Question

For a reaction, $2NO + 2{H_2} \to {N_2} + 2{H_2}O$, the possible mechanism is $2NO \rightleftharpoons {N_2}{O_2}$
${N_2}{O_2} + {H_2}\xrightarrow{{slow}}{N_2}O + {H_2}O$
${N_2}{O_2} + {H_2}\xrightarrow{{fast}}{N_2} + {H_2}O$
What is the rate law and order of the reaction?
A. $Rate = \left[ {{N_2}{O_2}} \right],order = 1$
B. $Rate = \left[ {{N_2}{O_2}} \right]\left[ {{H_2}} \right],order = 2$
C. $Rate = {\left[ {{N_2}{O_2}} \right]^2},order = 2$
D. $Rate = {\left[ {{N_2}{O_2}} \right]^2}\left[ {{H_2}} \right],order = 3$

Answer 1

Hint: We can calculate the order of reaction with respect to reactants by using the rate law expression. The rate law expression for the reaction determines the order of the reaction. We have to know that the order of a chemical reaction is defined with the support of concentrations of reactants and not with concentrations of products.

Complete step by step answer:
We have to know that reaction order specifies the number of species whose concentration directly influences the rate of reaction. The order of reaction is dependent on the stoichiometric coefficients analogous to each species in the balanced reaction.
We know that order of the chemical reaction is a summation of the power of concentration of reactants present in the expression of rate law.
For a reaction, $xA + yB\xrightarrow{{}}P$
The rate expression is written as,
Rate = $k{\left[ A \right]^x}{\left[ B \right]^y}$
By summing up the power of the concentration of reactants we give the order of the reaction.
Order = \[x + y\]
The exponents x and y signifies the orders of the reactions. The order of the reaction is usually a small positive integer. The total of the orders of the reaction is known as the overall order of the reaction.
The given reaction is,
$2NO + 2{H_2} \to {N_2} + 2{H_2}O$
The mechanism of the reaction is,
${N_2}{O_2} + {H_2}\xrightarrow{{slow}}{N_2}O + {H_2}O$
${N_2}{O_2} + {H_2}\xrightarrow{{fast}}{N_2} + {H_2}O$
Generally, the rate determining step is the slowest step of the reaction. In the given reaction, the rate determining step is,
${N_2}{O_2} + {H_2}\xrightarrow{{slow}}{N_2}O + {H_2}O$
Therefore, the rate law expression for the given reaction is,
$Rate = \left[ {{N_2}{O_2}} \right]\left[ {{H_2}} \right]$
The rate of the reaction is $k = \left[ {{N_2}{O_2}} \right]\left[ {{H_2}} \right]$ and we can see the power of the reactant concentration $\left[ {{N_2}{O_2}} \right]$ is one. The power of the reactant concentration $\left[ {{H_2}} \right]$ is one. So, the order of the reaction is 2.

Therefore, the option B is correct.

Note: We have to know that the order of a chain reaction could be restructured with the help of steady state rough calculation for the concentration of reactive intermediates like free radicals. We have to know that the order of a chemical reaction would also be fraction. Such reactions are called fractional order reactions.