Consider the reaction: 2 N2O(g) → 2 N2(g) + O2(g). In the first 15.0 s of the reaction, 0.015 mol of O2 is produced in a reaction vessel with a volume of 0.500 L. a. What is the average rate of the reaction during this time interval? b. Predict the rate of change in the concentration of N2O during this time interval, i.e., what is ∆[N2O]/∆t?

Verified step by step guidance

1. <Step 1: Understand the reaction and the stoichiometry.> The balanced chemical equation is 2 N2O(g) → 2 N2(g) + O2(g). This tells us that for every 2 moles of N2O that decompose, 1 mole of O2 is produced.
2. <Step 2: Calculate the concentration of O2 produced.> Use the formula for concentration: [O2] = moles of O2 / volume of the vessel. Here, moles of O2 = 0.015 mol and volume = 0.500 L.
3. <Step 3: Determine the average rate of formation of O2.> The average rate of formation of O2 is given by the change in concentration of O2 over the change in time: rate = Δ[O2]/Δt. Use the concentration from Step 2 and the time interval of 15.0 s.
4. <Step 4: Relate the rate of formation of O2 to the rate of reaction.> According to the stoichiometry of the reaction, the rate of formation of O2 is half the rate of decomposition of N2O. Therefore, rate of reaction = 2 * rate of formation of O2.
5. <Step 5: Calculate the rate of change in concentration of N2O.> Use the relationship from Step 4 to find Δ[N2O]/Δt. Since the rate of reaction is equal to the rate of disappearance of N2O, Δ[N2O]/Δt = -2 * rate of formation of O2.>

Key Concepts

Average Rate of Reaction

The average rate of a chemical reaction is defined as the change in concentration of a reactant or product over a specific time interval. It is calculated using the formula: rate = Δ[product]/Δt or rate = -Δ[reactant]/Δt. In this case, the average rate can be determined by measuring the amount of O2 produced and dividing it by the time interval, providing insight into the speed of the reaction.

Concentration and Molarity

Concentration refers to the amount of a substance (in moles) present in a given volume of solution, typically expressed in mol/L (molarity). In the context of the reaction, the concentration of O2 produced can be calculated by dividing the number of moles of O2 by the volume of the reaction vessel. Understanding concentration is crucial for predicting how the amounts of reactants and products change over time.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in a chemical reaction, based on the balanced chemical equation. For the given reaction, the stoichiometric coefficients indicate that for every 2 moles of N2O that decompose, 2 moles of N2 and 1 mole of O2 are produced. This relationship allows us to predict the rate of change in concentration of N2O based on the rate of O2 production.