How can the mass of air in a room be computed from the room's dimensions?

The density of air at ordinary atmospheric pressure and 25°C is 1.19 g/L. What is the mass in kilograms of the air in a room that measures 12.5 × 15.5 × 8.0 ft?? Please help me set this problem up to solve it.
Angela

This problem is can be solved by breaking it into a chain of simpler problems. Follow these steps.
  1. Identify the unknown, including units. In your problem, the unknown is kg of air.

    ? kg air

  2. List the given information. You know the following:
    • The density of the air is 1.19 g/L. That means that 1 L of air has a mass of 1.19 g.
    • The volume of the room is 12.5 ft × 15.5 ft × 8.0 ft = 1550 ft3 (with 2 significant figures, but don't round anything yet...)
  3. Connect the given information with the unknown. The density relates mass to volume. If you start with volume of air, you can use the density to convert it into kg air:

    1550 ft3 ?
    		 L air 1 L air =
    1.19 g air
    		 g air ?
    		 kg air
    Now you need some way of converting cubic feet into litres. You can work out a conversion factor for cubic feet and cubic inches:

    1 ft = 12 in
    13 ft3 = 123 in3
    1 ft3 = 1728 in3

    Then build a conversion factor for cubic inches to cubic cm:

    1 in = 2.54 cm
    13 in3 = 2.543 cm3
    1 in3 = 16.38706 cm3

    The complete roadmap for the problem is
    1550 ft3 1 ft3 =
    1728 in3
    		 in3 air 1 in3 =
    16.38706 cm3
    		 cm3 air 1 L air =
    1000 cm3 air
    		 L air 1 L air =
    1.19 g air
    		 g air 1000 g air =
    1 kg air
    		 kg air
  4. Do the math. Use the roadmap above to set up a string of conversion factors so that all units but "kg air" cancel.
  5. Check the result Does the answer make sense? Check to see if you can work back towards the given information from your final answer, or try to devise another way to solve the problem.

    Author: Fred Senese senese@antoine.frostburg.edu


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