Following data is for a reaction between reactants $A$ and $B$ : \ The order of the reaction with

Question

Following data is for a reaction between reactants $A$ and $B$ : \  The order of the reaction with respect to $A$ and $B$, respectively are

Professor PC Thomas Classes · Answer

$$ \begin{aligned} & (\mathrm{c}): 	ext { Rate }=k[A]^x[B]^y \ & 2 	imes 10^{-3}=k[0.1]^x[0.1]^y \ & 4 	imes 10^{-3}=k[0.2]^x[0.1]^y \ & 1.6 	imes 10^{-2}=k[0.2]^x[0.2]^y \end{aligned} $$ Dividing eq. (i) by (ii), we get $ \frac{1}{2}=\left(\frac{1}{2}ight)^x \Rightarrow\left(\frac{1}{2}ight)^1=\left(\frac{1}{2}ight)^x \Rightarrow x=1 $ Similarly, dividing eq. (ii) by (iii), we get $ \frac{1}{4}=\left(\frac{1}{2}ight)^y \Rightarrow\left(\frac{1}{2}ight)^2=\left(\frac{1}{2}ight)^y \Rightarrow y=2 $ Thus, order of the reaction with respect to $A$ and $B$,respectively are 1 and 2 .