At a certain temperature the following data were collected for the reaction: 4 NO2(g) + O2(g) → 2 N2O5(g)

[NO2](M) [O2](M) Initial rate (M/s)
0.0250 0.0110 3.10 10–4
0.0250 0.0220 6.20 10–4
0.0500 0.0110 6.20 10–4

What is the rate law for this reaction? What is the value of the rate constant for this reaction?

Question

At a certain temperature the following data were collected for the reaction: 4 NO2(g) + O2(g) → 2 N2O5(g)

[NO2](M)	[O2](M)			Initial rate (M/s)
0.0250	0.0110			3.10  10–4
0.0250	0.0220			6.20  10–4
0.0500	0.0110			6.20  10–4

What is the rate law for this reaction? What is the value of the rate constant for this reaction?

BlackTom AI · Accepted Answer

The question provides the reaction 4 NO2(g) + O2(g) → 2 N2O5(g) and three data points for initial rates with varying concentrations. To determine the rate law, I will compare how the rate changes when one reactant's concentration is varied at a time.

First data set: [NO2] = 0.0250 M, [O2] = 0.0110 M, rate = 3.10 × 10^-4 M/s.
Second data set: [NO2] = 0.0250 M, [O2] = 0.0220 M (double), rate = 6.20 × 10^-4 M/s.
Third data set: [NO2] = 0.0500 M (double), [O2] = 0.0110 M, rate = 6.20 × 10^-4 M/s.

Observing the first two data sets, when [NO2] is unchanged and [O2] is doubled, the initial rate also doubles (from 3.10×10^-4 to 6.20×10^-4). This indicates that the rate is first order in O2: doubling the concentration of O2 doubles the rate.

Next, comparing the first and third data sets, when [O2] is unchanged and [NO2] is doubled, the initial rate remains the same (still 6.20×10^-4). This indicates that the rate is zero order in NO2: changing [NO2] does not affect the rate.

From these observations, the rate law takes the form: rate = k[O2]^1[NO2]^0 = k[O2]. In words, the reaction rate depends linearly on the concentration of O2 and is independent of NO2 concentration (within the ranges tested).

Now calculate the rate constant k using any data point. Using the first data set:
rate = k[O2] ⇒ k = rate/[O2] = (3.10 × 10^-4 M/s) / (0.0110 M) ≈ 2.82 × 10^-2 s^-1.

A quick check with the second data set: rate = k[O2] = (2.82 × 10^-2 s^-1)(0.0220 M) ≈ 6.20 × 10^-4 M/s, which matches the given rate, confirming consistency.

In summary, the rate law is rate = k[O2], and the rate constant k is approximately 2.82 × 10^-2 s^-1. Note: if you attempt to express the rate law in terms of reactants with the given stoichiometry, be careful to base the order on the experimental data rather than the stoichiometric coefficients; the data indicate the orders rather than the coefficients in the rate law. Also, the provided answer options (if any) should reflect a first-order dependence on O2 and zero-order on NO2, with the corresponding k value around 2.8 × 10^-2 s^-1.

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