Question

A sample of 0.900 mol N2O is placed in a sealed

Answer 1

Answer:

• t = 284 min (rounded to 3 significant figures).

Explanation:

1. Decomposition reaction:

Chemical equation:

• 2N₂O → 2N₂ + O₂

2. First order reaction:

Rate law:

$r=-\frac{d[N_2O]}{dt}= k[N_2O]\\ \\ \frac{d[N_2O]}{dt}= -k[N_2O]$

Integrated rate law:

$\frac{d[N_2O]}{[N_2O]}=-kdt\\ \\ ln[N_2O]-ln[N_2O]_0=-kt$

3. Determine the rate constant, k

• t = 42.0 min, [N₂O] = 0.640 mol

• [N₂O]₀ = 0.900

• $ln(0.640)-ln(0.900)=-k(42.0min)$

• k = 0.00812 min⁻¹

4. Time taken for the reaction to be 90.0% complete

• [N₂O] = 0.100[N₂O]=0.100×0.900 mol = 0.0900 mol

• ln(0.0900) - ln(0.900) = - 0.00812 min⁻¹ × t

• t = (2.30 / 0.00812) min ≈ 283.6 min ≈ 284 min (rounded to 3 significant figures).