Question

Following data were obtained for the decomposition of N₂O₅ which is a first order reaction.

t (min)	[N2O5] (mol L−1)
0	1.000
10	0.705
20	0.497
30	0.349

From the data given above, determine the value of

1. specific reaction rate and
2. half-life of the reaction

Answer 1

We are given that the decomposition of N₂O₅ is a first-order reaction, and we are to determine:

Specific reaction rate (rate constant k)

Half-life t_1/2

By using first order rate law

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

We’ll use the data at t = 10 min:
[A]₀ = 1.000 mol/L,

[A] = 0.705 mol/L,

[A]₀ = 1.000 mol/L,

[A] = 0.705 mol/L

`k = 2.303/10 log (1.000/0.765)`

= `2.303/10 log (1.418)`

= `(2.303 xx 0.151)/10`    ...(log(1.418) = 0.151

= `0.3486/10`

k = 0.0349 min⁻¹

Half life of first order reaction 

`t_(1//2) = 0.693/k`

= `0.693/0.0349`

t_1/2 = 19.85 minutes