Question

The decomposition of [N₂O₅] in a carbon tetrachloride solution has been found to be of first order with rate constant k = 6.2 × 10⁻⁴ s^−l.

\[\ce{N2O5 (Solution) -> 2NO2 (Solution) + \frac{1}{2} O2_{(g)}}\]

Calculate the rate of reaction when [N₂O₅] = 1.75 mol L^−l. At what concentration of N₂O₅ the reaction would have a rate of 3.8 × 10⁻³ mol L⁻¹ s⁻¹?

Answer 1

Given:

\[\ce{N2O5 (Solution) -> 2NO2 (Solution) + \frac{1}{2} O2_{(g)}}\]

Rate constant: k = 6.2 × 10⁻⁴ s⁻¹

Rate = k [N₂O₅]

1. Calculate rate when [N₂O₅] = 1.75 mol L^−l

Rate = 6.2 × 10⁻⁴ × 1.75

= 1.085 × 10⁻³ mol L^−l

2. [N₂O₅] when rate = 3.8 × 10⁻³ mol L⁻¹ s⁻¹

Rate = k[N₂O₅]

⇒ [N₂O₅] = `"Rate"/k`

= `(3.8 xx 10^-3)/(6.2 xx 10^-4)`

= 6.13 mol L^−l