For the reaction A + B $$ \to $$ products, it is observed that

(i)  on doubling the initial concentration of A only, the rate of reaction is also doubled and
(ii)  on doubling the initial concentration of both A and B, there is a change by a factor of 8 in the rate of the reaction.

The rate of this reaction is given by

Half-life period of a first order reaction is 1386 seconds. The specific rate constant of the reaction is

The bromination of acetone that occurs in acid solution is represented by this equation.
CH₃COCH_3(aq) + Br_2(aq)  $$ \to $$
     CH₃COCH₂Br(aq) + H⁺_(aq) + Br^$$-$$_(aq)
These kinetic data were obtained for given reaction concentrations.

Initial concentrations, M
[CH3COCH3		[Br2]		[H+]
0.30		0.05		0.05
0.30		0.10		0.05
0.30		0.10		0.10
0.40		0.05		0.20

Initial rate, disappearance of Br2, Ms$$-$$1
			5.7$$ \times $$10$$-$$5
			5.7$$ \times $$10$$-$$5
			1.2$$ \times $$10$$-$$4
			3.1$$ \times $$10$$-$$4

Based on these data, the rate equation is

The rate constants k₁ and k₂ for two different reactions are 10¹⁶ $$ \cdot $$ e^$$-$$2000/T and 10¹⁵ $$ \cdot $$ e^$$-$$1000/T, respectively.
The temperature at which k₁ = k₂ is