The time taken for 90% of a 1st order reaction to complete is approximately

Explanation

For first-order reactions, the time it takes for the reactant concentration to decrease to 10% of its initial value (90% completion) is approximately 3.3 times the half-life.Here's why:First-order reaction kinetics:The rate of a first-order reaction is directly proportional to the remaining reactant concentration. This can be expressed by the following equation:rate = k * [A]where:rate is the rate of the reactionk is the rate constant[A] is the concentration of the reactantThis means that as the reaction progresses, the reactant concentration decreases, leading to a slower reaction rate.Half-life:The half-life (t₁/₂ ) of a first-order reaction is the time it takes for the reactant concentration to decrease to half its initial value. It can be calculated using the following equation:t₁/₂ = ln(2) / kTime for 90% completion:To determine the time (t₉₀) it takes for the reactant concentration to reach 10% of its initial value, we can use another equation derived from the first-order rate law:t₉₀ = (2.303 log 10) / k ≈ 3 * t₁/₂Therefore, the time for 90% completion is approximately 3.3 times the half-life of a first-order reaction.