Question

What is the reaction order for each reactant and the rate coefficient for the following reaction?

A + B + C B> Z

[A] (mol L- 1)	[B] (mol L-1)	[C] (mol L-1)	[v] (mol L-1 sec-1 )
0.01	0.01	0.1	3.0 x 10-2
0.01	0.02	0.1	1.2 x 10-1
0.02	0.01	0.1	1.5 x 10-2
0.02	0.01	0.2	2.1 x 10-2

Answer 1

Let the rate equation be,

rate = k[A]^x[B]^y[C]^z

with,

k = rate constant

x, y, and z are order with respect to A, B and C

consider first and and second run, concentration of [A] and [C] are same and gets cancelled out,

rate1/rate2 = 3 x 10^-2/1.2 x 10^-1 = (0.01/0.02)^y

0.25 = 0.5^y

taking log on both sides,

log(0.25) = y log(0.5)

y = 2

Now, take run 3 and 4, [A] and [B] are constant gets cancelled out,

rate3/rate4 = 1.5 x 10^-2/2.1 x 10^-2 = (0.1/0.2)^z

0.714 = 0.5^z

taking log on both sides,

log(0.714) = z log(0.5)

z = 0.5

and last taking run 1 and 3, [B] and [C] are constant and gets cancelled out,

rate1/rate3 = 3 x 10^-2/1.5 x 10^-2 = (0.01/0.02)^x

2 = 0.5^x

taking log on both sides,

x = -1

So the rate equation becomes,

rate = k[B]^2[C]^1/2/[A]

rate coefficient or rate constant,

run 1,

3 x 10^-2 = k(0.01)^2(0.1)^1/2/(0.01)

k = 3.16 x 10^-3