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 $\mathrm{K}^{2}$ 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 atm and a temperature of 295 $\mathrm{K} ?$

Key Concepts

Ideal Gas Law

This concept relates pressure, volume, temperature, and the number of moles of a gas using the equation PV = nRT. It is fundamental for calculating any one variable when the others are known and is crucial in predicting how gases behave under different conditions.

Mole Concept and Molar Mass

This concept involves converting a given mass of a substance to moles using its molar mass, which is essential for linking the amount of substance in grams to the number of particles or moles. This conversion is necessary for applying the ideal gas law, as the law uses the mole value to relate to other state variables.

Gas Expansion and Pressure-Volume Relationship

When a gas expands, its pressure and volume change according to Boyle's Law (a component of the ideal gas law), assuming temperature and number of moles remain constant. Understanding how expanding gases fill larger volumes or are diluted to reach new equilibrium states is critical for solving problems related to gas dispensing and storage.

Transcript

00:01 For this question, they're asking about an argon canister that's used to preserve wine in wine bottles.

00:07 And so it tells us some information about the canister.

00:09 It tells us the volume is 55 milliliters and it contains 26 grams of argon.

00:14 Assuming ideal behavior, what is the pressure of the canister at 295 kelvin, which is our temperature, before it's released from the bottle? and so what we want to think about is i have a volume, a mass, a temperature, and a pressure.

00:29 So right away we should be thinking about the ideal gas law.

00:34 The ideal gas law is pv equals nrt.

00:37 So i'm solving for pressure.

00:38 So i'm going to divide by volume.

00:40 So i'm going to rewrite this as p is nrt over v.

00:45 We want to be very careful with our units for the ideal gas law.

00:48 So our volume needs to be in liters.

00:50 So i need to first divide my volume here by a thousand to get a thousand milliliters is one liter.

00:59 So that would give me 0 .055 liters on the bottom.

01:06 And then i also need, instead of mass, i need moles, which is n.

01:10 So i need to divide by the molar mass.

01:11 And our molar mass for argon is 39 .95 grams per mole, which again i got from my periodic table.