The Rate Law Question 1

When free $\ce{Cl(g)}$ atoms encounter $\ce{O3(g)}$ molecules in the upper atmosphere, the following reaction mechanism is proposed to occur.

\begin{array}{c c c} \ce{Cl(g) + O3(g) -> ClO(g) + O2(g)} & \textit{slow step} & \\ \ce{ClO(g) + O3(g) -> Cl(g) + 2O2(g)} & \textit{fast step} & \\ \hline \ce{2O3(g) -> 3O2(g)} & \textit{overall reaction} & \Delta H=\pu{-285 kJ/mol_{rxn}} \end{array}

Which of the following rate laws for the overall reaction corresponds to the proposed mechanism?

\text{Rate}=k[\ce{O3}]^2

\text{Rate}=k[\ce{Cl}][\ce{O3}]

\text{Rate}=k[\ce{ClO}][\ce{O3}]^2

\text{Rate} = k\dfrac{[\ce{O2}]^3}{[\ce{O3}]^2}

Approach

The rate law can be determined from the slowest step, which is known as the rate-determining step.

\ce{1Cl(g) + 1O3(g) -> ClO(g) + O2(g)}

In this step, 1 molecule of chlorine and 1 molecule of ozone react. We can use the coefficients of the reactants to write the rate law.

\text{Rate}=k[\ce{Cl}]^1[\ce{O3}]^1