Question

Assertion (A): Gibbs free energy determines spontaneity at constant T and P.
Reason (R): A process is spontaneous when Gibbs free energy is minimum.

• A. Both A and R are true, and R is the correct explanation of A
• B. Both are true, but R is not the correct explanation of A
• C. A is true, R is false
• D. A is false, R is true

Hint:

Remember the criteria:
- Constant $T$ and $P \Rightarrow$ Gibbs Free Energy ($G$) is minimized.
- Constant $T$ and $V \Rightarrow$ Helmholtz Free Energy ($A$) is minimized.
- Isolated System $\Rightarrow$ Entropy ($S$) is maximized.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question consists of an Assertion (A) and a Reason (R) about the Gibbs free energy criterion for thermodynamic spontaneity and equilibrium.
We need to evaluate the individual truth of both statements and determine if there is a direct cause-and-effect explanatory link between them.

Step 2: Key Formula or Approach:
The change in Gibbs free energy ($dG$) at constant temperature ($T$) and pressure ($P$) is defined as:
\[ dG_{T,P} = dH - T dS \] The fundamental thermodynamic criteria are:
For a spontaneous process: $dG_{T,P} < 0$.
At equilibrium: $dG_{T,P} = 0$, meaning the Gibbs free energy is minimized at a stable equilibrium state.

Step 3: Detailed Explanation:

• Assertion (A): "Gibbs free energy determines spontaneity at constant $T$ and $P$." This statement is true because the function was specifically designed to evaluate the total entropy change of the universe (system + surroundings) using only the system's properties under constant $T$ and $P$.

• Reason (R): "A process is spontaneous when Gibbs free energy is minimum." This statement is also true. A system naturally progresses spontaneously toward a state of minimum free energy, which represents the thermodynamic equilibrium.

• Connection between A and R: While both statements are true, the Reason (R) does not explain *why* the Gibbs function is the correct thermodynamic potential to determine spontaneity.

• The determination of spontaneity by Gibbs free energy is mathematically derived from the Second Law of Thermodynamics (Clausius inequality).

• The minimization of $G$ at equilibrium is a consequence of the spontaneity condition, not the underlying explanation for why it serves as the spontaneity criterion. Thus, R is not the correct explanation of A.

Step 4: Final Answer:
Both A and R are true, but R is not the correct explanation of A, which is option (B).