For the 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 thrice the `(1)/(2)` of the reaction
D. the pre-exponential factor in the Arrhenius equation has dimension of time, `T^(-1)`

Explanation

To solve the question regarding first-order reactions, we will analyze each of the options provided and determine their validity step by step.

### Step 1: Analyze Option 1
The statement is: "The degree of dissociation (α) is equal to 1 minus e raised to the power of -kt."

1. **Understanding Degree of Dissociation**: For a first-order reaction, the degree of dissociation (α) is defined as the fraction of the reactant that has reacted.
2. **Using the First-Order Reaction Formula**: The relationship can be derived from the first-order kinetics equation:
\[ k = \frac{1}{T} \log \frac{1}{1 - \alpha} \]
Rearranging gives:
\[ kt = \log \frac{1}{1 - \alpha} \]
Taking the antilogarithm results in:
\[ e^{-kt} = 1 - \alpha \]
Thus, we can express α as:
\[ \alpha = 1 - e^{-kt} \]
3. **Conclusion for Option 1**: This confirms that Option 1 is correct.

### Step 2: Analyze Option 2
The statement is: "A plot of reciprocal concentration of reactant versus time graph gives a straight line."

1. **Understanding the Plot**: For first-order reactions, the concentration of reactants decreases exponentially over time.
2. **Correct Plot Type**: The correct plot for a first-order reaction is a plot of the natural logarithm of concentration versus time, which gives a straight line, not the reciprocal concentration.
3. **Conclusion for Option 2**: This statement is incorrect.

### Step 3: Analyze Option 3
The statement is: "The time taken for the completion of 75% reaction is thrice the half-life of the reaction."

1. **Calculating Time for 75% Completion**:
- For 75% completion, we use the formula:
\[ t_{75\%} = \frac{2.303}{k} \log \frac{100}{25} = \frac{2.303}{k} \log 4 \]
2. **Calculating Time for 50% Completion**:
- For 50% completion (half-life):
\[ t_{50\%} = \frac{2.303}{k} \log \frac{100}{50} = \frac{2.303}{k} \log 2 \]
3. **Comparing Times**:
- Dividing the two times:
\[ \frac{t_{75\%}}{t_{50\%}} = \frac{\log 4}{\log 2} = 2 \]
This means that the time taken for 75% completion is 2 times the half-life, not 3 times.
4. **Conclusion for Option 3**: This statement is incorrect.

### Step 4: Analyze Option 4
The statement is: "The pre-exponential factor in the Arrhenius equation has dimensions of time (t inverse)."

1. **Understanding the Arrhenius Equation**: The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where A is the pre-exponential factor.
2. **Units of Rate Constant (k)**: For a first-order reaction, the units of k are s^-1 (time inverse).
3. **Conclusion for Option 4**: The pre-exponential factor A does not have dimensions of time; it is a frequency factor. Therefore, this statement is incorrect.

### Final Conclusion
Based on the analysis:
- **Correct Options**: Option 1 is correct.
- **Incorrect Options**: Options 2, 3, and 4 are incorrect.