Question

What is the time required for 99% completion of a first order reaction if rate constant is 23.03 min$^{-1}$?

• A. 0.2 minute
• B. 0.4 minute
• C. 6.2 minute
• D. 8.1 minute

Hint:

For first order kinetics, memorize these shortcut relationships to save time on exams:
$t_{99%} = 2 \times t_{90%}$
$t_{99.9%} = 3 \times t_{90%}$
$t_{75%} = 2 \times t_{50%}$ (two half-lives)

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For a first-order reaction, the time $t$ is given by $t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$.

Step 2: Formula Application:
$k = 23.03$ min$^{-1}$. For 99% completion, $[A]_0 = 100$ and $[A]_t = 100 - 99 = 1$.

Step 3: Explanation:
$t = \frac{2.303}{23.03} \log \frac{100}{1}$ $t = 0.1 \times \log(10^2)$ $t = 0.1 \times 2 = 0.2$ minutes.

Step 4: Final Answer:
The time required is 0.2 minute.