For a first order reaction `A to B` the reaction rate at reactant concentration of 0.01 M is found to be` 2.0 xx 10 ^-5mol L^(-1) s^(-1)`. The half-life period of the reaction is

Options

A. 30 s
B. 220 s
C. 300s
D. 347s

Explanation

To find the half-life period of the first-order reaction \( A \to B \), we can follow these steps:

### Step 1: Understand the relationship between rate, concentration, and the rate constant (k).
For a first-order reaction, the rate of the reaction can be expressed as:

\[ \text{Rate} = k[A] \]

Where:
- Rate is given as \( 2.0 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} \)
- \([A]\) is the concentration of reactant A, which is \( 0.01 \, \text{M} \).

### Step 2: Rearrange the equation to solve for k.
We can rearrange the equation to find the rate constant \( k \):

\[ k = \frac{\text{Rate}}{[A]} \]

Substituting the values:

\[ k = \frac{2.0 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1}}{0.01 \, \text{mol L}^{-1}} \]

### Step 3: Calculate k.
Now we perform the calculation:

\[ k = \frac{2.0 \times 10^{-5}}{0.01} = 2.0 \times 10^{-5} \times 10^{2} = 2.0 \times 10^{-3} \, \text{s}^{-1} \]

### Step 4: Use the formula for half-life of a first-order reaction.
The half-life (\( t_{1/2} \)) for a first-order reaction is given by the formula:

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

### Step 5: Substitute the value of k into the half-life formula.
Now we substitute \( k = 2.0 \times 10^{-3} \, \text{s}^{-1} \):

\[ t_{1/2} = \frac{0.693}{2.0 \times 10^{-3}} \]

### Step 6: Perform the calculation.
Calculating the half-life:

\[ t_{1/2} = 0.693 \div 0.002 = 346.5 \, \text{s} \]

### Final Answer:
The half-life period of the reaction is approximately \( 346.5 \, \text{s} \).

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