Question

At ${800}^{\circ }C$ the rate of reaction
$2NO+H_2\to N_2+H_{2}O$
Changes with the concentration of NO and $H_2$ are shown in the figure.
Choose the correct option for the following questions.
(a) What is the order of this reaction?
(b) What is the rate equation for the reaction?
(c) What is the rate when $\left[H_2\right]=1.5\times {10}^{-3}Mand\left[NO\right]=1.1\times {10}^{-3}M$?

• A. (a) Third order, (b) $r=k\left[NO{]}^2\right[H_2],$ (c) $8.85\times {10}^{-3}Mse{c}^{-1}$
• B. (a) Third order, (b) $r=k\left[NO{]}^{-2}\right[H_2{]}^{-1},$ (c) $1.27times{10}^{3}Mse{c}^{-1}$
• C. (a) Third order, (b) $r=k\left[NO{]}^{-2}\right[H_2],$ (c) $88.5\times {10}^{-5}Mse{c}^{-1}$
• D. None of these

Answer 1

Answer: (A)

(a) Third order, (b) $r=k\left[NO{]}^2\right[H_2],$ (c) $8.85\times {10}^{-3}Mse{c}^{-1}$

(a) From experiments (ii) and (iii), when the concentration of NO is doubled and that of hydrogen is held constant, the rate of the reaction increases four times. Hence, the order of the reaction with respect to NO is 2.
From experiments (1) and (ii), when the concentration of hydrogen is reduced to half and that of NO is held constant, the rate of the reaction is reduced to half. Hence, the order of the reaction with respect to hydrogen is 1.

The overall order of the reaction is
$2+1=3$
(b) The rate equation for the reaction is
$r=k\left[NO{]}^2\right[H_2]$
(c) When $\left[NO\right]=1.5\times {10}^{-4}$ M and $\left[H_2\right]=4\times {10}^{-3}$ M (experiment (i)), the rate is
$4.4\times {10}^{-4}$
Substitute this in the rate equation.

$4.4\times {10}^{-4}=k[1.5\times {10}^{-4}{]}^2\times 4\times {10}^{-3}$
$k=4.8\times {10}^6$
When $\left[H_2\right]=1.5\times {10}^{-3}Mand\left[NO\right]=1.1\times {10}^{-3}M$, the rate is $r=k\left[NO{]}^2\right[H_2]$

$r=4.8\times {10}^6\times [1.1\times {10}^{-3}{]}^2\times 1.5\times {10}^{-3}$
$r=8.85\times {10}^{-3}Mse{c}^{-1}$