Question

For the reaction 2A + B $\to$ C, the values of initial rate at different reactant concentrations are given in the table below. The rate law for the reaction is :

$[A](mol{L}^{-1})$	$[B](mol{L}^{-1})$	$InitialRate(mol{L}^{-1}{s}^{-1})$
0.05	0.05	0.045
0.10	0.05	0.090
0.20	0.10	0.72

• A. Rate = k [A][B]
• B. Rate = $k[A{]}^2[B{]}^2$
• C. Rate = $k[A][B{]}^2$
• D. Rate = $k[A{]}^2[B]$

Answer 1

Answer: (C)

$r=K[A{]}^x[B{]}^y$
$0.045=K(0.05{)}^x(0.05{)}^y$ ....(1)
$0.090=K(0.10{)}^x(0.05{)}^y$....(2)
$0.72=K(0.20{)}^x(0.10{)}^y$ ....(3)
From $\left(1\right)÷\left(2\right),\frac{0.045}{0.090}={\left(\frac{0.05}{0.10}\right)}^x\Rightarrow x=1$
From $\left(2\right)÷\left(3\right),\frac{0.090}{0.720}={\left(\frac{0.10}{0.20}\right)}^x.{\left(\frac{0.05}{0.10}\right)}^y\Rightarrow y=2$
Hence $r=K\left[A\right]{\left[B\right]}^2$