For the non –stoichiometric reaction $2A+B\to C+D$, the following kinetic data were obtained in three separate experiments, all at 298k.

Initial concentration (A)	Initial concentration (B)	Initial rate of formation of C  $\left(mol{L}^{-1}{s}^{-1}\right)$
0.1M	0.1M	$1.2\times {10}^{-3}$
0.1M	0.2M	$1.2\times {10}^{-3}$
0.2M	0.1M	$2.4\times {10}^{-3}$

The rate law for the formation of C is
 

$\begin{array}{l}letrateofreaction=\frac{d\left[c\right]}{t}=k {\left[A\right]}^x {\left[B\right]}^y \\ nowfromthegivendata\\ 1.2\times {10}^{-3}=k {\left[0.1\right]}^x{\left[0.1\right]}^y ...\left(i\right)\\ 1.2\times {10}^{-3}=k {\left[0.1\right]}^x{\left[0.2\right]}^y.....\left(ii\right)\\ 2.4\times {10}^{-3}=k{\left[0.1\right]}^x{\left[0.2\right]}^y.......\left(iii\right)\\ Dividingequation\left(i\right)and\left(ii\right)\\ \Rightarrow \frac{1.2\times {10}^{-3}}{1.2\times {10}^{-3}}=\frac{k{\left[0.1\right]}^x{\left[0.1\right]}^y}{k{\left[0.1\right]}^x{\left[0.1\right]}^y}\\ wefind,y=0\\ nowdividingequatin\left(i\right)by\left(iii\right)\\ \Rightarrow \frac{1.2\times {10}^{-3}}{1.2\times {10}^{-3}}=\frac{k{\left[0.1\right]}^x{\left[0.1\right]}^y}{k{\left[0.2\right]}^x{\left[0.1\right]}^y}\\ wefindx=1\\ Hence\frac{d\left[C\right]}{dt}=k {\left[A\right]}^1 {\left[B\right]}^0 \\ \end{array}$