Question

Nitrogen monoxide reacts with chlorine according to the equation:

2NO(g) + Cl\({}_2\)(g)⟶ 2NOCl(g) The following initial rates of reaction have been observed for certain reactant concentrations:

What is the rate law that describes the rate’s dependence on the concentrations of NO and Cl₂? What is the rate constant? What are the orders with respect to each reactant?

Short answer

Rate law that describes the rate’s dependence on the concentration of NO and Cl is

represented as

\({\bf{rate = k(NO}}{{\bf{)}}^{\bf{2}}}{{\bf{(Cl)}}^{\bf{1}}}\)

The value of the rate constant is\({\bf{9}}{\bf{.1}}\,{{\bf{L}}^{\bf{2}}}\,{\bf{mo}}{{\bf{l}}^{{\bf{ - 2}}\,}}{{\bf{h}}^{{\bf{ - 1}}}}\)

The order with respect to NO is 2, and the order with respect to Cl is 1

Step-by-step solution

Rate law

General rate law

\({\bf{Rate = k(NO}}{{\bf{)}}^m}{{\bf{(Cl}}{}_{\bf{2}}{\bf{)}}^n}\)

From the table, we can make the following equation

\(\begin{align}1.14mol{L^{ - 1}}{h^{ - 1}} &= k{(0.50)^m}{(0.50)^n}\,\,\,\,\,......(1)\\4.56mol{L^{ - 1}}{h^{ - 1}} &= k{(1.00)^m}{(0.50)^n}\,\,\,\,\,......(2)\\9.12mol{L^{ - 1}}{h^{ - 1}} &= k{(1.00)^m}{(1.00)^n}\,\,\,\,\,......(3)\end{align}\)

Order of NO

Cl₂remains constant, but NO is double, and the rate becomes 4 times large. so, m=2

Second-order in NO.

It is calculated by dividing equation (2) by (1)

\(\begin{align}\frac{{1.14mol{L^{ - 1}}{h^{ - 1}} = k{{(0.50)}^m}{{(0.50)}^n}}}{{4.56mol{L^{ - 1}}{h^{ - 1}} = k{{(1.00)}^m}{{(0.50)}^n}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0.25 &= {(0.5)^m}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,m &= 2\end{align}\)

Order of Cl

NO remains constant, but Cl\({}_2\) is double, and the rate becomes times large. so, \({\bf{n = 1}}\)

First-order in Cl₂

The order of Cl can be calculated by dividing equation (3) from (2)

\(\begin{align}\frac{{4.56mol{L^{ - 1}}{h^{ - 1}} = k{{(1.00)}^m}{{(0.50)}^n}}}{{9.12mol{L^{ - 1}}{h^{ - 1}} = k{{(1.00)}^m}{{(1.00)}^n}}}\\0.5 &= {(0.5)^m}\\m &= 1\end{align}\)

Rate constant

The rate constant is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentration of reacting substances.

It can be calculated as

\(\begin{align}k &= \frac{{rate}}{{{{(NO)}^m}{{(Cl{}_2)}^n}}}\\ &= \frac{{1.14mol\,{L^{ - 1}}\,{h^{ - 1}}}}{{{{(0.50\,mol\,{L^{ - 1}})}^2}(0.50\,mol\,{L^{ - 1}})}}\\ &= 9.1\,{L^2}\,mo{l^{ - 2\,}}{h^{ - 1}}\end{align}\)