Question

The rate equation for the reaction $\mathrm{A}+\mathrm{B}\to \mathrm{P}$ is rate $=\mathrm{k}{\left[\mathrm{A}\right]}^{\frac{1}{2}}{\left[\mathrm{B}\right]}^2$. What is the order of reaction?

Answer 1

Step 1: Order of the reaction:

• “The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction.”

Step 2: Given information:

• The given reaction is $\mathrm{A}+\mathrm{B}\to \mathrm{P}$
• Rate $=\mathrm{k}{\left[\mathrm{A}\right]}^{\frac{1}{2}}{\left[\mathrm{B}\right]}^2$

Step 3: Calculation for order of the reaction:

• For the given reaction,

$\mathrm{aA}+\mathrm{bB}\to \mathrm{cC}$

• The rate of the reaction is given by $\mathrm{r}=\mathrm{k}{\left[\mathrm{A}\right]}^{\mathrm{a}}{\left[\mathrm{B}\right]}^{\mathrm{b}}$

Order of the reaction = $\mathrm{a}+\mathrm{b}$ ,where $\mathrm{a}=\frac{1}{2},\mathrm{b}=2$

$$\begin{gathered} \mathrm{Order}\mathrm{of}\mathrm{the}\mathrm{reaction}=\frac{1}{2}+2=\frac{1+4}{2} \\ \mathrm{Order}\mathrm{of}\mathrm{the}\mathrm{reaction}=\frac{5}{2} \end{gathered}$$

Therefore, the order of the reaction is $\frac{5}{2}$.