Question

From the following data for decomposition of N₂O₅ in CCl₄ at 48°C, show that the reaction is of first order. 

Time in minutes	10	15	20	25	∞
Volume in mL	6.30	8.90	11.40	13.50	34.75

Answer 1

N₂O₅ decomposes as follows.

\[\ce{N2O5 -> 2NO2 + \frac{1}{2} O2}\]

If the reaction is of first order, it must obey the following equation:

k = `2.303/t log_10  a/(a - x)`

= `2.303/t log_10  V_infty/(V_infty - V_t)`

In the present case, V_∞ = 34.75 ml.

The values of k at different instants can be calculated as given below.

t (min)	Vt (mL)	V∞ − Vt (mL)	k = `bb(2.303/t log_10  V_infty/(V_infty - V_t))` (min−1)
10	6.30	34.75 − 6.30 = 28.45	k = `2.303/10 log_10  34.75/28.45` = 0.0200 min−1
15	8.90	34.75 − 8.90 = 25.85	k = `2.303/15 log_10  34.75/25.85` = 0.0197 min−1
20	11.40	34.75 − 11.40 = 23.35	k = `2.303/20 log_10  34.75/23.35` = 0.0199 min−1
25	13.50	34.75 − 13.50 = 21.25	k = `2.303/25 log_10  34.75/21.25` = 0.0197 min−1

The given reaction is of first order since the values of k obtained at various time periods are nearly identical.