Question

The decomposition of N₂O₅ in CCl₄ solution follows the first order rate law. The concentration of N₂O₅ measured at different time intervals are given below.

Time in seconds (t)	0	80	160	410	600	1130	1720
[N2O5] (mol/L)	5.5	5.0	4.8	4.0	3.4	2.4	1.6

Calculate its rate constant at t = 410 s and t = 1130 s. What do these results show?

Answer 1

Given:

The decomposition of N₂O₅ follows first-order kinetics

We are to calculate the rate constant at two time intervals:

t = 410 s

t = 1130 s

By using first-order rate law

`k = 2.303/t log ([A]_0/([A]))`

Let, [A]₀​ = 5.5 mol/L at t = 0

1. At t = 410 s, [A] = 4.0 mol/L

`k_410 = 2.303/410 log (5.5/4.0)`

= `2.303/410 log (1.375)`

= `(2.303 xx 0.1379)/410`

= `0.3177/410`    ...(log 1.375 = 0.1379)

k₄₁₀ = 7.75 × 10⁻⁴ s⁻¹

2. At t = 1130 s, [A] = 2.4 mol/L

`k_1130 = 2.303/1130 log (5.5/2.4)`

= `2.303/1130 log (2.2917)`

= `(2.303 xx 0.3603)/1130`    ...(log 2.2917 = 0.3603)

= `0.8299/1130`

k₁₁₃₀ = 7.34 × 10⁻⁴ s⁻¹