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.$X+Y\to XY$ (fats)
The overall order of the reaction will be:
A. $1.5$
B. $1$
C. $2$
D. $0$

Answer 1

Hint: A chemical reaction takes place step by step one after another. The conjecture which describes the steps in which the reaction is taking place is known as the chemical mechanism of the reaction.

Complete step by step answer:
Most of the reactions do not occur in a single step. The different ways in which we can show how the reaction is taking place can be a potential energy diagram which represents the energy state of the reaction flow or just simply writing the steps as written in the question.
The given steps show the mechanism of the reaction. With each step the pace of the reaction is written along we could have been provided with the enthalpy, entropy, exothermic or endothermic or energy states to precise each step of the reaction.
Rate(R) of the reaction will be
$\begin{align}
  & R=K[X][{{Y}_{2}}] \\
 & {{K}_{eq}}=\frac{{{[X]}^{2}}}{[{{X}_{2}}]} \\
 & [X]=\sqrt{{{K}_{eq}}[{{X}_{2}}]}={{K}_{eq}}^{\frac{1}{2}}{{X}_{2}}^{\frac{1}{2}} \\
 & \therefore K[{{Y}_{2}}]{{K}_{eq}}^{\frac{1}{2}}{{[{{X}_{2}}]}^{\frac{1}{2}}}={{K}^{1}}{{[{{X}_{2}}]}^{\frac{1}{2}}}[{{Y}_{2}}] \\
\end{align}$
Hence, the order of the reaction will be $1\dfrac{1}{2}$ that is $1.5$.

So, the correct answer is Option A.

Note: We have calculated the rate of the reaction from the slowest step because the slowest step is the rate determining step, it determines the overall rate of the reaction. We got to know about the slowest step from the mechanism of the reaction( as also given in the question).