Ozone (O3) can be prepared in the laboratory by passing an...

Ozone $\left(\mathrm{O}_{3}\right)$ can be prepared in the laboratory by passing an electrical discharge through oxygen gas: 3 $\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{O}_{3}(g) .$ Assume that an evacuated steel vessel with a volume of 10.00 $\mathrm{L}$ is filled with 32.00 atm of $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and an electric discharge is passed through the vessel, causing some of the oxygen to be converted into ozone. As a result, the pressure inside the vessel drops to 30.64 atm at $25.0^{\circ} \mathrm{C}$ . What is the final mass percent of ozone in the vessel?

Ozone $\left(\mathrm{O}_{3}\right)$ can be prepared in the laboratory by passing an electrical discharge through oxygen gas: 3 $\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{O}_{3}(g) .$ Assume that an evacuated steel vessel with a volume of 10.00 $\mathrm{L}$ is filled with 32.00 atm of $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and an electric discharge is passed through the vessel, causing some of the oxygen to be converted into ozone. As a result, the pressure inside the vessel drops to 30.64 atm at
$25.0^{\circ} \mathrm{C}$ . What is the final mass percent of ozone in the vessel?

Key Concepts

Mass Percent Composition

Mass percent composition is defined as the ratio of the mass of a component to the total mass of the mixture, multiplied by 100. This concept is used to express the concentration of a component (in this case, ozone) in a mixture by weight. Calculating the mass percent requires both the mass of the component and the total mass of the mixture after the reaction.

Mole-to-Mass Conversion

Converting moles to mass using the molar mass of each substance is essential in relating the chemical amounts to measurable quantities. Once the number of moles of ozone produced is determined through stoichiometry, this concept allows its conversion into mass, which is needed for further calculations such as mass percent.

Ideal Gas Law

The ideal gas law (PV = nRT) connects pressure, volume, temperature, and the amount of gas in moles. It is key for determining how changes in pressure (or other conditions) affect the number of moles present in a gaseous mixture. In this context, it allows for the conversion of the measured pressures before and after the reaction into corresponding mole quantities of oxygen and ozone.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships determined by a balanced chemical equation. For the reaction 3 O? ? 2 O?, stoichiometry enables the calculation of how many moles of oxygen must react to yield a given number of moles of ozone. This step is crucial when converting changes in the amount of oxygen (as inferred from pressure data) into the amount of ozone formed.

Extent of Reaction

The extent of reaction concept is used to determine the fraction or amount of the reactant that has been converted into the product. In this problem, the drop in total pressure indicates that a certain portion of oxygen has reacted to form ozone. Understanding this concept helps link the initial and final conditions of the system through the material balance.

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