The half-life for the first-order reaction: (aq) - (l) + 1/2 (g) is 30 min. If the volume of (g) collected is 100 ml after a long time, then the volume of (g) collected (at the same pressure and temp

Question

The half-life for the first-order reaction: $H_2O_2$(aq) -> $H_2O$(l) + 1/2 $O_2$(g) is 30 min. If the volume of $O_2$(g) collected is 100 ml after a long time, then the volume of $O_2$(g) collected (at the same pressure and temperature) after 60 min from the start of reaction is

Prashant Kotian · Accepted Answer

Correct answer: C. For the first-order decomposition of , the volume of collected at infinite time (V_inf) is ∝ the initial amount of reactant: V_inf ∝ a = 100 mL. After t = 60 min (2 × t_1/2), the fraction of reactant decomposed is 1 - (1/2)^2 = 3/4 = 75%. Since the volume of product is ∝ the amount decomposed: V_t = 0.75 × V_inf = 0.75 × 100 mL = 75 mL.

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