A wine-dispensing system uses argon canisters to pressurize...

A wine-dispensing system uses argon canisters to pressurize and preserve wine in the bottle. An argon canister for the system has a volume of $55.0 \mathrm{~mL}$ and contains $26.0 \mathrm{~g}$ of argon. Assuming ideal gas behavior, what is the pressure in the canister at $295 \mathrm{~K} ?$ When the argon is released from the canister, it expands to fill the wine bottle. How many $750.0 \mathrm{~mL}$ wine bottles can be purged with the argon in the canister at a pressure of $1.20 \mathrm{~atm}$ and a temperature of $295 \mathrm{~K}$ ?

Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. It serves as a useful model for predicting and calculating the behavior of gases under various conditions, assuming that the gas particles do not interact with one another and that their individual volumes are negligible compared to the container's volume.

Mole Concept

The mole concept is a cornerstone of chemistry that connects the mass of a substance to the number of its particles through the substance's molar mass. By converting a given mass into moles, one can apply the ideal gas law and other chemical principles to determine various properties of a gas, such as its pressure or volume under specified conditions.

Pressure-Volume Relationship

The relationship between pressure and volume is a critical aspect of gas behavior, as described by the ideal gas law. When the number of moles and the temperature are held constant, pressure and volume are inversely related—a concept known as Boyle's law. This principle is essential for understanding how gases expand or compress in different applications.

Gas Expansion Calculations

Gas expansion calculations involve determining how a fixed amount of gas will occupy different volumes under varying pressure and temperature conditions. This is particularly relevant in practical applications, where the gas initially contained under one set of conditions is allowed to expand to fill another volume, allowing the calculation of the number of times a given volume can be purged or filled.

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