Question

Write the rate equation for each of the following elementary reactions:

\((a){\text{ }}{O_3}{\text{ }}\underrightarrow {sunlight}{\text{ }}{O_2}{\text{ }} + {\text{ }}O\).

\(\begin{array}\(b){\rm{ }}{O_3}{\rm{ }} + {\rm{ }}Cl{\rm{ }} \to {\rm{ }}{O_2}{\rm{ }} + {\rm{ }}ClO\\(c){\rm{ }}ClO{\rm{ }} + {\rm{ }}O{\rm{ }} \to {\rm{ }}Cl{\rm{ }} + {\rm{ }}{O_2}\\(d){\rm{ }}{O_3}{\rm{ }} + {\rm{ }}NO{\rm{ }} \to {\rm{ }}N{O_2}{\rm{ }} + {\rm{ }}{O_2}\\(e){\rm{ }}N{O_2}{\rm{ }} + {\rm{ }}O{\rm{ }} \to {\rm{ }}NO{\rm{ }} + {\rm{ }}{O_2}\end{array}\)

Short answer

The rate equations for the following elementary reactions are:

\((a){\text{ }}{O_3}{\text{ }}\underrightarrow {sunlight}{\text{ }}{O_2}{\text{ }} + {\text{ }}O\)

\({\bf{rate = k[}}{{\bf{O}}_{\bf{3}}}{\bf{]}}\)

\(\begin{align}{\bf{(b) }}{{\bf{O}}_{\bf{3}}}{\bf{ + Cl }} \to {\bf{ }}{{\bf{O}}_{\bf{2}}}{\bf{ + ClO}}\\{\bf{rate = k(}}{{\bf{O}}_{\bf{3}}}{\bf{)(Cl)}}\end{align}\)

\(\begin{align}{\bf{(c) ClO + O }} \to {\bf{ Cl + }}{{\bf{O}}_{\bf{2}}}\\{\bf{rate = k(ClO)(O)}}\end{align}\)

\(\begin{align}{\bf{(d) }}{{\bf{O}}_{\bf{3}}}{\bf{ + NO }} \to {\bf{ N}}{{\bf{O}}_{\bf{2}}}{\bf{ + }}{{\bf{O}}_{\bf{2}}}\\{\bf{rate = k(}}{{\bf{O}}_{\bf{3}}}{\bf{)(NO)}}\end{align}\)

\(\begin{align}{\bf{(e) N}}{{\bf{O}}_{\bf{2}}}{\bf{ + O }} \to {\bf{ NO + }}{{\bf{O}}_{\bf{2}}}\\{\bf{rate = k(N}}{{\bf{O}}_{\bf{2}}}{\bf{)(O)}}\end{align}\)

Step-by-step solution

Definition of Rate Equation

The rate equation is the mathematical expression which explains the the relationship between the rate of a chemical reaction and the concentration of its reactants.

\({\bf{rate = k(A}}{{\bf{)}}^{\bf{x}}}{{\bf{(B)}}^{\bf{y}}}{{\bf{(C)}}^{\bf{z}}}.....\)

Where,

(A), (B), and (C) denotes the molar concentrations of reactants.

kis the rate constant.

Exponents m, n, and pare generally positive integers.

Rate Equations for the Elementary Reactions    

For the elementary reaction (a), the reaction is first order with respect to \({{\rm{O}}_{\rm{3}}}\), thus the rate equation will be:

\((a){\text{ }}{O_3}{\text{ }}\underrightarrow {sunlight}{\text{ }}{O_2}{\text{ }} + {\text{ }}O\)

\({\bf{rate = k[}}{{\bf{O}}_{\bf{3}}}{\bf{]}}\)

For the elementary reaction (b), the reaction is first order with respect to\({{\rm{O}}_{\rm{3}}}\) and \({\rm{Cl}}\)thus the rate equation will be:

\(\begin{align}{\bf{(b) }}{{\bf{O}}_{\bf{3}}}{\bf{ + Cl }} \to {\bf{ }}{{\bf{O}}_{\bf{2}}}{\bf{ + ClO}}\\{\bf{rate = k(}}{{\bf{O}}_{\bf{3}}}{\bf{)(Cl)}}\end{align}\)

For the elementary reaction (c), the reaction is first order with respect to \({\rm{ClO}}\) and \({\rm{O}}\)thus the rate equation will be:

\(\begin{align}{\bf{(c) ClO + O }} \to {\bf{ Cl + }}{{\bf{O}}_{\bf{2}}}\\{\bf{rate = k(ClO)(O)}}\end{align}\)

For the elementary reaction (d), the reaction is first order with respect to \({{\rm{O}}_{\rm{3}}}\) and \({\rm{NO}}\)thus the rate equation will be:

\(\begin{align}{\bf{(d) }}{{\bf{O}}_{\bf{3}}}{\bf{ + NO }} \to {\bf{ N}}{{\bf{O}}_{\bf{2}}}{\bf{ + }}{{\bf{O}}_{\bf{2}}}\\{\bf{rate = k(}}{{\bf{O}}_{\bf{3}}}{\bf{)(NO)}}\end{align}\)

For the elementary reaction (e), the reaction is first order with respect to \({\rm{N}}{{\rm{O}}_2}\) and \({\rm{O}}\)thus the rate equation will be:

\(\begin{align}{\bf{(e) N}}{{\bf{O}}_{\bf{2}}}{\bf{ + O }} \to {\bf{ NO + }}{{\bf{O}}_{\bf{2}}}\\{\bf{rate = k(N}}{{\bf{O}}_{\bf{2}}}{\bf{)(O)}}\end{align}\)