JEE Main 2026 — Chemistry Physical Chemistry

2026mcqeasy

An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text {th }}$ and $\left(\frac{1}{10}\right)^{\text {th }}$ of its initial concentration are $\mathrm{t}_{1 / 8}$ and $\mathrm{t}_{1 / 10}$ respectively. What is the value of $\frac{\mathrm{t}_{1 / 8}}{\mathrm{t}_{1 / 10}} \times 10$ ? ( $\log 2=0.3$ )

Official previous-year question

Held on 28 Jan 2026 · Verified 6 Jul 2026.

Options

A
3
B
9
C
0.9
D
30

Did you get this right?

Solution

For first-order decomposition with rate equation $[A] = [A]_0 e^{-kt}$ , the time for concentration to reduce to fraction f is: $t = \frac{1}{k}\ln\frac{1}{f} = \frac{\ln(1/f)}{k}$

For reduction to 1/8: $t_{1/8} = \frac{\ln 8}{k} = \frac{3\ln 2}{k}$

For reduction to 1/10: $t_{1/10} = \frac{\ln 10}{k}$

Therefore: $\frac{t_{1/8}}{t_{1/10}} = \frac{\ln 8}{\ln 10} = \frac{3\log 2}{\log 10} = \frac{3 \times 0.3}{1} = 0.9$

Thus: $\frac{t_{1/8}}{t_{1/10}} \times 10 = 0.9 \times 10 = 9$

Your note

JEE Main Physical Chemistry in other years

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JEE Main 2026 — Chemistry Physical Chemistry

2026mcqeasy

Official previous-year question

Held on 28 Jan 2026 · Verified 6 Jul 2026.

Options

A
3
B
9
C
0.9
D
30

Did you get this right?

Solution

For first-order decomposition with rate equation $[A] = [A]_0 e^{-kt}$ , the time for concentration to reduce to fraction f is: $t = \frac{1}{k}\ln\frac{1}{f} = \frac{\ln(1/f)}{k}$

For reduction to 1/8: $t_{1/8} = \frac{\ln 8}{k} = \frac{3\ln 2}{k}$

For reduction to 1/10: $t_{1/10} = \frac{\ln 10}{k}$

Therefore: $\frac{t_{1/8}}{t_{1/10}} = \frac{\ln 8}{\ln 10} = \frac{3\log 2}{\log 10} = \frac{3 \times 0.3}{1} = 0.9$

Thus: $\frac{t_{1/8}}{t_{1/10}} \times 10 = 0.9 \times 10 = 9$

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

Options

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

JEE Main 2026 — Chemistry Physical Chemistry

Options

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