Question

Mechanism of a hypothetical reaction ${X_2} + {Y_2} \to 2XY$ is given below:
I. \[{X_2} \rightleftharpoons X + X\] (Fast)
ii. $X + {Y_2} \to XY + Y$ (slow)
iii. $X + Y \to XY$ (Fast)
The overall order of the reaction will be:
A. $1.5$
B. $1$
C. $2$
D. $0$

Answer 1

Hint:Chemical substances do the reaction with each other and form a new product. During the reaction. To become stable every element donates or accepts a pair of electrons. Some reactions are very fast and some are slow.

Complete step by step answer:
Before finding the order of reaction, let's have a look at some point of the chemical reaction.
Hypothetical reaction - A reaction represented by any symbol that is known as the hypothetical reaction. The symbols like $A,B,X,Y$ , etc.
Fast reaction - A reaction in which reactants react within a time and produce a product is known as a fast reaction.
Slow reaction - A reaction in which the reactant takes time to react is known as a slow reaction.
Here, we have given a hypothetical representation of reaction that is in three steps fast, slow, and fast.
Now, find the order of the reaction.
The rate of reaction is $r$ =$K{[{x_2}]^a}{[{y_2}]^b}$ -equation 1
Now, find the value of $a,b$.
The rate of reaction is always in the slow step. So, using step 2 that is $X + {Y_2} \to XY + Y$, so the rate of reaction of this equation.
$r$ =$K[x][{y_2}]$ - equation 2
find the rate of reaction in terms of ${x_2}$.
Now, write the ${K_{eq}}$ (equilibrium) of step 1 that is \[{X_2} \rightleftharpoons X + X\].
${K_{eq}}$ =\[\dfrac{{[x][x]}}{{[{x_2}]}}\] =$\dfrac{{{{[x]}^2}}}{{[{x_2}]}}$
=> $[x]$ =${({K_{eq}}[{x_2}])^{1/2}}$
Now, this value in equation 2.
$r$ =\[K{({K_{eq}}[{x_2}])^{1/2}}{[{y_2}]^1})\]
=\[K.{K_{eq}}^{1/2}{[{x_2}]^{1/2}}{[{y_2}]^1}\] here, let $K.{K_{eq}}^{1/2}$ =$K$
so, $r$ =$K{[{x_2}]^{1/2}}{[{y_2}]^1}$
Here, we got the rate of reaction in the format of equation 1, so using the value of $a,b$ . We can find the order of the reaction.
Now, the order of the reaction is $\dfrac{1}{2} + 1$ =$1.5$
Therefore, the option $A$ is the correct answer.

Note:
There are many types of reactions in chemistry. Photochemical reaction - When atom and molecule absorb energy in the form of energy and convert into the excited state. Precipitation - During the chemical reaction, when a solid particle formed in a solution is known as a precipitation reaction.