Question:
The half life values for two different first order reaction A and B are 75 minute and 2.5 hour respectively. What is the $\frac{\text{r}_B}{\text{r}_A}$ ratio of rate constants?
The half life values for two different first order reaction A and B are 75 minute and 2.5 hour respectively. What is the $\frac{\text{r}_B}{\text{r}_A}$ ratio of rate constants?
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Ratio of rate constants is the inverse ratio of their half-lives.
Updated On: Apr 26, 2026
- $2.0$
- $0.5$
- $14.2$
- $22.0$
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The Correct Option is B
Solution and Explanation
Step 1: Formula
For 1st order reaction, $k = \frac{0.693}{t_{1/2}}$.
So, $k \propto \frac{1}{t_{1/2}}$.
Step 2: Uniform Units
$t_{1/2}(A) = 75 \text{ min}$
$t_{1/2}(B) = 2.5 \text{ hr} = 2.5 \times 60 = 150 \text{ min}$
Step 3: Ratio Calculation
$\frac{k_B}{k_A} = \frac{t_{1/2}(A)}{t_{1/2}(B)} = \frac{75}{150} = 0.5$
Final Answer: (B)
For 1st order reaction, $k = \frac{0.693}{t_{1/2}}$.
So, $k \propto \frac{1}{t_{1/2}}$.
Step 2: Uniform Units
$t_{1/2}(A) = 75 \text{ min}$
$t_{1/2}(B) = 2.5 \text{ hr} = 2.5 \times 60 = 150 \text{ min}$
Step 3: Ratio Calculation
$\frac{k_B}{k_A} = \frac{t_{1/2}(A)}{t_{1/2}(B)} = \frac{75}{150} = 0.5$
Final Answer: (B)
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