What is the order of a chemical reaction $\mathrm{A}+2\mathrm{B}\to \mathrm{C}$ . If the rate of formation of C increases by a factor of 2.82 on doubling the concentration of A and increases by a factor of 9 on tripling the concentration of B

The rate law expression is $\mathrm{R}=\mathrm{K}{\left[\mathrm{A}\right]}^{\mathrm{m}}{\left[\mathrm{B}\right]}^{\mathrm{n}}----\left(1\right)$

The rate of formation of C increases by a factor of 2.82 on doubling the concentration of A.

The rate law expression becomes ${\mathrm{R}}^1=2.82\mathrm{R}=\mathrm{K}{2}^{\mathrm{m}}{\left[\mathrm{A}\right]}^{\mathrm{m}}{\left[\mathrm{B}\right]}^{\mathrm{n}}---\left(2\right)$

Divide equation (2) with equation (1)

$\frac{2.82\mathrm{R}}{\mathrm{R}}=\frac{K{2}^m{\left[A\right]}^m{\left[B\right]}^n}{K{\left[A\right]}^m{\left[B\right]}^n}$

$\mathrm{Hence} 2.82=2^{\mathrm{m}}\Rightarrow \mathrm{m}\frac{3}{2}$

The rate of formation of C increases by a factor of 9 on tripling the concentration of B

The rate law expression becomes ${\mathrm{R}}^{"}=9\mathrm{R}=\mathrm{K}{\left[\mathrm{A}\right]}^{\mathrm{m}}{3}^{\mathrm{n}}{\left[\mathrm{B}\right]}^{\mathrm{n}}----\left(3\right)$

The over all order of the reaction is $\mathrm{m}+\mathrm{n}=\frac{3}{2}+2=\frac{7}{2}$