For a reaction, X + Y → Product quadrupling [x], increases the rate by a factor of 8. Quailrupling both [x] and [y]

Question

For a reaction, X + Y → Product quadrupling [x], increases the rate by a factor of 8. For a first order reaction the rate constant at 500K is 8 x 10^-4 s^-1.Quailrupling both [x] and [y] increases the rate by a factor of 16. Find the order of the reaction with respect to x and y. what is the overall order of the reaction?

Answer 1

z = k[x]^m [y]ⁿ …………(1) 

8z = k[x]^m [y]ⁿ …………(2)

16z = k[x]^m [y]ⁿ ……………(3) 

Dividing Eq (2) by Eq (1) we get,

8 = 4^m ⇒ 2³= (2²)m ⇒ 2 = 2^2m 

2m = 3

m = 3/2

1.5 order with respect to x.

Dividing Eq (3) by Eq (1) we get,

16 = 4^m . 4ⁿ

16 = 4² . 4ⁿ

= \(\frac{16}{16}\)= 4ⁿ 

1 = 4n

∴ n = 0 [Zero order with respect to y]

Overall order of the reaction.

k [x]^m[y]ⁿ 

k [x]^1.5 [y]⁰

Order (1.5 + 0) = 1.5