For a first order reaction `A rarr` Products, the half life is 100 seconds. The rate constant of the reaction is

Options

A. `6.93 times 10^-2 sec^-1`
B. `6.93 times 10^-3 sec^-1`
C. `6.93 times 10^-3 sec`
D. `6.93 sec`

Answer

To find the rate constant (k) for a first-order reaction given the half-life (t½), we can use the formula for the half-life of a first-order reaction:

1. **Identify the formula for half-life of a first-order reaction**:
\[ t_{1/2} = \frac{0.693}{k} \]

2. **Substitute the given half-life into the formula**:
Given that \( t_{1/2} = 100 \) seconds, we can substitute this value into the equation:
\[ 100 = \frac{0.693}{k} \]

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

4. **Calculate the value of k**:
Performing the calculation:
\[ k = 0.00693 \text{ seconds}^{-1} \]

5. **Convert k to scientific notation**:
To express this in scientific notation:
\[ k = 6.93 \times 10^{-3} \text{ seconds}^{-1} \]

6. **Final answer**:
The rate constant \( k \) for the reaction is:
\[ k = 6.93 \times 10^{-3} \text{ seconds}^{-1} \]

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