For a first order reaction, the rate of the reaction is measured at two different times. At t = 10 min, the rate is 0.04 mol L ⁻¹ min ⁻¹ , and at t = 20 min, the rate is 0.01 mol L ⁻¹ min ⁻¹ . The half-life of the reaction is ______ min.

Question

Quantrex Academy · Accepted Answer

Correct answer: 5

For a first order reaction, the rate r is directly proportional to the concentration of the reactant: r = k[A] . Let the concentrations at t₁ = 10 min and t₂ = 20 min be [A]₁ and [A]₂ , respectively. The ratio of the rates is: r₁ r₂ = k[A]₁ k[A]₂ = [A]₁ [A]₂ Given r₁ = 0.04 and r₂ = 0.01 , we have: [A]₁ [A]₂ = 0.04 0.01 = 4 Using the integrated rate law for a first order reaction: k = 1 t₂ - t₁ [A]₁ [A]₂ k = 1 20 - 10 4 = 1 10 (2^2) = 2 10 2 = 2 5 The half-life t_ 1/2 is given by: t_ 1/2 = 2 k = 2 2 5 = 5 min Answe

For a first order reaction, the rate of the reaction is measured at two different times. At t = 10 min, the rate is 0.04 mol L ⁻¹ min ⁻¹ , and at t = 20 min, the rate is 0.01 mol L ⁻¹ min ⁻¹ . The half-life of the reaction is ______ min.

Correct answer

Step-by-step solution

More from Chemical Kinetics