Question

Write the rate laws for the following elementary reactions. a. \(\mathrm{CH}_{3} \mathrm{NC}(g) \rightarrow \mathrm{CH}_{3} \mathrm{CN}(g)\) b. \(\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{NO}_{2}(g)\) c. \(\mathrm{O}_{3}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\) d. \(\mathrm{O}_{3}(g)+\mathrm{O}(g) \rightarrow 2 \mathrm{O}_{2}(g)\)

Short answer

a. Rate law: \(Rate = k[\mathrm{CH}_{3}\mathrm{NC}]\) b. Rate law: \(Rate = k[\mathrm{O}_{3}][\mathrm{NO}]\) c. Rate law: \(Rate = k[\mathrm{O}_{3}]\) d. Rate law: \(Rate = k[\mathrm{O}_{3}][\mathrm{O}]\)

Step-by-step solution

a. Rate law for $\mathrm{CH}_{3} \mathrm{NC}(g) \rightarrow \mathrm{CH}_{3} \mathrm{CN}(g)

Since this is an elementary reaction involving only one reactant, the rate law can be written as follows: Rate = k[\(\mathrm{CH}_{3} \mathrm{NC}\)] where k is the rate constant, and the concentration of the reactant is raised to the power of 1 because there is only one molecule involved in the reaction.

b. Rate law for \(\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{NO}_{2}(g)\)

This reaction involves two reactants, both with a stoichiometric coefficient of 1. The rate law for this elementary reaction is: Rate = k[\(\mathrm{O}_{3}\)][\(\mathrm{NO}\)] Again, the concentrations of each reactant are raised to the power of 1 because both reactants have a stoichiometric coefficient of 1 according to the chemical equation.

c. Rate law for \(\mathrm{O}_{3}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\)

In this elementary reaction, there is only one reactant, ozone. The stoichiometric coefficient of ozone is 1, so the rate law can be expressed as: Rate = k[\(\mathrm{O}_{3}\)] The concentration of the reactant, ozone, is raised to the power of 1 because there is only one molecule involved in the reaction.

d. Rate law for \(\mathrm{O}_{3}(g)+\mathrm{O}(g) \rightarrow 2 \mathrm{O}_{2}(g)\)

This reaction involves two reactants, \(\mathrm{O}_{3}\) and \(\mathrm{O}\), each with stoichiometric coefficients of 1 in the chemical equation. Thus, the rate law for this elementary reaction is: Rate = k[\(\mathrm{O}_{3}\)][\(\mathrm{O}\)] The concentrations of both reactants are raised to the power of 1 because each reactant has a stoichiometric coefficient of 1.