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 mL and contains 26.0 g of argon. When the argon is released from the canister, it expands to fill the wine bottle. How many 750.0-mL wine bottles can be purged with the argon in the canister at a pressure of 1.20 atm and a temperature of 295 K? Assuming ideal gas behavior, what is the pressure in the canister at 295 K?

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Calculate the number of moles of argon in the canister using the molar mass of argon (approximately 39.95 g/mol).

Use the ideal gas law equation \( PV = nRT \) to find the pressure in the canister. Here, \( P \) is the pressure, \( V \) is the volume of the canister, \( n \) is the number of moles calculated in the previous step, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.

Convert the volume of the canister from mL to L for consistency in units.

Calculate the total volume of argon gas at 1.20 atm and 295 K using the ideal gas law, rearranging it to solve for \( V \) (volume).

Determine how many 750.0-mL wine bottles can be filled by dividing the total volume of argon gas by the volume of one wine bottle (converted to liters).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to predict the behavior of gases under various conditions and is essential for solving problems involving gas expansion and compression.

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the number of moles of a gas, you can use the formula n = mass/molar mass. In this question, knowing the mass of argon (26.0 g) and its molar mass (approximately 40.00 g/mol) is crucial for determining how many moles of argon are available to fill the wine bottles.

Gas Expansion and Pressure Calculation

When a gas expands, it occupies a larger volume, which can affect its pressure and temperature. In this scenario, we need to calculate the pressure of the argon gas in the canister at a given temperature using the Ideal Gas Law. Additionally, understanding how to apply the law to find the number of wine bottles that can be purged involves calculating the final pressure and volume of the gas after expansion.

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