Question

The experimental data for the reaction,
$2NO(g)+C{l}_2(g)\to 2NOCl(g)$ is

Expt.	$[C{l}_2]$	$[NO]$	initial rate
1	0.020	0.010	$2.40\times 10^{-4}$
2	0.020	0.030	$2.16\times 10^{-3}$
3	0.040	0.030	$4.32\times 10^{-3}$

The reaction is of

• A. first order
• B. second order
• C. third order
• D. zero order

Answer 1

Answer: (C)

Let the order of reaction wrt $\left[C{l}_2\right]$ and $[NO]$ is $x$ and $y$ respectively
$\therefore$ I. $2.40\times 10^{-4}=(0.020{)}^x(0.010{)}^y$
II. $2.16\times 10^{-3}=(0.020{)}^x(0.030{)}^y$
III. $4.32\cdot 10^{-3}=(0.040{)}^x(0.030{)}^y$
From eq I and II ${\left(\frac{0.030}{0.010}\right)}^y$
$=\frac{2.16\times 10^{-3}}{2.40\times 10^{-4}}=9$
$3^{\gamma }=(3{)}^2$
$Y=2$
From eq III and II
${\left(\frac{0.040}{0.020}\right)}^x=\frac{4.32\times 10^{-3}}{2.16\times 10^{-3}}=2$
$2^x=2^1\text{ or }x=1$
Overall order of reaction $x+y=2+1=3$
Hence, the reaction is of third order.