Compare the density of helium to the density of air at a...

Compare the density of helium to the density of air at a pressure of $101 \mathrm{kPa}$ and a temperature of $25^{\circ} \mathrm{C}$. What are the specific volumes of these two gases at the given temperature and pressure?

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental equation in thermodynamics that relates the pressure, volume, and temperature of a gas with the number of moles present. It is used to predict the behavior of ideal gases under various conditions and forms the basis for calculating properties like density and specific volume when the gas is assumed to behave ideally.

Density

Density is defined as mass per unit volume. For gases, density can be determined using the Ideal Gas Law by relating the gas’s mass (or molar mass) to the volume it occupies at a given temperature and pressure. The density depends on the molecular weight of the gas, meaning lighter gases like helium have lower densities compared to heavier gas mixtures like air under the same conditions.

Specific Volume

Specific volume is the inverse of density and is defined as the volume occupied by a unit mass of a substance. In the context of gases, it represents how much space a unit mass of gas occupies at a specific pressure and temperature, allowing for direct comparisons between different gases, such as helium and air.

Molar Mass

Molar mass is the mass of one mole of a substance and plays a critical role in determining the density of a gas. Gases with lower molar masses, such as helium, will generally have a lower density than gases with higher molar masses, such as the composite mixture found in air, when both are compared under the same conditions of pressure and temperature.

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