Question

In the reaction x + y giving product p the reaction rate is tripled when the concentration of x is increased by 3 times without changing the concentration of y.The reaction rate gets doubled when the concentration of y is increased by 4 times without changing the concentration of x. Calculate the order of reaction with respect to x and y and also the overall order of the reaction.

Answer 1

$\frac{d\left[R\right]}{dt}=-K\left[x{]}^a\right[Y{]}^b...equ\left(1\right)\frac{3d\left[R\right]}{dt}=-K\left[3x{]}^a\right[Y{]}^b...equ\left(2\right)\frac{2d\left[R\right]}{dt}=-K\left[x{]}^a\right[4Y{]}^b...equ\left(3\right)$
To find the value of a divide equ1 and equ 2
$\frac{1}{3}=\frac{[x{]}^a}{[3x{]}^a}\frac{1}{3}=\frac{1}{3a}a=1$
To find the value of b divide equ1 and equ 3
$\frac{1}{2}=\frac{1}{4b}b=\frac{1}{2}$
Therefore overall order of the reaction is $=a+b=1+\frac{1}{2}=\frac{3}{2}$