It takes 15.4 minutes for the concentration of a reactant to...

It takes 15.4 minutes for the concentration of a reactant to drop to $5.0 \%$ of its initial value in a second-order reaction. What is the rate constant for the reaction in the units of $\mathrm{L} \mathrm{mol}^{-1} \min ^{-1}$ ?

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Key Concepts

Rate Constant and Units

The rate constant, denoted by k, quantifies the speed of a chemical reaction under given conditions. For a second-order reaction, the rate constant has units of L mol?¹ min?¹ (when time is measured in minutes), and its magnitude helps predict how quickly the reactant concentrations change over time.

Second-Order Kinetics

Second-order kinetics refers to reaction mechanisms where the rate is proportional to either the square of the concentration of one reactant or the product of the concentrations of two reactants. This overall reaction order impacts both the mathematical form of the rate law and how the reaction's progress is analyzed using integrated rate laws.

Integrated Rate Law for Second-Order Reactions

The integrated rate law for a second-order reaction is given by the equation 1/[A] = 1/[A?] + kt, where [A?] is the initial concentration, [A] is the concentration at time t, k is the rate constant, and t is time. This equation is fundamental for analyzing reaction kinetics and determining the rate constant from experimental data.

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