Question

For the reaction, A(g) + B(g) => 2 C(g), the following data were obtained at constant temperature.

Experiment	Initial [A], mol/L	Initial [B], mol/L	Initial Rate, M/min
1	0.10	0.10	2 x 10-4
2	0.30	0.30	5.4 x 10-3
3	0.10	0.30	1.8 x 10-3
4	0.20	0.40	6.4 x 10-3

Which of the following is the correct rate law for the reaction?

	1.	Rate = k[A][B]
	2.	Rate = k[A]2[B]
	3.	Rate = k[A]2[B]2
	4.	Rate = k[A]
	5.	Rate = k[A][B]2

Answer 1

Solution :-

Lets calculate the order of each reactant

Calculating the order of A using the data from experiment 2 and 3

Rate 3/ rate 2 = ([A]3/[A]2)^m

1.8*10^-3/5.4*10^-3 = [0.10/0.30]^m

0.33 = 0.33 ^m

Log 0.33 = m * log 0.33

Log 0.33 / log 0.33 = m

1=m

So order of A = 1

Now lets calculate the order with B using the data from experiment 1 and 3

Rate 3 / rate 1 = ([B]3/[B]1)^n

1.8*10^-3/2*10^-4 = [0.30/0.10]^n

9=3^n

Log 9 = n* log 3

Log 9 / log 3 = n

2=n

So order of B is 2

So the rate law for the reaction is

Rate = K[A][B]^2

So the correct answer is option 5