Question

The decomposition of ${{H}_{2}}{{O}_{2}}$ is represented as:
${{H}_{2}}{{O}_{2}}\to {{H}_{2}}O+O\text{ (slow)}$
$(O)+(O)\to {{O}_{2}}\text{ (fast)}$
The order of the reaction is:
A. $1$
B. $2$
C. $0$
D. $3$

Answer 1

Hint: To know the order of the reaction, first of all try to figure out the rate determining step in the chemical reaction. Then use the formula of rate law to find out the order of the reaction.

Complete step by step solution:
Let us have some knowledge about rate law.
Rate laws or rate equations are mathematical expressions that describe the relationship between the rate of a chemical reaction and the reactants concentration. The rate law is given as:
$rate=\text{ k }\!\![\!\!\text{ A}{{\text{ }\!\!]\!\!\text{ }}^{x}}{{\text{ }\!\![\!\!\text{ B }\!\!]\!\!\text{ }}^{y}}$ , where
k is the rate constant,
[A] and [B] are the molar concentrations of the reactants and
x and y represents the reaction order.
Given that,
The decomposition of ${{H}_{2}}{{O}_{2}}$ is represented as:
${{H}_{2}}{{O}_{2}}\to {{H}_{2}}O+O\text{ (slow)}$
$(O)+(O)\to {{O}_{2}}\text{ (fast)}$
We have to find out the order of the reaction.
Generally, the overall reaction is determined by the slowest step and it is referred to as the rate determining step or rate limiting step. And here it has been already given which is the slow step. Thus, the first step of the reaction involving the decomposition of ${{H}_{2}}{{O}_{2}}$ is the rate determining step and the reaction is:
${{H}_{2}}{{O}_{2}}\to {{H}_{2}}O+O$
So, the rate law for this reaction can be shown as:
$Rate=\text{ k }\!\![\!\!\text{ }{{\text{H}}_{2}}{{O}_{2}}]$
We can see that the order of the reaction is one as the rate of reaction is dependent on the concentration of a single reactant ${{H}_{2}}{{O}_{2}}$ only.

Hence, the correct option is A.

Note: It is important to note that; the rate of a reaction is a vital property because it says whether a reaction can occur during a lifetime. The rate law says about the concentration of the reactants and the order of the reaction.