Question

If time required for 90 % completion of a first order reaction is '\(t\)'. What is the time required for 99.9 % completion of reaction at same temperature?

• A. \(3t\)
• B. \(2t\)
• C. \(t\)
• D. \(\frac{3t}{2}\)

Hint:

For first order, \(t = \frac{2.303}{k}\log\frac{100}{100-x}\).

Answer 1

The Correct Option is A

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

Step 2: Key Formula or Approach
For \(x\) percent completion, \([A]_0/[A] = 100/(100-x)\).

Step 3: Detailed Explanation
90 percent: \(t = \dfrac{2.303}{k}\log 10 = \dfrac{2.303}{k}\).
99.9 percent: \(t' = \dfrac{2.303}{k}\log 1000 = \dfrac{2.303}{k}\times3\).
So \(t' = 3t\).

Final Answer:
The time for 99.9 percent completion is \(3t\), option (A). \[ \boxed{3t\ \text{(A)}} \]