Question

The experimental data for the reaction,
$2NO(g) + Cl_2(g) \to 2NOCl(g)$ is

Expt.	$[Cl_2]$	$[NO]$	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 $\left[ Cl _{2}\right]$ and $[N O]$ 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.