Question

Given the following data collected from experiments, determine the rate law, overall order, and the numerical value for the rate constant.

Experiement	[A]	[B]	Initial Rate (M min ^-1)
1	0.200	0.300	0.300
2	0.800	0.300	4.80
3	0.200	0.600	2.40

Answer 1

let, rate be r given by
r = k*[A]^a*[B]^b
substituting the value from experiment 1 and 2 and 3
0.3 = k*(0.2)^a*(0.3)^b (1)
4.80 = k*(0.8)^a*(0.3)^b (2)
2.4 = k*(0.2)^a*(0.6)^b (3)
dividing eq(1) by eq(2)
0.3/4.8 = (0.2/0.8)^a
1/16 = (1/4)^a
so, a = 2

dividing eq(1) by eq(3)
0.3/2.4 = (0.3/0.6)^b
1/8 = (1/2)^b
so, b = 3

now, put the value of a, b in rate law
r = k*[A]^2*[B]^3
overall order = a+b
= 2+3
= 5

now, again from experiment from 1 put value in rate law equation
0.3 = k*(0.2)^2*(0.3)^3
0.3 = k*0.04*0.027
k = (2.8*10^-4) (M^-4s^-1)