JEE Main 2021 — Chemistry Physical Chemistry

2021integerhard

$A$ and $B$ decompose via first order kinetics with half-lives $54.0\mathrm{min}$ and $18.0\mathrm{min}$ respectively. Starting from an equimolar non-reactive mixture of $A$ and $B$ , the time taken for the concentration of $A$ to become $16$ times that of $B$ is ______ $\mathrm{min}$ . (Round off to the Nearest Integer).

Official previous-year question

Held on 16 Mar 2021 · Verified 6 Jul 2026.

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Solution

Given $A={t}_{1/2}=54\mathrm{min}$

$B={t}_{1/2}=18\mathrm{min}$

$t=0$ ' $x$ ' $M$ $t=0$ ' $x$ ' $M$

$\Rightarrow$ To calculate : $[{A}_{t}]=16\times [{B}_{t}]$ time $=?$

$\Rightarrow$ For $I$ order kinetic : $[{A}_{t}]=\frac{{A}_{0}}{{(2)}^{n}}$

$n\rightarrow$ no. of Half lives

$\Rightarrow$ Now from the relation $(1)$

$\Rightarrow \frac{x}{{(2)}^{{n}_{1}}}=\frac{x}{{(2)}^{{n}_{2}}}\times 16\Rightarrow {(2)}^{{n}_{2}}={(2)}^{{n}_{1}}\times {(2)}^{4}$

$\Rightarrow {n}_{2}={n}_{1}+4\Rightarrow \frac{t}{{({t}_{1/2})}_{2}}=\frac{t}{{({t}_{1/2})}_{1}}+4$

$\Rightarrow t(\frac{1}{18}-\frac{1}{54})=4\Rightarrow t=\frac{4\times 18\times 54}{36}$

$\Rightarrow t=108\mathrm{min}$

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JEE Main 2021 — Chemistry Physical Chemistry

2021integerhard

Official previous-year question

Held on 16 Mar 2021 · Verified 6 Jul 2026.

Did you get this right?

Solution

Given $A={t}_{1/2}=54\mathrm{min}$

$B={t}_{1/2}=18\mathrm{min}$

$t=0$ ' $x$ ' $M$ $t=0$ ' $x$ ' $M$

$\Rightarrow$ To calculate : $[{A}_{t}]=16\times [{B}_{t}]$ time $=?$

$\Rightarrow$ For $I$ order kinetic : $[{A}_{t}]=\frac{{A}_{0}}{{(2)}^{n}}$

$n\rightarrow$ no. of Half lives

$\Rightarrow$ Now from the relation $(1)$

$\Rightarrow \frac{x}{{(2)}^{{n}_{1}}}=\frac{x}{{(2)}^{{n}_{2}}}\times 16\Rightarrow {(2)}^{{n}_{2}}={(2)}^{{n}_{1}}\times {(2)}^{4}$

$\Rightarrow {n}_{2}={n}_{1}+4\Rightarrow \frac{t}{{({t}_{1/2})}_{2}}=\frac{t}{{({t}_{1/2})}_{1}}+4$

$\Rightarrow t(\frac{1}{18}-\frac{1}{54})=4\Rightarrow t=\frac{4\times 18\times 54}{36}$

$\Rightarrow t=108\mathrm{min}$

Your note

JEE Main Physical Chemistry in other years

Keep practicing Physical Chemistry

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JEE Main 2021 — Chemistry Physical Chemistry

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JEE Main Physical Chemistry in other years

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JEE Main 2021 — Chemistry Physical Chemistry

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Solution

Your note

JEE Main Physical Chemistry in other years

More JEE Main Physical Chemistry questions

Other Chemistry topics for JEE Main

Organic Chemistry

Inorganic Chemistry

Keep practicing Physical Chemistry