For the reaction 2A + B → C , the values of initial rate at...

From the experiment (1) and (2)
${\left(\dfrac{0.05}{0.10}\right)}^{x}{\left(\dfrac{0.05}{0.05}\right)}^{y} = \dfrac{0.045}{0.090}$
${\left(\dfrac{1}{2}\right)}^{x} = \dfrac{1}{2} ⇒ x = 1$

From the experiment (2) and (3)
${\left(\dfrac{0.1}{0.2}\right)}^{x}{\left(\dfrac{0.05}{0.1}\right)}^{y} = \left(\dfrac{0.09}{0.72}\right)$
\left(\dfrac{1}{2}\right){\left(\dfrac{1}{2}\right)}^{y} = \dfrac{0.09}{0.72}$<br />${\left(\dfrac{1}{2}\right)}^{y} = \dfrac{0.09 \times 2}{0.72}$<br />${\left(\dfrac{1}{2}\right)}^{y} = \left(\dfrac{1}{4}\right)$<br />$y = 2$<br />Order of reaction with respect to A is$2 and B = 2$<br />$∴ R ∝ \left[A\right]{\left[B\right]}^{2}$<br />Or$R = K\left[A\right]{\left[B\right]}^{2}