The half-life period of a first order reaction is 100 sec. The rate constant of the reaction is

Options

A. `6.93 xx 10^(-3) sec^(-1)`
B. `6.93 xx 10^(-4) sec^(-1)`
C. `0.693 sec^(-1)`
D. `69.3 sec^(-1)`

Answer

To find the rate constant (K) of a first-order reaction given its half-life period (t_half), we can use the formula for the half-life of a first-order reaction:

### Step-by-Step Solution:

1. **Identify the formula for half-life of a first-order reaction**:
The half-life (t_half) of a first-order reaction is given by the equation:
\[ t_{half} = \frac{0.693}{K} \]
where \( K \) is the rate constant.

2. **Substitute the given half-life into the formula**:
We know from the problem that:
\[ t_{half} = 100 \text{ seconds} \]
Substituting this value into the half-life formula gives:
\[ 100 = \frac{0.693}{K} \]

3. **Rearrange the equation to solve for K**:
To find \( K \), we can rearrange the equation:
\[ K = \frac{0.693}{100} \]

4. **Calculate the value of K**:
Now, performing the calculation:
\[ K = 0.00693 \text{ s}^{-1} \]
This can also be expressed in scientific notation:
\[ K = 6.93 \times 10^{-3} \text{ s}^{-1} \]

5. **Conclusion**:
Therefore, the rate constant \( K \) for the reaction is:
\[ K = 6.93 \times 10^{-3} \text{ s}^{-1} \]