Question

Atomic chlorine in the atmosphere reacts with ozone in the following pair of elementary reactions:

\({\bf{Cl + \;O3}}\left( {\bf{g}} \right){\bf{ - - - ClO}}\left( {\bf{g}} \right){\bf{ + \;O2}}\left( {\bf{g}} \right)\)(rate constant k₁ )

\({\bf{ClO}}\left( {\bf{g}} \right){\bf{ + O - - - Cl}}\left( {\bf{g}} \right){\bf{ + \;O2}}\left( {\bf{g}} \right)\)(rate constant k₂ )

Determine the overall reaction, write the rate law expression for each elementary reaction, identify any intermediates, and determine the overall rate law expression.

Short answer

Overall reaction: \({{\bf{O}}_{\bf{3}}}\left( {\bf{g}} \right){\bf{ + O - - - - O2\;}}\left( {\bf{g}} \right)\)

\(\begin{aligned}{}{\bf{Rate1 = }}{{\bf{k}}_{\bf{1}}}{\bf{(}}{{\bf{O}}_{\bf{3}}}{\bf{)}}\left( {{\bf{Cl}}} \right){\bf{;}}\\{\bf{Rate2 = }}{{\bf{k}}_{\bf{2}}}\left( {{\bf{ClO}}} \right)\left( {\bf{O}} \right)\\{\bf{Intermediate: ClO}}\left( {\bf{g}} \right)\\{\bf{Overall rate = }}{{\bf{k}}_{\bf{2}}}{{\bf{k}}_{\bf{1}}}{\bf{(}}{{\bf{O}}_{\bf{3}}}\left) {\left( {{\bf{Cl}}} \right)} \right({\bf{O)}}{\bf{.}}\end{aligned}\)

Step-by-step solution

Rate of a Reaction

The rate of reaction may be defined as the speed of the reactant reacting to obtain a product in a particular reaction at a particular time. The concentration of the reactant and product are represented into mole/L.

Rate Law

The rate law or rate equation for a chemical reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants.

\({\bf{Rate = k}}{\left( {\bf{A}} \right)^{\bf{m}}}{\left( {\bf{B}} \right)^{\bf{n}}}\)

Explanation

\(\begin{aligned}{}{\bf{Cl + \;}}{{\bf{O}}_{\bf{3}}}\left( {\bf{g}} \right){\bf{ - - - ClO}}\left( {\bf{g}} \right){\bf{ + }}{{\bf{O}}_{\bf{2}}}{\bf{\;}}\left( {\bf{g}} \right){\bf{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\{\bf{ClO}}\left( {\bf{g}} \right){\bf{ + O - - - Cl}}\left( {\bf{g}} \right){\bf{ + \;}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right)\end{aligned}\) \(\)

Overall Reaction:

\({{\bf{O}}_{\bf{3}}}\left( {\bf{g}} \right){\bf{ + O - - - - O2\;}}\left( {\bf{g}} \right)\) \(\)

\({\bf{Overall rate = }}{{\bf{k}}_{\bf{2}}}{{\bf{k}}_{\bf{1}}}{\bf{(}}{{\bf{O}}_{\bf{3}}}\left) {\left( {{\bf{Cl}}} \right)} \right({\bf{O)}}{\bf{.}}\)

Reaction 1:

\({\bf{Cl + \;O3}}\left( {\bf{g}} \right){\bf{ - - - ClO}}\left( {\bf{g}} \right){\bf{ + \;O2}}\left( {\bf{g}} \right)\)

\({\bf{Rate1 = }}{{\bf{k}}_{\bf{1}}}{\bf{(}}{{\bf{O}}_{\bf{3}}}{\bf{)}}\left( {{\bf{Cl}}} \right)\)

Reaction 2:

\({\bf{ClO}}\left( {\bf{g}} \right){\bf{ + O - - - Cl}}\left( {\bf{g}} \right){\bf{ + \;O2}}\left( {\bf{g}} \right)\)

\({\bf{Rate2 = }}{{\bf{k}}_{\bf{2}}}\left( {{\bf{ClO}}} \right)\left( {\bf{O}} \right)\)

The intermediate stable product of a chemical reaction that is then used as a starting material for another reaction.

\({\bf{Intermediate: ClO}}\left( {\bf{g}} \right)\)