Question:
In a first order reaction, the concentration of the reactant is reduced from \(0.6\ \text{mol L}^{-1}\) to \(0.2\ \text{mol L}^{-1}\) in \(5\) min. What is the rate constant of the reaction? \((\log 3=0.4771)\)
In a first order reaction, the concentration of the reactant is reduced from \(0.6\ \text{mol L}^{-1}\) to \(0.2\ \text{mol L}^{-1}\) in \(5\) min. What is the rate constant of the reaction? \((\log 3=0.4771)\)
Show Hint
For a first-order reaction,
\[
k=\frac{2.303}{t}\log\left(\frac{[A]_0}{[A]_t}\right)
\]
The unit of the first-order rate constant is always reciprocal time \((\text{time}^{-1})\).
Updated On: Jun 26, 2026
- \(0.219\ \text{min}^{-1}\)
- \(0.325\ \text{min}^{-1}\)
- \(0.421\ \text{min}^{-1}\)
- \(0.522\ \text{min}^{-1}\)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Use the integrated rate equation for a first-order reaction.
For a first-order reaction, \[ k=\frac{2.303}{t}\log\left(\frac{[A]_0}{[A]_t}\right) \] where \[ [A]_0=\text{initial concentration} \] \[ [A]_t=\text{concentration after time }t \]
Step 2: Substitute the given values.
Given, \[ [A]_0=0.6\ \text{mol L}^{-1} \] \[ [A]_t=0.2\ \text{mol L}^{-1} \] \[ t=5\ \text{min} \] Therefore, \[ k=\frac{2.303}{5} \log\left(\frac{0.6}{0.2}\right) \] \[ k=\frac{2.303}{5}\log(3) \]
Step 3: Use the given value of \(\log 3\).
Given, \[ \log 3=0.4771 \] Hence, \[ k=\frac{2.303}{5}\times0.4771 \] \[ k=0.4606\times0.4771 \] \[ k=0.2197\ \text{min}^{-1} \] \[ k\approx0.219\ \text{min}^{-1} \]
Step 4: Final conclusion.
Therefore, the rate constant of the reaction is \[ \boxed{0.219\ \text{min}^{-1}} \] Hence, the correct option is \[ \boxed{(1)} \]
For a first-order reaction, \[ k=\frac{2.303}{t}\log\left(\frac{[A]_0}{[A]_t}\right) \] where \[ [A]_0=\text{initial concentration} \] \[ [A]_t=\text{concentration after time }t \]
Step 2: Substitute the given values.
Given, \[ [A]_0=0.6\ \text{mol L}^{-1} \] \[ [A]_t=0.2\ \text{mol L}^{-1} \] \[ t=5\ \text{min} \] Therefore, \[ k=\frac{2.303}{5} \log\left(\frac{0.6}{0.2}\right) \] \[ k=\frac{2.303}{5}\log(3) \]
Step 3: Use the given value of \(\log 3\).
Given, \[ \log 3=0.4771 \] Hence, \[ k=\frac{2.303}{5}\times0.4771 \] \[ k=0.4606\times0.4771 \] \[ k=0.2197\ \text{min}^{-1} \] \[ k\approx0.219\ \text{min}^{-1} \]
Step 4: Final conclusion.
Therefore, the rate constant of the reaction is \[ \boxed{0.219\ \text{min}^{-1}} \] Hence, the correct option is \[ \boxed{(1)} \]
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