75% of a first-order reaction was completed in 32 min. When was 50% of the reaction completed?
Answer & explanation
Correct answer: option 2
The correct answer is option 2. 16 min.
For First order reaction,
\(k = \frac{2.303}{t}log \frac{a}{a − x}\)
When the reaction is 75% complete then,
\(x = \frac{75}{100}a = 0.75 a\)
\(∴ k = \frac{2.303}{32}log \frac{a}{a −0.75 a}\)
\(⇒ k = \frac{2.303}{32}log \frac{1}{0.25}\)
\(⇒ k = \frac{2.303}{32} ×0.602\)
\(⇒k = 0.04332\)
Also we know ,
\(t_{1/2} = \frac{0.693}{k}\)
\(t_{1/2} = \frac{0.693}{0.04332}\)
\(⇒ t_{1/2} = 15.99\)
\(∴ t_{1/2} ≈ 16 min\)