If 75% of a first order reaction gets completed in 32 minutes, time t…

The correct answer is option 1. 16 minutes.

We know, for a first order reaction,

\(k = \frac{2.303}{t}log \frac{a}{a - x} -----(i)\)

Given, 75% of reaction gets completed in 32 minute, then for 75% of the reaction,

let \(a = 100\) and \(x = 75\)

Thus, \(a - x = 100 - 75 =25\)

Applying it in equation (i), we get

\(k = \frac{2.303}{32}log \frac{100}{25}\)

or, \(k = \frac{2.303}{32}log 4 \)

or, \(k = 0.0433\, \ min^{-1}\)

We know, half-life of the first order equation is

\(t_{50\%} = \frac{0.693}{k}\)

or, \(t_{50\%} = \frac{0.693}{0.0433\, \ min^{-1}}\)

or, \(t_{50\%} =  15.99\, \ min\)

or, \(t_{50\%} \approx 16\, \ min \)