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How Do You Find Mass From Vapor Density?

Published in Chemistry Calculations 3 mins read

You can find the molar mass of a gas from its vapor density using the following relationship: Molar Mass = 2 x Vapor Density. From the molar mass, and knowledge about the number of moles, you can then determine the mass.

Here's a breakdown of the concept and the steps involved:

Understanding Vapor Density

Vapor density is defined as the ratio of the mass of a certain volume of a gas to the mass of the same volume of hydrogen, both measured under the same conditions of temperature and pressure.

Mathematically:

Vapor Density = (Mass of n molecules of gas) / (Mass of n molecules of Hydrogen gas)

The Relationship Between Vapor Density and Molar Mass

The ideal gas law (PV = nRT) and the definition of molar mass are used to derive the direct relationship between vapor density and molar mass. A key point is that equal volumes of all gases at the same temperature and pressure contain the same number of molecules (Avogadro's Law). This leads to the direct proportionality between vapor density and molar mass.

The molar mass of a gas is approximately twice its vapor density:

Molar Mass ≈ 2 × Vapor Density

This approximation arises because the molar mass of hydrogen (Hâ‚‚) is approximately 2 g/mol.

Steps to Find Mass from Vapor Density

  1. Determine the Vapor Density: This value will either be provided or calculated based on experimental data.

  2. Calculate the Molar Mass: Use the formula: Molar Mass = 2 x Vapor Density. The units will be grams per mole (g/mol).

  3. Determine the Number of Moles: You'll need to know the number of moles (n) of the gas present. If not directly given, you may need additional information such as volume, pressure, and temperature to calculate the number of moles using the ideal gas law (PV=nRT) or other relevant equations.

  4. Calculate the Mass: Use the following formula to calculate the mass (m) of the gas:

    m = n × Molar Mass

    where:

    • m = mass of the gas (in grams)
    • n = number of moles of the gas
    • Molar Mass = molar mass of the gas (in g/mol)

Example

Let's say the vapor density of a gas is 22. You also know that you have 0.5 moles of this gas.

  1. Vapor Density: 22

  2. Molar Mass: Molar Mass = 2 x 22 = 44 g/mol

  3. Number of Moles: 0.5 moles

  4. Mass: Mass = 0.5 moles * 44 g/mol = 22 grams

Therefore, the mass of the gas is 22 grams.

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