The diagrams below represent equal volumes of four different...

The diagrams below represent equal volumes of four different gases. Use the diagrams to answer the following questions: a. Are these gases at the same temperature and pressure? How do you know? b. If the molar mass of gas B is 38 g/mol and that of gas C is 46 g/mol, which gas sample is denser? c. To make the densities of gas samples B and C equal, which gas should expand in volume? d. If the densities of gas samples A and C are equal, what is the relationship between their molar masses?

The diagrams below represent equal volumes of four different gases. Use the diagrams to answer the following questions:

a. Are these gases at the same temperature and pressure? How do you know?
b. If the molar mass of gas B is 38 g/mol and that of gas C is 46 g/mol, which gas sample is denser?
c. To make the densities of gas samples B and C equal, which gas should expand in volume?
d. If the densities of gas samples A and C are equal, what is the relationship between their molar masses?

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) links pressure, volume, temperature, and the number of moles of a gas, providing a framework to understand how changes in one property affect the others under controlled conditions. It is fundamental in comparing samples of gases if they are assumed to be ideal, meaning any differences in measured properties, such as density, are attributed to variables like molar mass or volume rather than discrepancies in temperature or pressure.

Gas Density

Gas density is defined as mass per unit volume and, for ideal gases, can be expressed as ? = (molar mass × pressure) / (RT). When gases are under the same temperature and pressure conditions, differences in density directly reflect differences in molar mass. This concept is crucial when comparing the densities of different gas samples in equal volumes.

Effect of Molar Mass on Gas Density

Under constant temperature and pressure, the density of an ideal gas is directly proportional to its molar mass. This means that, among gases with equal numbers of moles in an equal volume, the gas with a higher molar mass will exhibit a higher density. This concept aids in predicting and comparing the densities of various gases based solely on their molar masses.

Gas Expansion and Density Adjustment

Adjusting a gas’ volume while keeping its mass constant directly affects its density since density is mass divided by volume. In scenarios that require matching densities of different gas samples, understanding how expansion or compression alters density is essential. This concept allows for the determination of how to modify a gas sample's volume to achieve a desired density, independent of its molar mass.

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