A compressed-air cylinder stands 100 cm tall and has internal diameter 20.0 cm . At room tempe

step 1 belongs to the ideal gas in which we have a compressed air cylinder of height H equals to 100 cm

A compressed-air cylinder stands 100 cm tall and has...

A compressed-air cylinder stands $100 \mathrm{~cm}$ tall and has internal diameter $20.0 \mathrm{~cm} .$ At room temperature, its pressure is 180 atm. (a) How many moles of air are in the cylinder? (b) What volume would this air occupy at room temperature and 1 atm pressure?

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Key Concepts

Molar Volume and Gas Expansion

The molar volume concept relates the number of moles of a gas to the volume it occupies under specified conditions. This idea is key in understanding how gases expand or contract when subjected to different pressures and temperatures, allowing predictions of gas behavior when conditions change.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relationship that connects pressure, volume, number of moles, and temperature of an ideal gas. It is used to determine any one of the variables when the others are known, making it a central tool in analyzing gas behavior under various conditions.

Cylinder Volume Calculation

Calculating the volume of a gas confined within a cylinder requires the use of the geometric formula for the volume of a cylinder (V = ?r²h). This approach is essential when the physical dimensions of the container are given, as it allows the determination of the space available for the gas.

Unit Conversion

Correct unit conversion is crucial in gas calculations to ensure consistency in the applied formulas. This includes converting lengths, pressures, and other quantities into units that are compatible with the gas constant and other parameters in the formula.

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