A student has studied the decomposition of a gas A B 3 at 25 ° C . He obtained the following data p ( m m H g ) 50 100 200 400 Relative t 1 2 s 4 2 1 0 . 5 The order of the reaction is

Step-by-step solution

By observing the data given, by doubling the pressure, half-life is reduced to half. This result is following second order kinetics. Mathematically it can be proved as follows, The half-life and initial pressure of n th order reaction can be related as follows, t 1 2 ∝ P o 1 - n t 1 2 1 t 1 2 2 = P 0 1 1 - n P 0 2 1 - n ⇒ 4 2 = 50 100 1 - n ⇒ 2 = 1 2 1 - n ⇒ 2 = 2 n - 1 ⇒ n - 1 = 1 ⇒ n = 2 Hence, the order of the reaction is second order.