Question
For a reaction, $$2NO + 2{H_2} \to {N_2} + 2{H_2}O,$$ the possible mechanism is
\[\begin{align}
& 2NO\rightleftharpoons {{N}_{2}}{{O}_{2}} \\
& {{N}_{2}}{{O}_{2}}+{{H}_{2}}\xrightarrow{\text{slow}}{{N}_{2}}O+{{H}_{2}}O \\
& {{N}_{2}}O+{{H}_{2}}\xrightarrow{\text{fast}}{{N}_{2}}+{{H}_{2}}O \\
\end{align}\]
What is the rate law and order of the reaction?
A.
$${\text{Rate}} = \left[ {{N_2}{O_2}} \right],{\text{order}} = 1$$
B.
$${\text{Rate}} = \left[ {{N_2}{O_2}} \right]\left[ {{H_2}} \right],{\text{order}} = 2$$
C.
$${\text{Rate}} = {\left[ {{N_2}{O_2}} \right]^2},{\text{order}} = 2$$
D.
$${\text{Rate}} = {\left[ {{N_2}{O_2}} \right]^2}\left[ {{H_2}} \right],{\text{order}} = 3$$
Answer :
$${\text{Rate}} = \left[ {{N_2}{O_2}} \right]\left[ {{H_2}} \right],{\text{order}} = 2$$
Solution :
The slowest step of the reaction is rate determining step.
$$\eqalign{
& {N_2}{O_2} + {H_2} \to {N_2}O + {H_2}O \cr
& {\text{Rate of reaction}} = \left[ {{N_2}{O_2}} \right]\left[ {{H_2}} \right] \cr
& {\text{Hence, order of reaction}} = 2 \cr} $$