At 330^∘ C, the rate constant for the decomposition of NO2 is 0.775 L /(mol ·s) . If the reacti

step 1 Because this reaction is second order, we can then use the second order integrated rate law to c

At 330^∘ C, the rate constant for the decomposition of NO2...

At $330^{\circ} \mathrm{C}$, the rate constant for the decomposition of $\mathrm{NO}_{2}$ is $0.775 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s}) .$ If the reaction is second order, what is the concentration of $\mathrm{NO}_{2}$ after $2.5 \times 10^{2}$ seconds if the starting concentration was $0.050 M ?$ What is the half-life of this reaction under these conditions?

Key Concepts

Half-Life of a Second Order Reaction

The half-life of a second order reaction depends on the initial concentration of the reactant and is given by t?/? = 1/(k[A]?). This contrasts with first order reactions where the half-life is independent of the initial concentration. In second order kinetics, as the initial concentration increases, the half-life decreases, making it a dynamic measure of how quickly the concentration of the reactant is reduced by half.

Rate Constant in Kinetics

The rate constant (k) is a proportionality factor in the rate law that provides information about the speed of a reaction. For second order reactions, the units of the rate constant are typically L/(mol·s), reflecting the dependence on the square of the concentration. The magnitude of k is influenced by factors such as temperature and activation energy.

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 relationship allows for the calculation of the concentration of the reactant at any given time during the reaction.

Second Order Reaction Kinetics

In a second order reaction, the rate of the reaction is proportional to the square of the concentration of one reactant or to the product of the concentrations of two reactants. This means that as the reactant concentration decreases, the rate of the reaction drops off more significantly compared to first order reactions, and the kinetics exhibit a nonlinear relationship between concentration and time.

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