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What is Equal to the Molar Mass Divided by the Mass Density?

Published in Molar Volume 3 mins read

The result of dividing molar mass by mass density is the molar volume.

Based on the provided video transcript, the video explains that:

  • Molar mass is expressed in grams per mole.
  • Mass density is mass divided by volume.

When you divide molar mass (grams/mole) by mass density (grams/volume), you get a result with units of volume per mole, which is the definition of molar volume.

Understanding the Concepts

Here's a more detailed breakdown:

  • Molar Mass: The mass of one mole of a substance (typically expressed in grams/mole or g/mol).
  • Mass Density: The mass of a substance per unit volume (typically expressed in grams per liter, g/L or grams per milliliter, g/mL).
  • Molar Volume: The volume occupied by one mole of a substance (typically expressed in liters per mole, L/mol or milliliters per mole, mL/mol).

How to Calculate Molar Volume from Molar Mass and Density

  1. Understand the Formula: Molar Volume = Molar Mass / Density

    • Molar Volume (Vm) = grams/mole / grams/volume
    • Molar Volume (Vm) = volume / mole

  2. Identify the Units: Ensure all units are consistent. If molar mass is in grams/mol and density is in g/L, the resulting molar volume will be in L/mol.

  3. Perform the Calculation: Divide the molar mass by the density.

Example

Let's say:

  • The molar mass of a gas is 44 g/mol.
  • The density of the gas is 2 g/L.

Then:

  • Molar Volume = 44 g/mol / 2 g/L = 22 L/mol.

This means one mole of this gas occupies 22 liters under the given conditions.

Practical Insights

  • Ideal Gas Law: The concept of molar volume is closely related to the ideal gas law (PV=nRT). At a fixed temperature and pressure, the molar volume of an ideal gas is approximately the same, regardless of the type of gas.
  • Gases: Molar volumes are particularly useful when dealing with gases, as the volume can change significantly based on temperature and pressure.
  • Liquids and Solids: While molar volumes can be calculated for liquids and solids, their values are typically smaller and less variable compared to gases.

Conclusion

Dividing the molar mass of a substance by its mass density yields the molar volume, which represents the volume occupied by one mole of the substance.

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