The rate constant of a zero order reaction is `1.5 times 10^–2 mol l^–1 min^–1` at 0.5 M concentration of the reactant. The half life of the reaction is

Options

A. 0.8min
B. 23.1min
C. 16.6min
D. 7.53min

Answer

To find the half-life of a zero-order reaction, we can use the formula:

\[ t_{1/2} = \frac{[A]_0}{2k} \]

where:
- \( t_{1/2} \) = half-life of the reaction
- \([A]_0\) = initial concentration of the reactant
- \( k \) = rate constant of the reaction

### Step 1: Identify the given values
From the question, we have:
- \( [A]_0 = 0.5 \, \text{M} \)
- \( k = 1.5 \times 10^{-2} \, \text{mol L}^{-1} \text{min}^{-1} \)

### Step 2: Substitute the values into the half-life formula
Now, we can substitute the values into the half-life formula:

\[ t_{1/2} = \frac{0.5 \, \text{M}}{2 \times (1.5 \times 10^{-2} \, \text{mol L}^{-1} \text{min}^{-1})} \]

### Step 3: Calculate the denominator
First, calculate the denominator:

\[ 2 \times (1.5 \times 10^{-2}) = 3.0 \times 10^{-2} \, \text{mol L}^{-1} \text{min}^{-1} \]

### Step 4: Perform the division
Now, perform the division:

\[ t_{1/2} = \frac{0.5}{3.0 \times 10^{-2}} = \frac{0.5}{0.03} = \frac{50}{3} \approx 16.67 \, \text{min} \]

### Step 5: Round the result
Rounding to two decimal places, we get:

\[ t_{1/2} \approx 16.67 \, \text{min} \]

Thus, the half-life of the reaction is approximately **16.67 minutes**.

### Final Answer
The half-life of the zero-order reaction is **16.67 minutes**.

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