If the rate constant for a first order reaction is k, the time (t) required for the completion of 99% of the reaction is given by :

Options

A. `t=2.303//k`
B. `t=0.693//k`
C. `t=6.909//k`
D. `t=4.606//k`

Explanation

To solve the problem of finding the time (t) required for the completion of 99% of a first-order reaction with a rate constant k, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the First-Order Reaction Equation**:
The equation for the time required for a first-order reaction is given by:
\[ t = \frac{2.303}{k} \log\left(\frac{A_0}{A_t}\right) \]
where:
- \( A_0 \) is the initial concentration,
- \( A_t \) is the concentration at time \( t \),
- \( k \) is the rate constant.

2. **Identify Initial and Final Concentrations**:
In this case, since 99% of the reaction is completed, only 1% of the reactant remains. Therefore:
- \( A_0 = 100 \) (initial concentration),
- \( A_t = 1 \) (final concentration after 99% completion).

3. **Substitute Values into the Equation**:
Substitute \( A_0 \) and \( A_t \) into the equation:
\[ t = \frac{2.303}{k} \log\left(\frac{100}{1}\right) \]

4. **Calculate the Logarithm**:
Calculate the logarithm:
\[ \log(100) = \log(10^2) = 2 \log(10) = 2 \times 1 = 2 \]

5. **Substitute the Logarithm Value**:
Now substitute this value back into the equation:
\[ t = \frac{2.303}{k} \times 2 \]

6. **Simplify the Equation**:
Simplifying gives:
\[ t = \frac{4.606}{k} \]

7. **Final Answer**:
Therefore, the time required for the completion of 99% of the reaction is:
\[ t = \frac{4.606}{k} \]

### Conclusion:
The time required for the completion of 99% of the reaction is given by the formula:
\[ t = \frac{4.606}{k} \]