Given the following reactions and the corresponding rate laws, in which of the reactions might the elementary reaction and the overall reaction be the same?\(\begin{aligned}{\rm{(a) C}}{{\rm{l}}_2}{\rm{ + CO }} \to {\rm{ C}}{{\rm{l}}_2}{\rm{CO}}\\{\rm{rate = }}k{{\rm{(C}}{{\rm{l}}_2}{\rm{)}}^{\frac{3}{2}}}{\rm{(CO)}}\\{\rm{(b) PC}}{{\rm{l}}_3}{\rm{ + C}}{{\rm{l}}_{\rm{2}}}{\rm{ }} \to {\rm{ PC}}{{\rm{l}}_{\rm{5}}}\\{\rm{rate = }}k{\rm{(PC}}{{\rm{l}}_{\rm{3}}}{\rm{) (C}}{{\rm{l}}_{\rm{2}}}{\rm{)}}\\{\rm{(c) 2NO + }}{{\rm{H}}_{\rm{2}}}{\rm{ }} \to {\rm{ }}{{\rm{N}}_{\rm{2}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}}{\rm{O}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{H}}_{\rm{2}}}{\rm{)}}\\{\rm{(d) 2NO + }}{{\rm{O}}_{\rm{2}}}{\rm{ }} \to {\rm{ 2N}}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{{\rm{(NO)}}^{\rm{2}}}{\rm{(}}{{\rm{O}}_{\rm{2}}}{\rm{)}}\\{\rm{(e) NO + }}{{\rm{O}}_{\rm{3}}}{\rm{ }} \to {\rm{ N}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\end{aligned}\)

Chemical reactions generally occur in steps. Every step which occurs in the reaction mechanism is called the elementary reaction. For example, the decomposition of ozone occurs in a two-step mechanism.\(\begin{aligned}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ }}{{\rm{O}}_{\rm{2}}}{\rm{(g) + O}}\\{\rm{O + }}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ 2}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}}\end{aligned}\)The elementary steps combine to give the overall reaction, for the above decomposition of ozone, the overall reaction would be,\({\rm{2}}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ 3}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}}\)An elementary reaction can also be an overall reaction.

The below reactions have mechanisms involving a single bimolecular elementary reaction with the same overall reaction with a supporting rate equation for the reaction.\(\begin{aligned}{\rm{(b) PC}}{{\rm{l}}_3}{\rm{ + C}}{{\rm{l}}_{\rm{2}}}{\rm{ }} \to {\rm{ PC}}{{\rm{l}}_{\rm{5}}}\\{\rm{rate = }}k{\rm{(PC}}{{\rm{l}}_{\rm{3}}}{\rm{) (C}}{{\rm{l}}_{\rm{2}}}{\rm{)}}\end{aligned}\)\(\begin{aligned}{\rm{(e) NO + }}{{\rm{O}}_{\rm{3}}}{\rm{ }} \to {\rm{ N}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\end{aligned}\)The below reaction has a termolecular elementary reaction with the same overall reaction with a supporting rate equation for the reaction.\(\begin{aligned}{\rm{(d) 2NO + }}{{\rm{O}}_{\rm{2}}}{\rm{ }} \to {\rm{ 2N}}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{{\rm{(NO)}}^{\rm{2}}}{\rm{(}}{{\rm{O}}_{\rm{2}}}{\rm{)}}\end{aligned}\)

In the below reaction, the overall reaction cannot be an elementary reaction as from the given rate equation, it is highly doubtful to calculate the concentration with power raised to \(\frac{3}{2}\).\(\begin{aligned}{\rm{(a) C}}{{\rm{l}}_2}{\rm{ + CO }} \to {\rm{ C}}{{\rm{l}}_2}{\rm{CO}}\\{\rm{rate = }}k{{\rm{(C}}{{\rm{l}}_2}{\rm{)}}^{\frac{3}{2}}}{\rm{(CO)}}\end{aligned}\)In the below reaction, the overall reaction cannot be an elementary reaction as the given rate equation is different and should have been \({\rm{rate = }}k{{\rm{(NO)}}^2}{\rm{(}}{{\rm{H}}_{\rm{2}}}{\rm{)}}\)for both elementary and overall reaction to be the same. \(\begin{aligned}{\rm{(c) 2NO + }}{{\rm{H}}_{\rm{2}}}{\rm{ }} \to {\rm{ }}{{\rm{N}}_{\rm{2}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}}{\rm{O}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{H}}_{\rm{2}}}{\rm{)}}\end{aligned}\)Thus, equations (b), (d), (e) may have the same elementary and overall reaction.