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Question: The chemical reaction, \({\text{2}}{{\text{O}}_{\text{3}}} \to {\text{3}}{{\text{O}}_{\text{2}}}\) p...

The chemical reaction, 2O3→3O2{\text{2}}{{\text{O}}_{\text{3}}} \to {\text{3}}{{\text{O}}_{\text{2}}} proceeds as follows:
Step1: O3→O2 + O ......(Fast) Step2: O + O3→2O2 ......(Slow) \begin{gathered} {\text{Step1: }}{{\text{O}}_{\text{3}}} \to {{\text{O}}_{\text{2}}}{\text{ + O }}......{\text{(Fast)}} \\\ {\text{Step2: O + }}{{\text{O}}_{\text{3}}} \to 2{{\text{O}}_{\text{2}}}{\text{ }}......{\text{(Slow)}} \\\ \end{gathered}
The rate law expression should be:
A.r = k’[O3][O2]{\text{r = k'}}\left[ {{{\text{O}}_{\text{3}}}} \right]\left[ {{{\text{O}}_{\text{2}}}} \right]
B.r = k’[O3]2[O2]−1{\text{r = k'}}{\left[ {{{\text{O}}_{\text{3}}}} \right]^2}{\left[ {{{\text{O}}_{\text{2}}}} \right]^{ - 1}}
C.r = k’[O3]2{\text{r = k'}}{\left[ {{{\text{O}}_{\text{3}}}} \right]^2}
D.Unpredictable

Explanation

Solution

The chemical process in which one or more chemical reactants come together to form new products is known as chemical reaction. The mathematical expression used to describe the relation between the rate of reaction and the concentration of reactants is known as rate law expression.

Complete step by step answer:
A process in which one or more substances which are known as reactants come together to form new products via chemical process is known as a chemical reaction. The chemicals used in the reaction are known as reactants and the produced chemicals are known as products. To determine the speed of chemical reaction a new term ‘rate’ is defined. It determines the speed at which reactants are converted into products. The mathematical expression which describes the relation between the rate of reaction and the concentration of its reactant species is known as rate law expression. Sometimes rate law is called a differential rate law because it is derived from a mathematical differential method with respect to time.
The rate law expression for a chemical equation is written as follows:
rate = k[reactant1][reactant2]..........{\text{rate = k}}\left[ {{\text{reactant1}}} \right]\left[ {{\text{reactant2}}} \right]..........
This rate law depends upon the slow step of a reaction, and the other fast steps involved in the chemical reaction are involved to find relation between the concentration of species.
The slow step of the reaction is:
O + O3→2O2 {\text{O + }}{{\text{O}}_{\text{3}}} \to 2{{\text{O}}_{\text{2}}}{\text{ }}
r = k[O3][O]−−−−−−−−−−−−(1){\text{r = k}}\left[ {{{\text{O}}_{\text{3}}}} \right]\left[ {\text{O}} \right] - - - - - - - - - - - - (1)
The fast step of the reaction is:
O3→O2 + O {{\text{O}}_{\text{3}}} \to {{\text{O}}_{\text{2}}}{\text{ + O }}
For this reaction Keq = [O3][O2][O]{\text{Keq}}{\text{ = }}\dfrac{{{\text{[}}{{\text{O}}_{\text{3}}}{\text{][}}{{\text{O}}_{\text{2}}}{\text{]}}}}{{{\text{[O]}}}}
⇒  [O] = Keq[O3][O2]−−−−−−−−−−(2)\Rightarrow \;{\text{[O] = }}\dfrac{{{\text{Keq}}{\text{[}}{{\text{O}}_{\text{3}}}{\text{]}}}}{{{\text{[}}{{\text{O}}_{\text{2}}}{\text{]}}}} - - - - - - - - - - (2)
From eq(1) and eq(2)
r = kKeq[O3]2[O2]{\text{r = }}\dfrac{{{\text{kKeq}}{{{\text{[}}{{\text{O}}_{\text{3}}}{\text{]}}}^{\text{2}}}}}{{{\text{[}}{{\text{O}}_{\text{2}}}{\text{]}}}}
So we will introduce a new constant replacing the old ones.
r = k’[O3]2[O2] - 1{\text{r = k'}}{{\text{[}}{{\text{O}}_{\text{3}}}{\text{]}}^{\text{2}}}{{\text{[}}{{\text{O}}_{\text{2}}}{\text{]}}^{{\text{ - 1}}}}

Hence option (B) is correct.

Note: The reactions in which the product of one reaction becomes the reactant of another reaction are known as sequential reactions. These reactions play an important role in industrial processes. The slow step of the overall reaction is used to determine the rate of the reaction.