The time taken for the completion of 3/4 of a first order reaction is

Options

A. (2.303/k) log 3/4
B. (2.303/k) log 4
C. (2.303/k) log 1/4
D. (2.3033/0.75) log k

Explanation

To find the time taken for the completion of \( \frac{3}{4} \) of a first-order reaction, we can use the first-order reaction rate equation. Here’s a step-by-step solution:

### Step 1: Understand the first-order reaction equation
For a first-order reaction, the rate constant \( k \) is related to the time \( t \) and the concentrations of the reactants using the formula:
\[ t = \frac{2.303}{k} \log \left( \frac{A}{A - X} \right) \]
where:
- \( A \) is the initial concentration,
- \( X \) is the amount of reactant that has reacted.

### Step 2: Define the parameters for \( \frac{3}{4} \) completion
If \( \frac{3}{4} \) of the reaction is complete, then:
- The amount reacted \( X = \frac{3}{4}A \)
- The remaining amount \( A - X = A - \frac{3}{4}A = \frac{1}{4}A \)

### Step 3: Substitute values into the equation
Now, substituting \( A \) and \( A - X \) into the first-order equation:
\[ t = \frac{2.303}{k} \log \left( \frac{A}{\frac{1}{4}A} \right) \]
This simplifies to:
\[ t = \frac{2.303}{k} \log \left( \frac{A}{\frac{1}{4}A} \right) = \frac{2.303}{k} \log(4) \]

### Step 4: Final expression for time
Thus, the time taken for the completion of \( \frac{3}{4} \) of the reaction is:
\[ t = \frac{2.303}{k} \log(4) \]

### Conclusion
This is the final expression for the time taken for the completion of \( \frac{3}{4} \) of a first-order reaction.

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