Question

A hypothetical reaction ${\mathrm{A}}_2+{\mathrm{B}}_2\to 2\mathrm{AB}$ follows the mechanism as given below: ${\mathrm{A}}_2\rightleftharpoons \mathrm{A}+\mathrm{A}\left(\mathrm{fast}\right)\mathrm{A}+{\mathrm{B}}_2\to \mathrm{AB}+\mathrm{B}\left(\mathrm{slow}\right)\mathrm{A}+\mathrm{B}\to \mathrm{AB}\left(\mathrm{fast}\right)$The order of the overall reaction is:

• A. $2$
• B. $1$
• C. $1.5$
• D. $0$

Answer 1

The correct option is C

$1.5$

The explanation for the correct option:

Option(C):

• The order of reaction refers to the relationship between the rate of a chemical reaction and the concentration of the species taking part in it.
• In order to obtain the reaction order, the rate expression (or the rate equation) of the reaction in question must be obtained.
• Reaction order represents the number of species whose concentration directly affects the rate of reaction.

Step 1: Given data:

Since (A) is the intermediate reactive substance whose concentration is determined from the equilibrium step.

Let us consider the slow step of the reaction

$\mathrm{A}+{\mathrm{B}}_2\to \mathrm{AB}+\mathrm{B}$ (slow)

$\mathrm{r}=\mathrm{k}\left[\mathrm{A}\right]\left[{\mathrm{B}}_2\right]$…………….(1)

Step 2: Deriving rate law:

From the equilibrium step

${\mathrm{A}}_2\rightleftharpoons \mathrm{A}+\mathrm{A}$(fast)

$$\begin{gathered} {\mathrm{k}}_{\mathrm{eq}}={\left[\mathrm{A}\right]}^2/\left[{\mathrm{A}}_2\right] \\ \therefore \left[\mathrm{A}\right]={\mathrm{k}}_{\mathrm{eq}}{\left[{\mathrm{A}}_2\right]}^{1/2} \end{gathered}$$

Step 3:Determination of rate

Substitute the value of [A] in equation (1)

$$\begin{gathered} \mathrm{r}=\mathrm{k}[{\mathrm{k}}_{\mathrm{eq}}{\left[{\mathrm{A}}_2\right]}^{1/2}]\left[{\mathrm{B}}_2\right] \\ \mathrm{r}=\mathrm{k}.{\mathrm{k}}_{\mathrm{eq}}{}^{1/2}.\left[{\mathrm{A}}_2\right]1^{1/2}.{\mathrm{B}}_2 \end{gathered}$$

Step 4: Calculating the order of the reaction:

Thus, the order of the reaction is

$$\begin{gathered} 1/2+1 \\ \Rightarrow 3/2 \\ \Rightarrow 1.5 \end{gathered}$$

Hence the order of the overall reaction is $1.5$, option (C) is the correct answer.