Question

For a first order reaction A → Products, initial concentration of A is 0.1 M, which becomes 0.001M after 5 minutes. Rate constant for the reaction in min^-1 is

• A. 1.3818
• B. 0.4606
• C. 0.9212
• D. 0.2303

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The integrated rate law for a first-order reaction describes the decay of reactant over time.
Key Formula or Approach:
\[ k = \frac{2.303}{t} \log \left( \frac{[A]_{0}}{[A]_{t}} \right) \]
Step 2: Detailed Explanation:
Given:
$[A]_{0} = 0.1$ M
$[A]_{t} = 0.001$ M
$t = 5$ min
Calculating $k$:
\[ k = \frac{2.303}{5} \log \left( \frac{0.1}{0.001} \right) \]
\[ k = \frac{2.303}{5} \log (100) \]
Since $\log(100) = 2$:
\[ k = \frac{2.303}{5} \times 2 \]
\[ k = \frac{4.606}{5} \]
\[ k = 0.9212 \text{ min}^{-1} \]
Step 3: Final Answer:
The rate constant is $0.9212 \text{ min}^{-1}$. This matches option (2).