Q. The half-life of a first-order reaction is 20 minutes. The time required for 75% of the reaction to complete is:

प्रथम कोटि की प्रतिक्रिया का आधा जीवन 20 मिनट है। 75% प्रतिक्रिया को पूरा करने के लिए आवश्यक समय है:

10 minutes
10 मिनटों

20 minutes
20 मिनट

30 minutes
30 मिनट

40 minutes
40 मिनट

For first-order reactions:

t_{1/2} = \frac{0.693}{k} = 20 \text{ min} \Rightarrow k = \frac{0.693}{20} = 0.03465 \text{ min}^{-1}

Time for 75% completion means 25% remains:

\ln \left(\frac{[A]_0}{[A]}\right) = kt

\ln \left(\frac{1}{0.25}\right) = 0.03465 \times t \implies \ln 4 = 0.03465 t

1.386 = 0.03465 t \Rightarrow t = 40 \text{ min}

So correct answer is 40 minutes

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