Assertion (A): May endothermic reactions that are not spontaneous at room temperature become spontaneous at high temperature.
Reason (R ) : Entropy of the system increases with increase in temperature.

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-11
B. If both the statements are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-11
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 assertion and reason provided in the question, we can break down the concepts involved in thermodynamics, particularly focusing on Gibbs free energy and entropy.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "may endothermic reactions that are not spontaneous at room temperature become spontaneous at high temperature."
- An endothermic reaction is characterized by a positive change in enthalpy (ΔH > 0). For a reaction to be spontaneous, the change in Gibbs free energy (ΔG) must be negative (ΔG < 0).

2. **Gibbs Free Energy Equation**:
- The relationship between Gibbs free energy, enthalpy, and entropy is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
- Here, ΔS is the change in entropy. For an endothermic reaction, ΔH is positive.

3. **Conditions for Spontaneity**:
- For an endothermic reaction to become spontaneous at high temperatures, we need to consider the term \(T \Delta S\).
- If ΔS is positive (which is often the case for endothermic reactions that lead to increased disorder), increasing the temperature (T) will increase the value of \(T \Delta S\).

4. **Making ΔG Negative**:
- As temperature increases, the term \(T \Delta S\) becomes larger and more negative (since ΔH is positive).
- Therefore, at sufficiently high temperatures, it is possible for ΔG to become negative, making the reaction spontaneous.

5. **Conclusion on Assertion**:
- Thus, the assertion is true: endothermic reactions that are non-spontaneous at room temperature may become spontaneous at higher temperatures.

6. **Understanding the Reason (R)**:
- The reason states that "entropy of the system increases with increase in temperature."
- While it is true that the entropy of a system tends to increase with temperature, this statement does not specifically explain why endothermic reactions can become spontaneous at high temperatures.

7. **Correct Explanation**:
- The correct explanation involves the relationship between ΔH, ΔS, and temperature in the Gibbs free energy equation, rather than a general statement about entropy increasing with temperature.

8. **Conclusion on Reason**:
- Therefore, while the reason is true, it does not correctly explain the assertion.

### Final Answer:
- Assertion (A) is true, while Reason (R) is true but does not provide the correct explanation for the assertion.