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Half life

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Question

From the following data of initial concentration and rates, calculate the order of reaction ( $a A \to$ Products) and its rate constant.
$\begin{matrix} [A] m o l L^{- 1} & 0.1 & 0.2 & 0.4 [R a t e] m o l L^{- 1} s^{- 1} & 9 \times 10^{- 5} & 36 \times 10^{- 5} & 144 \times 10^{- 5} \end{matrix}$

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Solution

When [A] become double from $0.1 m o l L^{- 1}$ to
$0.2 m o l L^{- 1}$ then rate of reaction increases by
4 times.
Hence it is clear that it is second order
reaction with respect to [A]
Order of reaction is 2
Rate $= k [A]^{2} .$
Rate constant, $k = \frac{R a t e}{[A]^{2}} = \frac{9 \times 10^{- 5} m o l L^{- 1} s^{1}}{(0.1 m o l L^{- 1} L s^{1})}$
$= 9 \times 10^{- 3} m o l^{- 1} L s^{- 1}$
Order of reaction $= 2$
Rate constant $= 9 \times 10^{- 3} L m o l^{- 1} L s^{- 1}$

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