he decomposition of nitrogen dioxide at a high temperature is second order in this reactant.
NO2(g) NO(g) + 1/2 O2(g)
The rate constant for this reaction is 3.40 L/mol·min. Determine the time needed for the concentration of NO2 to decrease from 2.30 mol/L to 1.30 mol/L.
To determine the time needed for the concentration of NO2 to decrease from 2.30 mol/L to 1.30 mol/L, we can use the second-order rate equation:
1/[NO2]t - 1/[NO2]0 = kt
Where:
[NO2]t = concentration of NO2 at time t
[NO2]0 = initial concentration of NO2
k = rate constant
Let's substitute the given values into the equation:
[NO2]t = 1.30 mol/L
[NO2]0 = 2.30 mol/L
k = 3.40 L/mol·min
1/[NO2]t - 1/[NO2]0 = kt
1/1.30 - 1/2.30 = 3.40t
0.7692 - 0.4348 = 3.40t
0.3344 = 3.40t
Now, solve for t:
t = 0.3344 / 3.40
t ≈ 0.0984 min
Therefore, it takes approximately 0.0984 minutes for the concentration of NO2 to decrease from 2.30 mol/L to 1.30 mol/L.
To determine the time needed for the concentration of NO2 to decrease from 2.30 mol/L to 1.30 mol/L, we can use the integrated rate law for a second-order reaction. The integrated rate law for a reaction of the form:
A B + C
is given by:
1/[A] - 1/[A]₀ = kt
where [A] is the concentration of reactant A at a specific time, [A]₀ is the initial concentration of A, k is the rate constant, and t is the time.
In this case, we are given the rate constant (k = 3.40 L/mol·min), the initial concentration ([NO2]₀ = 2.30 mol/L), and the final concentration ([NO2] = 1.30 mol/L). We need to find the time (t) it takes for the concentration to decrease from the initial concentration to the final concentration.
First, let's substitute the values into the integrated rate law:
1/[NO2] - 1/[NO2]₀ = kt
1/1.30 - 1/2.30 = (3.40 L/mol·min) * t
Simplifying the equation:
(1/1.30 - 1/2.30) = (3.40 L/mol·min) * t
(2.30 - 1.30)/(1.30 * 2.30) = (3.40 L/mol·min) * t
1/2.30 = (3.40 L/mol·min) * t
Now, solve for t by rearranging the equation:
t = 1/[(3.40 L/mol·min) * (1/2.30)]
t = 2.30 / (3.40 L/mol·min)
t ≈ 0.68 min
Therefore, the time needed for the concentration of NO2 to decrease from 2.30 mol/L to 1.30 mol/L is approximately 0.68 minutes.
[A] = [A]o + akt
Substitute the numbers and solve for t. a in this reaction is 1.