The rate constant of a reaction has the unit min ⁻¹ . It takes 45 min for the concentration of the reactant to drop from 0.64 mol L ⁻¹ to 0.08 mol L ⁻¹ . What will be the concentration of the reactant remaining after 60 min from the start of the reaction?

Step-by-step solution

The unit of the rate constant ( min ⁻¹ ) indicates that it is a first-order reaction. The concentration drops from 0.64 mol L ⁻¹ to 0.08 mol L ⁻¹ . [ A ]₀ [ A ]_t = 0.64 0.08 = 8 = 2^3 This means 3 half-lives have elapsed in 45 min . 3 t_ 1/2 = 45 min t_ 1/2 = 15 min We need to find the concentration after 60 min from the start. Number of half-lives in 60 min = 60 15 = 4 The remaining concentration after 4 half-lives is: [ A ] = [ A ]₀ 2^4 = 0.64 16 = 0.04 mol L ⁻¹ Note that 0.60 mol L ⁻¹ is the amount of reactant