Consider the initial-rate data at a certain temperature in the table for the reaction described by: [NO2]o (M) 0.650 1.10 1.76 O3 0.800 0.800 1.40 Initial rate (Ms) 3.25 x 10^4 5.50 x 10^4 15.40 x 10^4 2 NO2(g) + O3(g) -> N2O5(g) + O2(g) Determine the value and units of the rate constant, k. Units: 4.9 x 10^4 M^-1 s^-1
The Correct Answer and Explanation is:
Correct Answer:
k = 6.25 x 10⁴
Units: M⁻¹s⁻¹
Explanation:
To determine the value and units of the rate constant, k, we must first establish the rate law for the reaction. The general form of the rate law is Rate = k[NO₂]^m[O₃]^n, where m and n are the reaction orders with respect to NO₂ and O₃, respectively.
- Determine the reaction order for NO₂ (m):
We use the method of initial rates by comparing two experiments where the concentration of one reactant changes while the other remains constant. Comparing experiments 1 and 2, the concentration of O₃ is constant at 0.800 M.- Ratio of rates: Rate₂ / Rate₁ = (5.50 × 10⁴) / (3.25 × 10⁴) ≈ 1.69
- Ratio of [NO₂] concentrations: [NO₂]₂ / [NO₂]₁ = 1.10 / 0.650 ≈ 1.69
Since (1.69)^m = 1.69, the reaction order m is 1.
- Determine the reaction order for O₃ (n):
Now that we know m=1, we can use any two experiments to find n. Let’s use experiments 2 and 3. We set up the ratio of their rate laws:
Rate₃ / Rate₂ = (k[NO₂]₃¹[O₃]₃ⁿ) / (k[NO₂]₂¹[O₃]₂ⁿ)
(15.40 × 10⁴) / (5.50 × 10⁴) = (1.76 / 1.10) * ([1.40] / [0.800])ⁿ
2.8 = 1.6 * (1.75)ⁿ
Dividing both sides by 1.6 gives 1.75 = (1.75)ⁿ, so the reaction order n is 1. - Determine the rate law and units of k:
With m=1 and n=1, the rate law is: Rate = k[NO₂][O₃].
The overall reaction order is m + n = 1 + 1 = 2.
The units of k can be found by rearranging the rate law: k = Rate / ([NO₂][O₃]).
Units = (M/s) / (M * M) = M⁻¹s⁻¹. - Calculate the value of k:
We can use the data from any experiment to solve for k. Using experiment 1:
k = Rate / ([NO₂][O₃])
k = (3.25 × 10⁴ M/s) / (0.650 M * 0.800 M)
k = (3.25 × 10⁴) / (0.52) M⁻¹s⁻¹
k = 6.25 × 10⁴ M⁻¹s⁻¹
Using data from the other experiments yields the same result, confirming the value.
