The rate of a first-order reaction is 0.04 mol litre^-1 s^-1 at 10 minutes and 0.03 mol litre^-1 s^-1 at 22 minute after initiation. The half-life of the reaction (in seconds) is (ln 2 = 0.7, ln 3 = 1

Question

The rate of a first-order reaction is 0.04 mol litre^-1 s^-1 at 10 minutes and 0.03 mol litre^-1 s^-1 at 22 minute after initiation. The half-life of the reaction (in seconds) is (ln 2 = 0.7, ln 3 = 1.1)

Prashant Kotian · Accepted Answer

Correct answer: 1680. For a first-order reaction, Rate ∝ [A]. Ratio of rates = Ratio of concentrations: A1/A2 = 0.04 / 0.03 = 4/3. Time difference Δt = 12 min = 720 s. k × Δt = ln(A1/A2) => k × 720 = ln(4/3) = 2 ln 2 - ln 3 = 1.4 - 1.1 = 0.3. Thus, k = 0.3 / 720 s^-1. Half-life t1/2 = ln 2 / k = 0.7 / (0.3 / 720) = 720 × (7/3) = 1680 s. Therefore, correct answer is 1680.

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