During Kinetic study of reaction $2 A+B \rightarrow C+D$, the following results were obtained :…

During Kinetic study of reaction $2 A+B \rightarrow C+D$, the following results were obtained : $\begin{aligned} & \text { A [M] } & \text { B [M] } & \text { initial rate of formation of D } \\ \text { I } & 0.1 & 0.1 & 6.0 \times 10^{-3} \\ \text { II } & 0.3 & 0.2 & 7.20 \times 10^{-2} \\ \text { III } & 0.3 & 0.4 & 2.88 \times 10^{-1} \\ \text { IV } & 0.4 & 0.1 & 2.40 \times 10^{-2} \\ \end{aligned}$ Based on above data, overall order of the reaction is ______

Solution

$\begin{aligned} & \mathrm{r}=\mathrm{K}[\mathrm{A}]^{\mathrm{x}}[\mathrm{B}]^{\mathrm{y}} \\ & (\mathrm{I}) 6 \times 10^{-3}=\mathrm{K}[0.1]^{\mathrm{x}}[0.1]^{\mathrm{y}} \\ & (\mathrm{IV}) 2.4 \times 10^{-2}=\mathrm{K}[0.4]^{\mathrm{x}}[0.1]^{\mathrm{y}} \\ & \quad(\mathrm{IV}) /(\mathrm{I}) \\ & 4=(4)^{\mathrm{x}} \\ & \quad \mathrm{x}=1 \\ & \mathrm{r}=\mathrm{K}[\mathrm{A}]^{\mathrm{x}}[\mathrm{B}]^{\mathrm{y}}\end{aligned}$ $\begin{aligned} & \text { (III) } 2.88 \times 10^{-1}=\mathrm{K}[0.3]^{\mathrm{x}}[0.4]^{\mathrm{y}} \\ & \text { (II) } 7.2 \times 10^{-2}=\mathrm{K}[0.3]^{\mathrm{x}}[0.2]^{\mathrm{y}} \\ & \text { (III)/(II) }\end{aligned}$ $\begin{aligned} & 4=2^y \\ & y=2\end{aligned}$ Overall order $=x+y=1+2=3$

Asked in: JEE Main 2024 (05 Apr Shift 1)

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