Question

Short answer

The reactions given below may have the same elementary reaction and overall reaction.

\(\begin{array}{l}{\rm{(b) PC}}{{\rm{l}}_3}{\rm{ + C}}{{\rm{l}}_{\rm{2}}}{\rm{ }} \to {\rm{ PC}}{{\rm{l}}_{\rm{5}}}\\{\rm{rate = }}k{\rm{(PC}}{{\rm{l}}_{\rm{3}}}{\rm{) (C}}{{\rm{l}}_{\rm{2}}}{\rm{)}}\\{\rm{(d) 2NO + }}{{\rm{O}}_{\rm{2}}}{\rm{ }} \to {\rm{ 2N}}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{{\rm{(NO)}}^{\rm{2}}}{\rm{(}}{{\rm{O}}_{\rm{2}}}{\rm{)}}\\{\rm{(e) NO + }}{{\rm{O}}_{\rm{3}}}{\rm{ }} \to {\rm{ N}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\end{array}\)

Step-by-step solution

Definition of Elementary Reaction

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.

\(\begin{array}{l}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ }}{{\rm{O}}_{\rm{2}}}{\rm{(g) + O}}\\{\rm{O + }}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ 2}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}}\end{array}\)

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.

Reactions that may have the same Elementary Reaction and 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.

\(\begin{array}{l}{\rm{(b) PC}}{{\rm{l}}_3}{\rm{ + C}}{{\rm{l}}_{\rm{2}}}{\rm{ }} \to {\rm{ PC}}{{\rm{l}}_{\rm{5}}}\\{\rm{rate = }}k{\rm{(PC}}{{\rm{l}}_{\rm{3}}}{\rm{) (C}}{{\rm{l}}_{\rm{2}}}{\rm{)}}\end{array}\)

\(\begin{array}{l}{\rm{(e) NO + }}{{\rm{O}}_{\rm{3}}}{\rm{ }} \to {\rm{ N}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\end{array}\)

The below reaction has a termolecular elementary reaction with the same overall reaction with a supporting rate equation for the reaction.

\(\begin{array}{l}{\rm{(d) 2NO + }}{{\rm{O}}_{\rm{2}}}{\rm{ }} \to {\rm{ 2N}}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{{\rm{(NO)}}^{\rm{2}}}{\rm{(}}{{\rm{O}}_{\rm{2}}}{\rm{)}}\end{array}\)

Reactions that may not have the same Elementary Reaction and Overall Reaction

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 \(\frac{3}{2}\).

\(\begin{array}{l}{\rm{(a) C}}{{\rm{l}}_2}{\rm{ + CO }} \to {\rm{ C}}{{\rm{l}}_2}{\rm{CO}}\\{\rm{rate = }}k{{\rm{(C}}{{\rm{l}}_2}{\rm{)}}^{\frac{3}{2}}}{\rm{(CO)}}\end{array}\)

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.

Thus, equations (b), (d), (e) may have the same elementary and overall reaction.