Question

The rate constant for a first order reaction is \(6.93\times 10^{-2}\) per minutes. What is the time required for the completion of \(99.9\%\) of the reaction?

• A. \(693\) minutes
• B. \(20\) minutes
• C. \(50\) minutes
• D. \(99.7\) minutes

Hint:

Use t = (2.303/k) log(100/(100-99.9)) for a first order reaction.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a first order reaction, \(t = \dfrac{2.303}{k}\log\dfrac{[A]_{0}}{[A]}\).

Step 2: Remaining reactant
After 99.9 percent completion, \([A] = 0.1\%\) of \([A]_{0}\), so \(\dfrac{[A]_{0}}{[A]} = 1000\).

Step 3: Calculation
\(t = \dfrac{2.303}{6.93\times10^{-2}}\times\log1000 = \dfrac{2.303\times3}{0.0693} \approx 99.7\ \text{min}\).

Final Answer:
The time required is about 99.7 minutes. \[ \boxed{\text{(D) }99.7\text{ minutes}} \]