Statement-1: Decrease of free energy during the process under constant temperature and pressure provides a measure of its spontaneity.
Statement -2: A spontaneous change must have +ve sign of `DeltaS_("system").`

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-12
B. If both the statements are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-12
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To analyze the statements given in the question, we will break down the concepts of free energy and entropy in thermodynamics.

### Step-by-Step Solution:

1. **Understanding Free Energy and Spontaneity**:
- The Gibbs free energy (G) is a thermodynamic potential that helps predict whether a process will occur spontaneously at constant temperature (T) and pressure (P).
- The change in Gibbs free energy (ΔG) during a process is given by the equation:
\[ \Delta G = \Delta H - T\Delta S \]
- For a process to be spontaneous, ΔG must be negative (ΔG < 0). Thus, the first statement is correct: a decrease in free energy indicates that the process is spontaneous.

2. **Understanding Entropy (ΔS)**:
- Entropy (S) is a measure of the disorder or randomness of a system.
- The second statement claims that a spontaneous change must have a positive change in entropy of the system (ΔS_system > 0).
- However, the total entropy change (ΔS_total) for a spontaneous process must be positive:
\[ \Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} > 0 \]
- This means that even if the entropy change of the system (ΔS_system) is negative, the entropy change of the surroundings (ΔS_surroundings) can be positive enough to make the total entropy change positive.

3. **Conclusion**:
- Therefore, while Statement 1 is true (a decrease in free energy indicates spontaneity), Statement 2 is false because a spontaneous process does not necessarily require a positive change in the entropy of the system.

### Final Answer:
- Statement 1 is true.
- Statement 2 is false.