Ozone decomposes to oxygen according to the equation\({\bf{2}}{{\bf{O}}_{\bf{3}}}{\bf{(g)}} \to {\bf{3}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\). Write the equation that relates the rate expressions for this reaction in terms of the disappearance of\({{\bf{O}}_{\bf{3}}}\)and the formation of oxygen.

Rate is defined as the change in the concentration of reactant or product per unit of timeand is given by the following formula:

\({\bf{Rate of reaction = }}\frac{{{\bf{Change in concentration of reactant or product}}}}{{{\bf{Time taken}}}}\)

When the reactant is being used up in the reaction, it tends to disappear and is given by the following formula.

\({\bf{Rate of disapearance = }}\frac{{{\bf{Disapearance of reactant}}}}{{{\bf{Time taken}}}}\)

A negative sign denotes that the substance is used up in the reaction. Thus, while writing the rate of disappearance, negative sign is used.

Let us consider the following reaction:\({\bf{aA}} \to {\bf{bB}}\)

While writing the reaction with coefficients, the stoichiometric factor is considered. The rate of disappearance is written as follows for the given reaction:

\({\bf{Rate of disapearance = - }}\frac{{\bf{1}}}{{\bf{a}}}\frac{{{\bf{\Delta }}\left( {\bf{A}} \right)}}{{{\bf{\Delta t}}}}\)

The following reaction is given:

\({\bf{2}}{{\bf{O}}_{\bf{3}}}{\bf{(g)}} \to {\bf{3}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

The rate of disappearance is as follows:

\({\bf{Rate of disapearance of ozone = - }}\frac{{\bf{1}}}{{\bf{2}}}\frac{{{\bf{\Delta }}\left( {{{\bf{O}}_{\bf{3}}}} \right)}}{{{\bf{\Delta t}}}}\)