Which of the following statements is not correct?

Options

A. For a zero order reaction `t_(1//2)` is proportional to initial concentraion.
B. The relationship of variation of rate constant with temperature is given by
`log (k_(2))/(k_(1)) = (E_(a))/(2.303 R) [(T_(2) - T_(1))/(T_(1)T_(2))]`
C. The unit of rate constant for a reaction is `mol^(1 - n) L^(n - 1) s^(-1)` where n is order of the reaction.
D. The unit of rate of reaction changes with order of reaction.

Explanation

To determine which statement is not correct regarding chemical kinetics, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement 1:** For a zero-order reaction, T_half is proportional to initial concentration.

- For a zero-order reaction, the half-life (T_half) is given by the formula:
\[ T_{1/2} = \frac{[A_0]}{2k} \]
where \([A_0]\) is the initial concentration and \(k\) is the rate constant.
- From this equation, it is clear that T_half is directly proportional to the initial concentration \([A_0]\).
- **Conclusion:** This statement is correct.

### Step 2: Analyze the Second Statement
**Statement 2:** The relationship of variation of rate constant with temperature is given by the Arrhenius equation.

- The Arrhenius equation describes how the rate constant \(k\) varies with temperature \(T\) and is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, and \(R\) is the universal gas constant.
- The statement regarding the relationship involving logarithms is also correct.
- **Conclusion:** This statement is correct.

### Step 3: Analyze the Third Statement
**Statement 3:** The unit of rate constant for a reaction is \( \text{mol}^{1-n} \cdot \text{L}^{n-1} \cdot \text{s}^{-1} \) where \(n\) is the order of the reaction.

- The units of the rate constant \(k\) depend on the order of the reaction \(n\).
- For example:
- For a zero-order reaction (\(n=0\)), units are \(\text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1}\).
- For a first-order reaction (\(n=1\)), units are \(\text{s}^{-1}\).
- For a second-order reaction (\(n=2\)), units are \(\text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1}\).
- Therefore, the given formula for the unit of rate constant is indeed correct.
- **Conclusion:** This statement is correct.

### Step 4: Analyze the Fourth Statement
**Statement 4:** The unit of rate of a reaction changes with the order of the reaction.

- The rate of a reaction is defined as the change in concentration over time, typically expressed in units of \(\text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1}\).
- This unit does not depend on the order of the reaction; it remains constant regardless of whether the reaction is zero, first, or second order.
- Therefore, the statement claiming that the unit of rate changes with the order of the reaction is incorrect.
- **Conclusion:** This statement is incorrect.

### Final Answer
The statement that is not correct is **Statement 4**: "The unit of rate of a reaction changes with the order of the reaction."

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