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Chemistry Question on p -Block Elements

The process of conversion of ozone into oxygen (2O3⟶3O2)\left(2O_{3} \longrightarrow 3O_{2}\right) involves following steps O3<=>[ Fast ]O2+OO _{3} {<=>[{\text { Fast }}]} O _{2}+ O O+O3−>[ Slow ]2O2O + O _{3} {->[{\text { Slow }}]} 2 O _{2} The rate law expression for this process is

A

r=k[O3]2r=k{{[{{O}_{3}}]}^{2}}

B

r=k[O3]2[O2]−1r=k{{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-1}}

C

r=k[O3][O2]r=k[{{O}_{3}}][{{O}_{2}}]

D

r=k[O3]2[O2]−3r=k{{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-3}}

Answer

r=k[O3]2[O2]−1r=k{{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-1}}

Explanation

Solution

O3<=>[ Fast ]O2+OO _{3} {<=>[{\text { Fast }}]} O _{2}+ O
O+O3−>[ Slow ]2O2O + O _{3} {->[{\text { Slow }}]} 2 O _{2}
From equation (i)
Kc=[O2][O][O3]K_{c}=\frac{\left[ O _{2}\right][ O ]}{\left[ O _{3}\right]}
or [O]=Kc[O3][O2][ O ] =\frac{K_{ c }\left[ O _{3}\right]}{\left[ O _{2}\right]}
Rate =k[O3][O]=k\left[ O _{3}\right][ O ]
=k[O3].Kc[O3][O2]=k\left[ O _{3}\right] . \frac{K_{c}\left[ O _{3}\right]}{\left[ O _{2}\right]}
=k′[O3]2[O2]−1=k^{'}\left[ O _{3}\right]^{2}\left[ O _{2}\right]^{-1}