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

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.

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:

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