Assertion (A) : The value of K for a reaction may increase or decrease with increase in temperature depending upon whether the reaction is exothermic or endothermic.
Reason (R) : With increase in temperature, the extent of reaction increases.

Options

A. If both (A) and (R) are correct, and (R) is the correct explanation for (A)
B. If both (A) and (R) are correct, but (R) is not the correct explanation of (A)
C. If (A) is correct, but (R) is incorrect
D. If (A) is incorrect, but (R) is correct.

Answer

To solve the assertion-reason question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the equilibrium constant (K) for a reaction can either increase or decrease with an increase in temperature, depending on whether the reaction is exothermic or endothermic.
- This is based on the principle that the equilibrium constant is affected by temperature changes, which is described by the Van't Hoff equation.

2. **Analyzing the Van't Hoff Equation**:
- The Van't Hoff equation is given by:
\[ \ln \left( \frac{K_2}{K_1} \right) = \frac{\Delta H}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \]
- Here, \(K_1\) is the equilibrium constant at temperature \(T_1\), and \(K_2\) is the equilibrium constant at temperature \(T_2\). \(\Delta H\) is the change in enthalpy of the reaction, and \(R\) is the universal gas constant.

3. **Exothermic vs. Endothermic Reactions**:
- For **endothermic reactions** (\(\Delta H > 0\)), increasing the temperature results in an increase in K (K increases).
- For **exothermic reactions** (\(\Delta H < 0\)), increasing the temperature results in a decrease in K (K decreases).
- Therefore, the assertion is correct.

4. **Understanding the Reason (R)**:
- The reason states that with an increase in temperature, the extent of the reaction increases.
- This is true because higher temperatures provide more energy to the molecules, allowing more of them to overcome the activation energy barrier, thus increasing the rate of the reaction.

5. **Evaluating the Relationship Between A and R**:
- While both statements are correct, the reason does not directly explain the assertion. The assertion specifically relates to how temperature affects the equilibrium constant, while the reason discusses the general effect of temperature on reaction rates.
- Therefore, the reason is not a correct explanation for the assertion.

6. **Conclusion**:
- Both the assertion and the reason are correct, but the reason is not the correct explanation for the assertion. Thus, the correct answer is that both A and R are true, but R is not the correct explanation of A.

### Final Answer:
Both assertion and reason are correct, but the reason is not the correct explanation of the assertion.

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