For the reaction `ArarrB` , the initial reaction -rate gets halved when the initial concentration of A is doubled . Determine the order of the reaction.

Explanation

For a reaction of order 'n' , the rate of the reaction is -
`r=k[A]^(n) " "…[1]`
If the concentration of the reactant is 2 [A] , the rate of the reaction is `(r)/(2)` . This `(r)/(2)=k[2A]^(n)=2^(n)xxk[A]^(n)" " …[2]`
From equations [1] and [2] we get , `(1)/(2)=2^(n)`
or, `2^(-1)=2^(n) ` i.e. n = -1
Thus ,order of the reaction is -1.