Assertion (A) : Equilibrium constant of a reaction increases if temperature is increased
Reason (R) : The forward reaction becomes faster with increase of temperature.

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.

Explanation

To solve the assertion and reason question regarding the equilibrium constant and temperature, we will analyze both the assertion (A) and the reason (R) step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the equilibrium constant (Kc) of a reaction increases if the temperature is increased.
- The relationship between the equilibrium constant and temperature is described by the Van 't Hoff equation:
\[ \log K_c = -\frac{\Delta H}{2.303 R} \left(\frac{1}{T}\right) + \text{constant} \]
- Here, \(\Delta H\) is the change in enthalpy of the reaction, and R is the universal gas constant.

2. **Analyzing the Effect of Temperature**:
- If \(\Delta H > 0\) (endothermic reaction), increasing temperature (T) leads to an increase in Kc.
- If \(\Delta H < 0\) (exothermic reaction), increasing temperature leads to a decrease in Kc.
- Therefore, the assertion that Kc increases with temperature is **not universally true**; it depends on whether the reaction is endothermic or exothermic.

3. **Conclusion on Assertion (A)**:
- The assertion is **false** because it does not hold true for exothermic reactions.

4. **Understanding the Reason (R)**:
- The reason states that the forward reaction becomes faster with an increase in temperature.
- According to the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
- Here, \(k\) is the rate constant, \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, and \(T\) is the temperature.
- As temperature increases, the term \(-\frac{E_a}{RT}\) becomes less negative, leading to an increase in the rate constant \(k\).

5. **Conclusion on Reason (R)**:
- The reason is **true** because an increase in temperature generally increases the rate of the forward reaction.

6. **Final Conclusion**:
- Since the assertion (A) is false and the reason (R) is true, the correct answer is that **A is incorrect but R is correct**.