.
• $n$ is the number of moles of electrons transferred in the electrochemical reaction.
• $F$ is Faraday's constant (approximately 96485 C/mol).
• $E_{\text{cell}}$ is the cell potential measured in volts (V).

The value of $\Delta_rG$ indeed depends on $n$ because as the number of moles of electrons transferred increases, the Gibbs free energy change will also change proportionally, given a constant $E_{\text{cell}}$.

Reason R:

$E_{\text{cell}}$ is an intensive property and $\Delta_rG$ is an extensive property.

This reasoning is also true.

• An intensive property is a property that does not depend on the amount of substance present. Cell potential ($E_{\text{cell}}$) remains the same regardless of the scale of the system.
• An extensive property, on the other hand, is one that depends on the amount of material present, such as Gibbs free energy change ($\Delta_rG$), which scales with the number of moles of reactants/products.

Conclusion:

Since both the assertion and the reason are true, the next step is to determine if the reason correctly explains the assertion. The reason explains how $\Delta_rG$ and $E_{\text{cell}}$ relate in terms of extensive and intensive properties, confirming that changes in the number of moles ($n$) affect the Gibbs free energy.

Thus, the correct answer is D) Both A and R are true and R is the correct explanation of A.

Explanation of Incorrect Options:

• Option A: Both A and R are true and R is NOT the correct explanation of A. (Incorrect because R correctly explains A).
• Option B: A is true but R is false. (Incorrect, as both A and R are true).
• Option C: A is false but R is true. (Incorrect, as A is true).

Summary:

Both assertions are true, and the reason provided serves to explain the relationship between the extensive and intensive properties in the context of electrochemistry. Therefore, the correct answer is indeed D. This understanding is crucial for mastering electrochemical principles in NEET/JEE exam preparation.