Question

Decomposition of N₂O_5(g) into NO_2(g) and O_2(g) is a first order reaction. If the initial concentration of N2O_5(g), i.e., [N₂O₅] is 0.030 mol L⁻¹, what will be its concentration after 30 minutes? Rate constant of the reaction is 1.35 × 10⁻⁴ s⁻¹.

Answer 1

Given: k = 1.35 × 10⁻⁴ s⁻¹,

t = 30 min = 30 × 60 s,

[A]₀ = 0.030 mol L⁻¹, 

[A] = ?

For a first-order reaction,

k = `2.303/t log_10  ([A]_0)/([A])`

or, `log_10  ([A]_0)/([A]) = (kt)/2.303`

Substituting the values, we have

`log_10  0.030/([A]) = (1.35 xx 10^-4 xx 30 xx 60)/2.303`

`log_10  0.030/([A]) = 0.243/2.303`

`log_10  0.030/([A])` = 0.1055

∴ `0.030/([A])` = antilog₁₀ 0.1055

`0.030/([A])` = 1.275

or, [A] = `0.030/1.275`

= 0.023 mol L⁻¹