Question

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

Experiment	Rate (M/s)	[A] (M)	[B] (M)	[C] (M)
1	0.4416	0.6	0.58	0.54
2	1.9672	1.26	0.58	0.54
3	0.4549	0.6	1.856	0.54
4	5.857	1.26	0.58	1.674

Answer 1

Let the rate (r) be -r = K [A]^m [B]ⁿ [C]^p

m,n and p are orders w.r.t to A, B and C respectively. K is rate constant

From experiment 1,   K[ 0.6]^m [0.58]ⁿ [0.54]^p = 0.4416   (1)

From experiment 2, K[ 1.26]^m [0.58]ⁿ [0.54]^p = 1.9672     (2)

Eq.2/ Eq.1   (1.26/0.6)^m =1.9672/0.4416, m= 2

From experiment 3, K[ 0.6]^m [1.856]ⁿ [0.54]^p = 0.4549 (3)

Eq.3/ Eq.1 (1.856/0.58)ⁿ= 0.4549/0.4416= (3)ⁿ= 1     n =0

From experiment 4, K[ 1.26]^m [0.58]ⁿ [1.674]^p =5.857   (4)

Eq.4/ Eq.2 gives   (1.674/0.54)^p= 5.857/1.9672 p =1

The rate becomes -r = K[A]² [C]

From Eq.1   0.4416= K[ 0.6]² [0.54]

K =2.271 /M2.s

So the rate becomes –r = 2.271[A]² [C]