Question

Nitrogen dioxide decomposes to nitric oxide and oxygen via the reaction:

2NO₂(g)→2NO(g)+O₂(g)
In a particular experiment at 300 °C, [NO₂] drops from 0.0100 to 0.00800 M in 100 s. The rate of appearance of O₂ for this period is ________ M/s.
A) 2.0 x10⁻³
B) 1.0 x10⁻⁵
C) 4.0 x10⁻³
D) 4.0 x10⁻⁵
E) 2.0 x10⁻⁵

Answer 1

The rate of appearance of O₂ in the given reaction is 1.0 × 10⁻⁵ M/s.

Step-by-step explanation:

In the given reaction:

2NO₂(g) → 2NO(g) + O₂(g)

Since the stoichiometry of the reaction is 2:1 for NO₂ to O₂, the rate of appearance of O₂ is half the rate of disappearance of NO₂. Therefore, we need to calculate the rate of disappearance of NO₂ and divide it by 2 to find the rate of appearance of O₂.

The rate of disappearance of NO₂ can be calculated using the initial and final concentrations:

1. Initial concentration: [NO₂]₀ = 0.0100 M
2. Final concentration: [NO₂] = 0.00800 M
3. Time: Δt = 100 s

Using the formula:

Rate of disappearance of NO₂ = ([NO₂] - [NO₂]₀) / Δt

Plugging in the values, we have:

Rate of disappearance of NO₂ = (0.00800 M - 0.0100 M) / 100 s = -0.00002 M/s

Finally, the rate of appearance of O₂ is half of the rate of disappearance of NO₂, so:

Rate of appearance of O₂ = -0.00002 M/s ÷ 2 = -0.00001 M/s = 1.0 × 10⁻⁵ M/s