Lesson 7-8

Density of Gases

     As you now know, unlike solids and liquids, the volume and density of a gas will change in a significant way as its temperature and or pressure changes.  Sometimes, you will be asked to calculate the density that a gas would have at a given temperature and pressure.  The key to this type of problem is to realize that the mass of the gas will not change, just because the pressure and temperature do.  You simply do a combined gas law problem and then divide the given mass by the new volume.

Example 1.  A sample of gas with a mass of 125 mg occupies a volume of 213 cm³ at 21.0 ^oC and 103.5 kPa.  What will the density of the gas be at STP?

First, let us change the temperature to Kelvin, as we do with all gas law problems.

Example 1.  A sample of gas with a mass of 125 mg occupies a volume of 213 cm³ at 21.0 ^oC 294 K and 103.5 kPa.  What will the density of the gas be at STP?

Next, we list all of the givens and the unknown.

m = 125 mg
V₁ = 213 cm³
P₁ = 103.5 kPa
T₁ = 294 K
V₂ = ?
P₂ = 101.3 kPa (standard pressure)
T₂ = 273 K (standard temperature)

Now, write the formula and solve for the unknown:

V₂ = V₁P₁T₂
       -----------
           P₂T₁

V₂ = 213 cm³ x 103.5 kPa x 273 K
          ---------------------------------------
101.3 kPa x 294 K

V₂ = 202 cm³

Next, use the formula for density, where:

m = 125 mg
V = 202 cm³

D = m/V

D = 125 mg/202 cm³

Density of the gas at STP = 0.619 mg/cm³

Now, practice what you have learned with the links below.

Please forward all questions, comments and criticisms to Gregory L. Curran.
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Last Modified February 07, 2008