JEE Main 2026 — Chemistry Physical Chemistry

2026numerical valuemedium

If the half life of a first order reaction is $6.93$ minutes then the time required for completion of $99$ % of the reaction will be _____ minutes.

(Given : $\log 2 = 0.3010$ )

Official previous-year question

Held on 5 Apr 2026 · Verified 6 Jul 2026.

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Solution

For a first-order reaction, the rate constant $k$ is given by:

$k = \dfrac{2.303 \log 2}{t_{1/2}}$

Using the standard approximation $2.303 \log 2 \approx 0.693$ :

$k = \dfrac{0.693}{6.93} = 0.1 \text{ min}^{-1}$

The time required for $99\%$ completion of the reaction is given by the integrated rate law:

$t = \dfrac{2.303}{k} \log \left( \dfrac{a}{a - x} \right)$

Here, the initial concentration $a = 100$ and the amount reacted $x = 99$ , so $a - x = 1$ .

$t = \dfrac{2.303}{0.1} \log \left( \dfrac{100}{1} \right)$

$t = 23.03 \times \log(10^2)$

$t = 23.03 \times 2 = 46.06 \text{ minutes}$

Answer: $46.06$

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JEE Main Physical Chemistry in other years

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JEE Main 2026 — Chemistry Physical Chemistry

2026numerical valuemedium

If the half life of a first order reaction is $6.93$ minutes then the time required for completion of $99$ % of the reaction will be _____ minutes.

(Given : $\log 2 = 0.3010$ )

Official previous-year question

Held on 5 Apr 2026 · Verified 6 Jul 2026.

Did you get this right?

Solution

For a first-order reaction, the rate constant $k$ is given by:

$k = \dfrac{2.303 \log 2}{t_{1/2}}$

Using the standard approximation $2.303 \log 2 \approx 0.693$ :

$k = \dfrac{0.693}{6.93} = 0.1 \text{ min}^{-1}$

The time required for $99\%$ completion of the reaction is given by the integrated rate law:

$t = \dfrac{2.303}{k} \log \left( \dfrac{a}{a - x} \right)$

Here, the initial concentration $a = 100$ and the amount reacted $x = 99$ , so $a - x = 1$ .

$t = \dfrac{2.303}{0.1} \log \left( \dfrac{100}{1} \right)$

$t = 23.03 \times \log(10^2)$

$t = 23.03 \times 2 = 46.06 \text{ minutes}$

Answer: $46.06$

Your note

JEE Main Physical Chemistry in other years

Keep practicing Physical Chemistry

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

Browse all Chemistry topics

JEE Main 2026 — Chemistry Physical Chemistry

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Answer

Solution

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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

JEE Main 2026 — Chemistry Physical Chemistry

Did you get this right?

Answer

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