Question

What is the rate constant for a reaction based on the following experimental information?

Experiment	Rate (M/s)	[A] (M)	[B] (M)
1	0.1172	0.32	0.56
2	0.3389	0.544	0.56
3	0.1741	0.32	0.84

Answer 1

let the rate -r =K[A]^m [B]ⁿ     (1) m and n are orders of reaction w.r.t A and B respectively

from experiment 1,                        0.1172= K[ 0.32)^m [0.55]ⁿ   (2)

from experiment 2,                        0.3389 =K[ 0.544]^m [0.56]ⁿ    (3)

Eq.3/ Eq.2   (0.3389/0.1172)= (0.544/0.32)^m

2.89 = (1.7)^m, m=2

From experiments 3 0.1741= K[0.32]^m [0.84]^m,    (4)

Eq.4/Eq.1 gives( 0.1741/0.1172)= (0.84/0.56)ⁿ   n= 1

So the rarte becomes -r= K [ A]2 [B] from experimet -1 0.1172= K[ 0.32^]2 [0.56], K =2.074/M2.s

The rate becomes -r = 2.074*[A]² [B]