Assertion (A) : When a catalyst is added to a reaction mixture in equilibrium the amount of the products increases.
Reason (R) : The forward reaction becomes faster on adding the catalyst.

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

**Step-by-Step Solution:**

1. **Understanding the Assertion (A):**
The assertion states that when a catalyst is added to a reaction mixture at equilibrium, the amount of products increases. This implies that the presence of a catalyst affects the concentrations of reactants and products at equilibrium.

2. **Analyzing the Role of a Catalyst:**
A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. It does this by providing an alternative reaction pathway with a lower activation energy. However, it does not change the position of the equilibrium or the concentrations of reactants and products at equilibrium.

3. **Understanding the Equilibrium Concept:**
In a chemical equilibrium, the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant. The addition of a catalyst speeds up both the forward and reverse reactions equally, but it does not favor one direction over the other.

4. **Conclusion on Assertion (A):**
Since a catalyst does not change the concentrations of reactants or products at equilibrium, the assertion that the amount of products increases when a catalyst is added is **incorrect**.

5. **Understanding the Reason (R):**
The reason states that the forward reaction becomes faster upon adding a catalyst. This is true because a catalyst lowers the activation energy for the forward reaction, allowing it to proceed more quickly.

6. **Conclusion on Reason (R):**
While the reason is correct, it does not support the assertion. The increase in the rate of the forward reaction does not lead to an increase in the amount of products at equilibrium.

7. **Final Evaluation:**
- Assertion (A) is **false**.
- Reason (R) is **true**.
- Therefore, the correct answer is that the assertion is incorrect while the reason is correct.