Question

The half-life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 torr initially. When the pressure was 250 torr, the half-life was found to be 4 min. The order of the reaction is ______ (Nearest integer).

Answer 1

The half-life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 torr initially. When the pressure was 250 torr, the half-life was found to be 4 min. The order of the reaction is 1.

Explanation:

Given Data: At P₁ = 500 torr, `t_(1//2, 1)` = 240 s

At P₂ = 250 torr, `t_(1//2, 2)` = 4 min = 240 s

`t_(1//2) prop 1/([A]^(n - 1))`

So, `(t_(1//2, 1))/(t_(2//2, 2)) = (([A]_2)/([A]_1))^(n - 1)`

⇒ `240/240 = (250/500)^(n - 1)`

⇒ `1 = (1/2)^(n - 1)`

⇒ n − 1 = 0

⇒ n = 1

Since the half-life is independent of initial concentration, the reaction follows first-order kinetics.

∴ The order of reaction is 1.