Question

In the reaction, ${\text{2NO + C}}{{\text{l}}_2}{\text{ }} \to {\text{ 2NOCl}}$, it has been found that doubling the concentration of both the reactants increases the rate by a factor of eight but doubling the chlorine concentration only doubles the rate. Which of the following statements is incorrect?
(A) The reaction is first order in ${\text{C}}{{\text{l}}_2}$.
(B) The reaction is second order in ${\text{NO}}$.
(C) The overall order of reaction is ${\text{2}}$.
(D) The overall order of reaction is ${\text{3}}$.

Answer 1

Hint: The sum of the powers of concentration of the reactants in the rate equation of the chemical equation is known as the order of the reaction. The order and molecularity of the reaction are not the same.

Step by step answer: The reaction is,
${\text{2NO + C}}{{\text{l}}_2}{\text{ }} \to {\text{ 2NOCl}}$
The rate of the reaction is,
${r_1} = k{\left[ {{\text{NO}}} \right]^x}{\left[ {{\text{C}}{{\text{l}}_2}} \right]^y}$
Where ${r_1}$ is the rate of the reaction,
$k$ is the rate constant of the reaction,
$x$ is the order with respect to ${\text{NO}}$,
 $y$ is the order with respect to ${\text{C}}{{\text{l}}_2}$.
When the concentrations of both the reactants are doubled, the rate increases by a factor of eight.
Thus,
${r_2} = 8{r_1} = k{\left[ {{\text{2NO}}} \right]^x}{\left[ {{\text{2C}}{{\text{l}}_2}} \right]^y}$
$\Rightarrow {r_2} = 8{r_1} = k{\left[ {{\text{NO}}} \right]^x}{\left[ {{\text{C}}{{\text{l}}_2}} \right]^y} \cdot {2^x} \cdot {2^y}$ …… (2)
When the concentration of chlorine is doubled, the rate doubles. Thus,
${r_3} = 2{r_1} = k{\left[ {{\text{NO}}} \right]^x}{\left[ {{\text{2C}}{{\text{l}}_2}} \right]^y}$
$\Rightarrow {r_3} = 2{r_1} = k{\left[ {{\text{NO}}} \right]^x}{\left[ {{\text{C}}{{\text{l}}_2}} \right]^y} \cdot {2^y}$ …… (3)
Determine the order with respect to ${\text{C}}{{\text{l}}_2}$ as follows:
Divide equation (1) by equation (3). Thus,
$\dfrac{{{r_1}}}{{2{r_1}}} = \dfrac{{k{{\left[ {{\text{NO}}} \right]}^x}{{\left[ {{\text{C}}{{\text{l}}_2}} \right]}^y}}}{{k{{\left[ {{\text{NO}}} \right]}^x}{{\left[ {{\text{C}}{{\text{l}}_2}} \right]}^y} \cdot {2^y}}}$
$\Rightarrow \dfrac{1}{2} = \dfrac{1}{{{2^y}}}$
$\Rightarrow {\left( 2 \right)^1} = {\left( 2 \right)^y}$
$y = 1$
Thus, the order with respect to ${\text{C}}{{\text{l}}_2}$ is ${\text{1}}$.
Determine the order with respect to ${\text{NO}}$ as follows:
Thus, the statement ‘the reaction is first order in ${\text{C}}{{\text{l}}_2}$’ is correct.
Divide equation (1) by equation (2).
Thus,
$\dfrac{{{r_1}}}{{8{r_1}}} = \dfrac{{k{{\left[ {{\text{NO}}} \right]}^x}{{\left[ {{\text{C}}{{\text{l}}_2}} \right]}^y}}}{{k{{\left[ {{\text{NO}}} \right]}^x}{{\left[ {{\text{C}}{{\text{l}}_2}} \right]}^y} \cdot {2^x} \cdot {2^y}}}$
$\Rightarrow \dfrac{1}{8} = \dfrac{1}{{{2^x} \cdot {2^y}}}$
Substitute $y = 1$
$\Rightarrow 4 \times 2 = {2^x} \cdot {2^1}$
$\Rightarrow {2^2} = {2^x}$
$\Rightarrow x = 2$
Thus, the order with respect to ${\text{NO}}$ is ${\text{2}}$.
Thus, the statement ‘the reaction is second order in ${\text{NO}}$’ is correct.
Determine the overall order of the reaction as follows:
Thus, the rate of the reaction is,
${r_1} = k{\left[ {{\text{NO}}} \right]^x}{\left[ {{\text{C}}{{\text{l}}_2}} \right]^y}$ …… (1)
${r_1} = k{\left[ {{\text{NO}}} \right]^2}{\left[ {{\text{C}}{{\text{l}}_2}} \right]^1}$
The sum of the powers of concentration of the reactants in the rate equation of the chemical equation is known as the order of the reaction. Thus,
${\text{Order}} = 2 + 1$
$\Rightarrow {\text{Order}} = 3$
Thus, the overall order of the reaction is ${\text{3}}$.
Thus, the statement ‘the overall order of reaction is ${\text{3}}$’ is correct.
Thus, the statement ‘the overall order of reaction is ${\text{2}}$’ is not correct.

Thus, the correct option is (C) the overall order of reaction is ${\text{2}}$.

Note: While solving such sort of problems one must take care that the overall order is the sum of the order of reaction with respect to each reactant involved in the reaction.