JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Chemical Kinetics

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In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are

t_{1}

and

t_{2} (s)

, respectively. The ratio

t_{1} / t_{2}

will :

(A) $\frac{4}{3}$
(B) $\frac{3}{2}$
(C) $\frac{3}{4}$
(D) $\frac{2}{3}$ ✓ Correct

Answer: (D)

Solution

A first order reaction follows

t = \frac{1}{k} ln \frac{[ A ] _{0}}{[ A ]}

. Falling to one fourth of the initial concentration needs

t_{1} = \frac{1}{k} ln 4 = \frac{2 ln 2}{k}

, while falling to one eighth needs

t_{2} = \frac{1}{k} ln 8 = \frac{3 ln 2}{k}

. Dividing one by the other, the ratio

\frac{t _{1}}{t _{2}}

equals

\frac{2}{3}

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option

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