Question

a student performs a set of three experiments for the reaction A+ B -> C, measuring the initial reaction rate each time. Their data is as follows

[A]0	[B]0	initial rate (mol L-1s-1)
0.250	0.100	0.0151
0.500	0.200	0.0595
0.250	0.200	0.0601

Answer 1

Initial rate = k([A]₀)^m([B]₀)ⁿ

Where k is the rate constant of the reaction, m is the order of reaction with respect to A and n is the order of reaction with respect to B.

First experiment: 0.0151 = k(0.25)^m(0.1)ⁿ ....... Equation 1

Second experiment: 0.0595 = k(0.5)^m(0.2)ⁿ ....... Equation 2

Third experiment: 0.0601 = k(0.25)^m(0.2)ⁿ ....... Equation 3

Equation 3/Equation 1 gives (0.2/0.1)ⁿ = 0.0601/0.0151

i.e. 2ⁿ = 4

i.e. 2ⁿ = 2²

i.e. n = 2

Therefore, the order of reaction with respect to B = 2

Now, Equation 2/equation 3 gives (0.5/0.25)^m = 0.0595/0.0601

i.e. 2^m = 1

i.e. 2^m = 2⁰

i.e. m = 0

Therefore, the order of reaction with respect to A = 0

Now, from equation 1: 0.0151 mol L^-1 s^-1 = k(0.25)⁰(0.1 mol L^-1)²

i.e. k = 0.0151/0.01 = 1.51 L mol^-1 s^-1 = 1.51 M^-1 s^-1 ( 1 M = 1 mol/L = 1 mol L^-1)

i.e. The rate constant of the given reaction = 1.51 M^-1 s^-1