Question

Consider the reaction X + Y → Z From the data in the table, obtained at 360 K, (a) determine the overall order of the reaction Initial Rate of Disappearance of X (M/s) [X] (M) [Y](M) 0.053 0.10 0.50 0.127 0.20 0.30 1.02 0.40 0.60 0.254 0.20 0.60 0.509 0.40 0.30 (b) determine the initial rate of disappearance of X when the concentration of X is 0.50 M and that of Y is 0.30 M.

Answer 1

rate of disappearance, -r= K[X]^m [y]ⁿ

m, n are ordes of reaction with respect to [X] and [Y] respectively. K is the rate constant

given 0.127= K[0.2]^m [0.3]ⁿ   (1)

also given 0.509 =K[0.4]^m [0.3]ⁿ   (2)

Eq.2/ Eq.1 give

0.509/0.127= [2]^m

2^m=4, m=2

It is mentioned 0.254 =K[0.2]^m [0.6]ⁿ    (3)

Eq.3/Eq.2 gives 2= 2ⁿ

n=1

so the rate expresion becomes -r =K[X]² [Y]¹

from Eq.1   0.053= K[0.1]² [0.5]1

K= 0.053/0.005 =10.6 /M².s

so the rate expression becomes -r = 10.6 [X]² [Y]

at X=0.5M and Y=0.3 M

-r =10.6 [0.5]² [0.3] =0.795 M/s