The reaction 2 NO2 ⟶2 NO+O2 has the rate constant k=0.63 M^-1 s^-1 . (a) Based on the units for

step 1 For this question, the units give away the order of the reaction. Because the units for K are 1

The reaction 2 NO2 ⟶2 NO+O2 has the rate constant k=0.63...

The reaction $2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2}$ has the rate constant $k=0.63 M^{-1} \mathrm{s}^{-1}$ . (a) Based on the units for $k,$ is the reaction first or second order in $\mathrm{NO}_{2} ?$ ? (b) If the initial concentration of $\mathrm{NO}_{2}$ is $0.100 \mathrm{M},$ how would you determine how long it would take for the concentration to decrease to 0.025 $\mathrm{M}$ ?

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Key Concepts

Reaction Order Determination via Rate Constant Units

The units of the rate constant are directly related to the order of the reaction. In general, for a reaction of order n, the units of k are M^(1-n) s^(-1). In the given reaction, k has units of M^-1 s^-1, which indicates that the reaction is second order overall. This relationship between k's units and the reaction order helps chemists deduce the reaction mechanism even if the stoichiometry might initially seem to suggest a different order.

Integrated Rate Law for Second Order Reactions

For a second order reaction, the concentration of the reactant as a function of time is given by the integrated rate law, 1/[A]_t = 1/[A]_0 + kt. This equation allows one to calculate the time required for the concentration of the reactant to decrease from an initial value [A]_0 to any later concentration [A]_t. By substituting the known concentrations and the given rate constant into the equation, one can solve for the reaction time.

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