Question

The following questions refer to the hypothetical reaction A + B → products. The kinetics data given can be analyzed to answer the questions.

		[A]0	[B]0	Rate of decrease
		(mol/L)	(mol/L)	of [A] (M/s)

		5.0	5.0	X
		10.0	5.0	2X
		5.0	10.0	2X

		Time (s)	[B] (mol/L)
		10.0	100
		20.0	100

30.0

100

Reference: Ref 12-11
The rate law for the reaction is Rate = k[A]^x[B]^y. What are the values of x and y?

Answer 1

The concentration of B remains same with time and most probably act as a solvent or present in excess.

Also from the rate data it is clear that the rate of the reaction depends on the initial concentration of both A and B.

For data-1:

rate = rate of decrease of [A] = X = k * [5.0]^x[5.0]^y ----- (1)

For data - 2:

rate = rate of decrease of [A] = 2X = k * [10.0]^x[5.0]^y ----- (2)

For data - 3:

rate = rate of decrease of [A] = 2X = k * [5.0]^x[10.0]^y ----- (3)

Dividing eqn(1) by eqn(2) we get

X / 2X = k * [5.0]^x[5.0]^y / k * [10.0]^x[5.0]^y

=> 1/2 = {[5.0]^x[5.0]^y} / 2^x *{[5.0]^x[5.0]^y}

=>   1 / 2^x = 1/2

=> x = 1 (answer)

Dividing eqn(2) by eqn(3) we get

2X / 2X = k * [10.0]^x[5.0]^y / k * [5.0]^x[10.0]^y

=> 1 = 2^x *{[5.0]^x[5.0]^y} / 2^y *{[5.0]^x[5.0]^y}

=> 2^x / 2^y = 1

=> x = y = 1 (answer)