Given the data below, find k.

Question

Given the data below for the reaction, 2A + 2B + 4C => D + E + 3F

Experiment	Initial conc of A, mol/L	Initial conc of B, mol/L	Initial conc of C, mol/L	Initial rate, mol/L.s
1	0.1	0.2	0.4	2 x 10-3
2	0.2	0.2	0.4	4 x 10-3
3	0.3	0.4	0.4	2.4 x 10-2
4	0.4	0.6	0.2	3.6 x 10-2

Calculate the value of k to 3 significant figures and do not use scientific notation.

I found the rate for A which is first order. When I try and calculate B, the number don't add up to the correct rate law. When I use experiment 2 and 3 for B, I get .1666 = .3333^m, which doesn't add up. When I use experiment 1 and 3 for B, I get .083 = .1666^m, which also doesn't add up. How do I find the rate of B? And k?

The answer given is 1.25

Answer 1

I'm assuming that you found this to be FIRST order in A. (compare exp. 1 and 2). To find the order with respect to B, I would use experiments 1 and 3 where [A] triples, [B] doubles [C] is constant, and the rate increases by 12 times. This shows that the reaction is SECOND order in B. This was arrived at as follows:

(3)¹ x (2)ⁿ = 12 and n = 2. To find the order with respect to C, compare experiments 2 and 4 where [A] doubles, [B] triples, [C] is halved and the rate increases 8 times. This indicates the reaction is

FIRST order in C.

Rate = k [A][B]²[C]

2x10^-3 = k (0.1)(0.2)²(0.4)

k = 2x10^-3/(0.0016)

k = 1.25 <-- ANSWER