In a first order reaction A `to` B, if k is rate constant and initial concentration of the reactant A is 2 M then the half life of the reaction is:

Options

A. `(log 2)/k`
B. `( log 2)/(ksqrt0.5)`
C. `(l n 2)/k`
D. `0.693/0.5k`

Answer

To find the half-life of a first-order reaction where the initial concentration of reactant A is 2 M, we can use the formula for the half-life of a first-order reaction. The half-life (t₁/₂) for a first-order reaction is given by:

\[ t_{1/2} = \frac{0.693}{k} \]

Where:
- \( k \) is the rate constant.

### Step-by-Step Solution:

1. **Identify the Reaction Order**:
The reaction is a first-order reaction, which is important as it determines the formula we will use for calculating the half-life.

2. **Use the Half-Life Formula**:
The formula for the half-life of a first-order reaction is:
\[ t_{1/2} = \frac{0.693}{k} \]

3. **Substituting Values**:
In this case, we do not have a specific value for \( k \) (the rate constant). However, we can still express the half-life in terms of \( k \):
\[ t_{1/2} = \frac{0.693}{k} \]

4. **Conclusion**:
The half-life of the reaction depends on the rate constant \( k \). If the value of \( k \) is provided, we can substitute it into the formula to find the numerical value of the half-life.