A cylinder fitted with a movable piston initially contains...

A cylinder fitted with a movable piston initially contains 2.00 moles of $\mathrm{O}_{2}(g)$ and an unknown amount of $\mathrm{SO}_{2}(g) .$ The oxygen is known to be in excess. The density of the mixture is 0.8000 $\mathrm{g} / \mathrm{L}$ at some $T$ and $P$ . After the reaction has gone to completion, forming $\mathrm{SO}_{3}(g),$ the density of the resulting gaseous mixture is 0.8471 $\mathrm{g} / \mathrm{L}$ at the same $T$ and $P$ . Calculate the mass of $\mathrm{SO}_{3}$ formed in the reaction.

Key Concepts

Gas Density and the Ideal Gas Law

This concept explains that, for a gas or gas mixture at constant temperature and pressure, the density is directly related to its molar mass using the ideal gas law (PV = nRT). By rearranging the ideal gas law, one can relate the mass and volume of a gas to its number of moles, which is especially useful when determining the molar mass or composition of an unknown gas mixture from measured density values.

Reaction Stoichiometry

Reaction stoichiometry involves using the stoichiometric coefficients from a balanced chemical equation to relate the quantities of reactants and products. In reactions involving gases, this relationship allows us to determine how many moles of a product are formed from given amounts of reactants, which is key in calculating the mass of a product formed in a chemical transformation.

Molecular Mass of Gas Mixtures

Understanding the concept of molecular mass in gas mixtures is critical, as the overall density of the mixture reflects the average molecular mass. By combining the known amounts of some gases with the overall density, one can deduce the contribution of each component to the mixture, which is essential when calculating the mass of a specific product in a reaction.

Conservation of Mass

The law of conservation of mass states that mass cannot be created or destroyed in a chemical reaction. This fundamental principle ensures that the total mass of reactants before the reaction is equal to the total mass of products after the reaction, providing a basis for setting up calculations to determine the mass of a product formed, given the measured densities and known reactant amounts.

Excess Reactant Concept

When one of the reactants is in excess, it does not limit the extent of the chemical reaction; instead, the other reactant determines how much product is formed. Recognizing an excess reactant simplifies calculations because it allows focus on the limiting reactant, making it possible to accurately apply stoichiometric relationships to determine the yield or mass of the desired product.

Transcript

Please give Ace some feedback