Question

Expt. No.	Initial Conc. $\left(mol{L}^{-1}\right)$		Initial rate $\left(mol{L}^{-1}{s}^{-1}\right)$
	$\left[A\right]$	$\left[B\right]$
1.	0.03	0.03	$0.3\times {10}^{-4}$
2.	0.06	0.06	$1.2\times {10}^{-4}$
3.	0.06	0.09	$2.7\times {10}^{-4}$

For a reaction in which $A$ and $B$ form $C$, the data obtained from three experiments is given above. What is the rate equation of the reaction and what is the value of the rate constant?

Answer 1

Let the rate equation be $k{\left[A\right]}^x{\left[B\right]}^y$.
From expt. (1), $0.3\times {10}^{-4}=k{\left[0.03\right]}^x{\left[0.03\right]}^y$ ...(i)
From expt. (2), $1.2\times {10}^{-4}=k{\left[0.06\right]}^x{\left[0.06\right]}^y$ ...(ii)
$\frac{1.2\times {10}^{-4}}{0.3\times {10}^{-4}}=\frac{{\left[0.06\right]}^x{\left[0.06\right]}^y}{{\left[0.03\right]}^x{\left[0.03\right]}^y}$
$=2^x\times 2^y=4$ ....(iii)
Similarly, from expt. (1) and expt. (3),
$2^x\times 3^y=9$ ...(iv)
Solving equations (iii) and (iv),
$x=0$, $y=2$
Rate equation, Rate $=k{\left[B\right]}^2$
Considering equation (i) again,
$k=\frac{0.3\times {10}^{-4}}{{\left[0.03\right]}^2}=3.33\times {10}^{-2}$ ${mol}^{-1}$ $L{s}^{-1}$