Experiment	[A] Mole/lit	[B] Mole/lit	Rate of reaction Mole ${\mathrm{lit}}^{-1}{\min }^{-1}$
I	0.2	0.2	$1.2\times {10}^{-2}$
II	0.6	0.4	$1.44\times {10}^{-1}$
III	0.6	0.8	$5.76\times {10}^{-1}$
IV	0.8	0.2	$4.8\times {10}^{-2}$

The above data is recorded for  $\mathrm{A}+\mathrm{B}\to \mathrm{AB}$, the correct rate law equation is

consider Experiment II & III

[A] is constant

 [B] is doubled and rate increased by a factor of four

$$\begin{gathered} \mathrm{rate}={\mathrm{KC}}^{\mathrm{n}} \\ {\mathrm{C}}^{\mathrm{n}}\propto \mathrm{rate} \end{gathered}$$

     Order w.r.t B

$$\begin{gathered} 2^{\mathrm{x}}=4 \\ {2}^{\mathrm{x}}=2^2 \\ \mathrm{X} = 2 \end{gathered}$$

Consider experiment I & IV

[B] is constant

[A] is quadrapled and rate  increased by factor of four

 Order w.r.t A

$$\begin{gathered} 4^{\mathrm{y}}=4 \\ \mathrm{Y} = 1 \end{gathered}$$

Rate = $\mathrm{K} \left[\mathrm{A}\right] {\left[\mathrm{B}\right]}^2$