JEE Main 2023 — Chemistry Physical Chemistry

2023integermedium

An organic compound undergoes first order decomposition. If the time taken for the $60%$ decomposition is $540s$ , then the time required for $90%$ decomposition will be is _____ s. (Nearest integer).

Given : $\mathrm{ln}10=2.3;\mathrm{log}2=0.3$

Official previous-year question

Held on 30 Jan 2023 · Verified 6 Jul 2026.

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Solution

For the First order reaction, integrated rate equation can be written as follows,

$t=\frac{1}{k}\mathrm{ln}\frac{{a}_{0}}{{a}_{t}} t=\mathrm{time} k=\mathrm{rate}\mathrm{constant} {a}_{0}=\mathrm{intial}\mathrm{concentration} {a}_{t}=\mathrm{concentration}\mathrm{at}\mathrm{time}t$

$\frac{{t}_{1}}{{t}_{2}}=\frac{\frac{1}{k}\mathrm{ln}\frac{{a}_{0}}{0.4{a}_{0}}}{\frac{1}{k}\mathrm{ln}\frac{{a}_{0}}{0.1{a}_{0}}}$

$\frac{540}{{t}_{2}}=\frac{\mathrm{ln}\frac{10}{4}}{\mathrm{ln}10}$

$\frac{540}{{t}_{2}}=\frac{\mathrm{log}10-\mathrm{log}4}{\mathrm{log}10}$

$\frac{540}{{t}_{2}}=\frac{1-0.6}{1}$

$\Rightarrow \frac{540}{{t}_{2}}=0.4$

$\Rightarrow {t}_{2}=\frac{540}{0.4}=1350\mathrm{sec}$

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JEE Main 2023 — Chemistry Physical Chemistry

2023integermedium

Given : $\mathrm{ln}10=2.3;\mathrm{log}2=0.3$

Official previous-year question

Held on 30 Jan 2023 · Verified 6 Jul 2026.

Did you get this right?

Solution

For the First order reaction, integrated rate equation can be written as follows,

$\frac{{t}_{1}}{{t}_{2}}=\frac{\frac{1}{k}\mathrm{ln}\frac{{a}_{0}}{0.4{a}_{0}}}{\frac{1}{k}\mathrm{ln}\frac{{a}_{0}}{0.1{a}_{0}}}$

$\frac{540}{{t}_{2}}=\frac{\mathrm{ln}\frac{10}{4}}{\mathrm{ln}10}$

$\frac{540}{{t}_{2}}=\frac{\mathrm{log}10-\mathrm{log}4}{\mathrm{log}10}$

$\frac{540}{{t}_{2}}=\frac{1-0.6}{1}$

$\Rightarrow \frac{540}{{t}_{2}}=0.4$

$\Rightarrow {t}_{2}=\frac{540}{0.4}=1350\mathrm{sec}$

Your note

JEE Main Physical Chemistry in other years

Keep practicing Physical Chemistry

Work through every JEE Main Physical Chemistry PYQ, year by year.

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JEE Main 2023 — Chemistry Physical Chemistry

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Solution

Your note

JEE Main Physical Chemistry in other years

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Other Chemistry topics for JEE Main

Organic Chemistry

Inorganic Chemistry

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JEE Main 2023 — Chemistry Physical Chemistry

Did you get this right?

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