For a first order reaction,

Options

A. The degree of dissociation is equal to `(1-e^(-kt))`.
B. A plot of reciprocal concentration of the reactant `vs` time gives a straight line.
C. The time taken for the completion of `75%` reaction is theice the `t_(1//2)` of reaction.
D. The pre-exponential factor in the Arrhenius equations has the dimenison of time, `T^(-1)`.

Explanation

To solve the question regarding the statements about first-order reactions, we will analyze each statement one by one and determine which ones are correct.

### Step-by-Step Solution:

1. **Understanding the Degree of Dissociation**:
- The degree of dissociation (α) for a first-order reaction can be expressed as:
\[ \alpha = 1 - e^{-kt} \]
- This means that the first statement, which states that the degree of dissociation is equal to \(1 - e^{-k}\), is correct.

2. **Analyzing the Plot of Reciprocal Concentration vs. Time**:
- For a first-order reaction, the concentration of reactant A at time t is given by:
\[ [A] = [A_0] e^{-kt} \]
- The reciprocal concentration versus time would be:
\[ \frac{1}{[A]} = \frac{1}{[A_0] e^{-kt}} = \frac{e^{kt}}{[A_0]} \]
- This relationship is not linear; hence, the second statement is incorrect.

3. **Time for 75% Completion of Reaction**:
- If 75% of the reaction is complete, then 25% of the reactant remains. The concentration can be expressed as:
\[ [A] = \frac{[A_0]}{4} \]
- The time taken for 75% completion can be calculated using the half-life formula. The half-life (t½) for a first-order reaction is:
\[ t_{1/2} = \frac{0.693}{k} \]
- The time for 75% completion is actually twice the half-life:
\[ t_{75\%} = 2 \times t_{1/2} \]
- Therefore, the third statement is also incorrect.

4. **Units of the Rate Constant (k)**:
- For a first-order reaction, the unit of the rate constant (k) is time inverse (e.g., s⁻¹).
- The unit of the rate of reaction (A) is also time inverse since it is related to the change in concentration over time.
- Thus, the fourth statement is correct.

### Conclusion:
- The correct statements regarding the first-order reaction are:
- Statement A: Correct
- Statement B: Incorrect
- Statement C: Incorrect
- Statement D: Correct

### Final Answer:
The correct statements are A and D.