The half-life of a first-order reaction is 6.93 minutes . The time required for the concentration of the reactant to drop from 0.4 M to 0.04 M is :

Step-by-step solution

First, calculate the rate constant ( k ) using the half-life formula for a first-order reaction: k = 0.693 t_ 1/2 k = 0.693 6.93 = 0.1 min ⁻¹ Next, use the integrated rate law to find the time ( t ) required for the concentration to drop from 0.4 M to 0.04 M : t = 2.303 k [A]₀ [A]_t t = 2.303 0.1 0.4 0.04 t = 23.03 (10) Since (10) = 1 : t = 23.03 min Answer: 23.03 min