Short Answer

The relationship between density and molar mass of a gas comes from the ideal gas equation. A gas with a higher molar mass will have a higher density if temperature and pressure are kept constant. This means heavier gases occupy the same volume but contain more mass, making them denser.

Using the formula , we can see that gas density increases when molar mass or pressure increases and decreases when temperature increases. This relationship helps compare different gases and calculate unknown molar masses.

Detailed Explanation

Relationship between density and molar mass of gas

The relationship between density and molar mass of a gas is an important concept in chemistry, especially when studying the behavior of gases under different conditions. It helps us understand how heavy or light a gas is compared to others and allows scientists to determine the molar mass of an unknown gas using simple laboratory measurements. This relationship is based on the ideal gas equation, which connects pressure, volume, temperature, moles, molar mass, and density. By rearranging this equation, we can clearly see how the density of a gas depends directly on its molar mass.

1. Using the ideal gas equation to find the relationship

The ideal gas law is expressed as:

Here:

•  = pressure
•  = volume
•  = number of moles
•  = gas constant
•  = temperature in Kelvin

Since  (mass divided by molar mass), we substitute it into the equation:

Rearranging for density ():

This formula shows a direct relationship between density (ρ) and molar mass (M) of a gas. If pressure and temperature remain the same, the density of a gas increases when its molar mass increases.

2. Meaning of the relationship

The formula  tells us:

• A gas with larger molar mass has greater density under the same conditions.
• A gas with smaller molar mass has lower density, meaning it is lighter.

For example:

• Helium (M = 4 g/mol) is very light and has low density.
• Carbon dioxide (M = 44 g/mol) is heavier and has a higher density.

This is why helium balloons rise and carbon dioxide stays close to the ground.

3. Dependence on pressure and temperature

The relationship also shows how density changes with pressure and temperature:

• Higher pressure → higher density
  When pressure increases, gas particles are pushed closer together, increasing density.
• Higher temperature → lower density
  When temperature rises, gases expand and density decreases because particles move farther apart.

Thus, even for the same gas, density varies with conditions.

4. How this relationship is useful

This relationship is widely used in chemistry and industry:

• To find the molar mass of an unknown gas by measuring its density.
• To identify gases based on their density.
• To predict how gases behave under different weather and atmospheric conditions.
• To design gas storage and transport systems.
• In environmental studies to understand pollutant distribution.

For example, if a gas’s density at STP is known, chemists can easily calculate its molar mass using:

This helps identify unknown gases.

5. Real-life examples

• Hot air balloons rise because heated air has lower density, not because its molar mass changes.
• LPG (liquefied petroleum gas) is stored under high pressure to increase its density and reduce its volume.
• Hydrogen, having very low molar mass, is extremely light and diffuses quickly.

All these examples show how closely density and molar mass are linked.

Conclusion

The density of a gas is directly proportional to its molar mass when temperature and pressure are constant. This relationship is expressed through the formula , which comes from the ideal gas equation. Understanding this relationship helps chemists identify gases, predict their behavior, and perform important calculations in laboratories and industries.