Question

If time required for \(99\%\) completion of a first order reaction is \(t\) minutes, find the time required for \(99.9\%\) completion.

• A. \(t\) minutes.
• B. \(2t\) minutes.
• C. \(3t/2\) minutes.
• D. \(t/2\) minutes.

Hint:

Use the integrated rate law of a first order reaction and compare the logarithm terms for 99% and 99.9% completion.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a first order reaction the time for a given completion is \(t=\dfrac{2.303}{k}\log\dfrac{100}{100-x}\), where \(x\) is the percentage completed.

Step 2: Time for 99% completion
\(t_{99}=\dfrac{2.303}{k}\log\dfrac{100}{1}=\dfrac{2.303}{k}\times 2\)

Step 3: Time for 99.9% completion
\(t_{99.9}=\dfrac{2.303}{k}\log\dfrac{100}{0.1}=\dfrac{2.303}{k}\times 3\)

Step 4: Take the ratio
\(\dfrac{t_{99.9}}{t_{99}}=\dfrac{3}{2}\), so \(t_{99.9}=\dfrac{3t}{2}\) minutes.

Final Answer:
The time required for 99.9% completion is 3t/2 minutes. \[ \boxed{\text{(C) }\dfrac{3t}{2}\text{ minutes}} \]