A : The rate constant of zero order reaction is equal to rate of reaction.
R : `t_(1//2)` for zero order reaction is directly proportional to initial concentration.

Options

A. Both Assertion & Reason are true and the reason is the correct explanation of the assertion
B. Both Assertion & Reason are true but the reason is not the correct explanation of the assertion
C. Assertion is true statement but Reason is false
D. Both Assertion and Reason are false statements

Answer

To solve the question, we need to analyze the two statements provided:

**Assertion (A):** The rate constant of a zero-order reaction is equal to the rate of the reaction.
**Reason (R):** \( t_{1/2} \) for a zero-order reaction is directly proportional to the initial concentration.

### Step-by-Step Solution:

1. **Understanding Zero-Order Reactions:**
- In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. The rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = k [A]^0 = k \]
- Here, \( k \) is the rate constant, and since \([A]^0 = 1\), the rate of the reaction is equal to the rate constant.

**Conclusion:** The assertion (A) is true.

2. **Deriving the Half-Life for Zero-Order Reactions:**
- The integrated rate law for a zero-order reaction can be written as:
\[ [A]_t = [A]_0 - kt \]
- To find the half-life (\( t_{1/2} \)), we set \([A]_t\) to \([A]_0/2\):
\[ \frac{[A]_0}{2} = [A]_0 - kt_{1/2} \]
- Rearranging gives:
\[ kt_{1/2} = [A]_0 - \frac{[A]_0}{2} = \frac{[A]_0}{2} \]
- Therefore, we can express the half-life as:
\[ t_{1/2} = \frac{[A]_0}{2k} \]
- This shows that the half-life is directly proportional to the initial concentration \([A]_0\).

**Conclusion:** The reason (R) is also true.

3. **Evaluating the Relationship Between A and R:**
- While both statements are true, the reason (R) does not explain the assertion (A). The assertion is about the relationship between the rate constant and the rate of reaction, while the reason discusses the half-life's dependence on initial concentration.

### Final Conclusion:
- Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion. Therefore, the correct option is that both A and R are true, but R is not the correct explanation of A.