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 a first-order reaction, we will analyze each of the provided options step by step.

### Step-by-Step Solution:

1. **Understanding First Order Reactions**:
A first-order reaction can be represented as:
\[ A \rightarrow P \]
The rate of the reaction depends linearly on the concentration of the reactant \( A \).

2. **Rate Law and Integrated Rate Equation**:
The integrated rate law for a first-order reaction is given by:
\[ \ln \left( \frac{[A]_0}{[A]} \right) = kt \]
Rearranging gives:
\[ [A] = [A]_0 e^{-kt} \]

3. **Degree of Dissociation**:
The degree of dissociation \( \alpha \) can be defined as the fraction of the reactant that has reacted. If \( [A]_0 \) is the initial concentration and \( [A] \) is the concentration at time \( t \), we can express:
\[ [A] = [A]_0 (1 - \alpha) \]
Substituting this into the integrated rate equation:
\[ [A]_0 e^{-kt} = [A]_0 (1 - \alpha) \]
Dividing both sides by \( [A]_0 \) gives:
\[ e^{-kt} = 1 - \alpha \]
Rearranging this yields:
\[ \alpha = 1 - e^{-kt} \]

4. **Evaluating the Options**:
- **Option 1**: The degree of dissociation is equal to \( 1 - e^{-kt} \).
- **Correct**: This matches our derived expression for \( \alpha \).

- **Option 2**: Plot of reciprocal concentration of reactant versus time is a straight line.
- **Incorrect**: For first-order reactions, the plot of concentration vs. time is not linear; it is an exponential decay.

- **Option 3**: Time taken for completion of 75% of the reactant is half of the reaction time.
- **Incorrect**: The half-life of a first-order reaction is independent of the initial concentration and is given by \( t_{1/2} = \frac{\ln 2}{k} \). It does not depend on the percentage of completion.

- **Option 4**: The pre-exponential factor of the Arrhenius equation has the dimension of time \( T^{-1} \).
- **Correct**: The rate constant \( k \) for a first-order reaction has units of \( T^{-1} \), and since \( k = A e^{-E_a/RT} \), the pre-exponential factor \( A \) must also have units of \( T^{-1} \).

5. **Final Conclusion**:
The correct options are **1 and 4**.