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

step 1 In this problem, we have to calculate half life for the decomposition of NO2, which is second -o

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 halflife of this reaction under these conditions?

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Key Concepts

Half-Life in Second Order Reactions

Unlike first order reactions, the half-life of a second order reaction depends on the initial concentration of the reactant. It is given by the formula t1/2 = 1/(k[A]0), meaning that the time required for the concentration to reduce to half its initial value increases as the initial concentration decreases and vice versa.

Integrated Rate Law for Second Order Reactions

The integrated rate law for a second order reaction relates the concentration of the reactant to time through the equation 1/[A]t = kt + 1/[A]0, where [A]0 is the initial concentration, [A]t is the concentration at time t, and k is the rate constant. This formulation is crucial for calculating the concentration of reactants at any given time in reactions that follow second order kinetics.

Second Order Reaction Kinetics

In second order reactions, the rate of reaction is proportional to the square of the concentration of a single reactant or the product of the concentrations of two reactants. This relationship is central to analyzing how such reactions progress over time and is used in writing and interpreting rate laws.

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