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.

Identify the unknown, including units. In your problem, the unknown is kg of air.
? kg air
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...)
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
Do the math. Use the roadmap above to set up a string of conversion factors so that all units but "kg air" cancel.
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

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