Question

A first order reaction takes 10 minute for 30% completion. Find rate constant of the reaction.

• A. 0.0177 minute\(^{-1}\)
• B. 0.0357 minute\(^{-1}\)
• C. 0.0526 minute\(^{-1}\)
• D. 0.0713 minute\(^{-1}\)

Hint:

Use k = (2.303/t) log[A0/(A0 - x)] with 30% of the reactant used up.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For a first order reaction, \(k = \dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]}\).

Step 2: Calculation
30% completion means 70% of the reactant remains.
\(k = \dfrac{2.303}{10}\log\dfrac{100}{70}\)
\(\log(1.4286) = 0.1549\)

Step 3: Result
\(k = 0.2303\times0.1549 = 0.0357\) min\(^{-1}\)
This matches option (B).

Final Answer:
The rate constant is \(0.0357\) min\(^{-1}\). \[ \boxed{\text{(B) }0.0357\ \text{minute}^{-1}} \]