Chemistry - Chemical Kinetics Question with Solution | TestHub

For the reaction$2\mathrm{A}+{\mathrm{B}}_2\rightleftharpoons 2\mathrm{A}\mathrm{B}$,

Rate$\propto \left[\mathrm{A}{]}^{\mathrm{x}}\right[{\mathrm{B}}_2{]}^{\mathrm{y}}$. On substituting the given data, we get

From experimental 1,$1.6\times 10^{-4}\propto {\left[0.50\right]}^{\mathrm{x}}{\left[0.50\right]}^{\mathrm{y}}$...(i)

From experimental 2,$3.2\times 10^{-4}\propto {\left[0.50\right]}^x{\left[1.00\right]}^y$...(ii)

From experimental 3,$3.2\times 10^{-4}\propto {\left[1.00\right]}^x{\left[1.00\right]}^y$...(iii)

$1={\left[\frac{1.00}{0.50}\right]}^{\mathrm{x}}$

or$1=2^{\mathrm{x}}$or$2^0=2^{\mathrm{x}}$or$\mathrm{x}=0$

Now, divide equation (ii) by equation (i) we get,

$2={\left[\frac{1.00}{0.50}\right]}^{\mathrm{y}}$

$2=2^{\mathrm{y}}$

$\mathrm{y}=1$

Thus rate equation is: Rate$=\mathrm{k}{\left[\mathrm{A}\right]}^0{\left[{\mathrm{B}}_2\right]}^1=\mathrm{k}\left[{\mathrm{B}}_2\right]$.