Question

For the reaction, the following mechanism has been given:
${\text{2NO + B}}{{\text{r}}_2} \to {\text{2NOBr}}$
Mechanism:
${\text{NO + B}}{{\text{r}}_2}\xrightarrow{{{\text{Fast}}}}{\text{NOB}}{{\text{r}}_2}$
${\text{NOB}}{{\text{r}}_2}{\text{ + NO}}\xrightarrow{{{\text{Slow}}}}{\text{2NOBr}}$. Hence, rate law is:

Answer 1

Hint: The change in concentration of a reactant or product per unit time is known as the rate of the reaction. The rate law gives the relationship between the rate of the reaction and the concentration of the reactants. In the rate law, the concentrations of the reactants are raised to exponents.

Complete step by step answer:
The slow step in the mechanism of the reaction is the rate determining step.
The slow step in the reaction is,
${\text{NOB}}{{\text{r}}_2}{\text{ + NO}}\xrightarrow{{{\text{Slow}}}}{\text{2NOBr}}$
Thus, the rate law is as follows:
${\text{Rate}} = k\left[ {{\text{NOB}}{{\text{r}}_{\text{2}}}} \right]\left[ {{\text{NO}}} \right]$ …… (1)
Where k is the rate constant of the reaction.
An expression that describes the state of equilibrium in terms of concentrations of reactant and product is known as the equilibrium constant expression.
Thus, for the reaction,
${\text{2NO + B}}{{\text{r}}_2} \to {\text{2NOBr}}$
The expression for the equilibrium constant is as follows:
\[K = \dfrac{{\left[ {{\text{NOB}}{{\text{r}}_{\text{2}}}} \right]}}{{\left[ {{\text{NO}}} \right]\left[ {{\text{B}}{{\text{r}}_{\text{2}}}} \right]}}\]
Where K is the equilibrium constant.
Rearrange the expression of the equilibrium constant for \[\left[ {{\text{NOB}}{{\text{r}}_{\text{2}}}} \right]\] as follows:
\[\left[ {{\text{NOB}}{{\text{r}}_{\text{2}}}} \right] = K\left[ {{\text{NO}}} \right]\left[ {{\text{B}}{{\text{r}}_{\text{2}}}} \right]\] …… (2)
Substitute equation (2) in equation (1) as follows:
\[{\text{Rate}} = kK\left[ {{\text{NO}}} \right]\left[ {{\text{B}}{{\text{r}}_{\text{2}}}} \right]\left[ {{\text{NO}}} \right]\]
Thus,
\[{\text{Rate}} = K'{\left[ {{\text{NO}}} \right]^2}\left[ {{\text{B}}{{\text{r}}_{\text{2}}}} \right]\]
Where $K' = kK$
Thus, the rate law is \[{\text{Rate}} = K'{\left[ {{\text{NO}}} \right]^2}\left[ {{\text{B}}{{\text{r}}_{\text{2}}}} \right]\].

Note: The rate constant for a chemical reaction can be defined as the rate of the reaction when the concentrations of all the reactions are unity. The rate constant is denoted by k. Larger the value of the rate constant faster is the reaction. smaller the value of the rate constant slower is the reaction. The applications of rate constant are as follows:
The rate constant is used to determine the rate of the chemical reaction.
The rate constant is used to predict the mechanism of the chemical reaction.