The density of air at ordinary atmospheric pressure and 25.0 degrees Celsius is 1.19 g/L. What is the mass in megagrams (Mg) of the air in a room which is 12.50 ft x 17.25 ft x 9.00 ft? 

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Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

I suppose that air in a room has the same pressure and temperature, and therefore has the given density. Because by definition density is mass divided by volume, we have `m=rho*V,` where `rho` is the density (it is given) and `V` is the volume of a room.

We have to compute the volume of a room and take into account different units of measure (liters, megagrams, feet). The volume is width*length*height, but remember they are given in feet. One liter is 10cm*10cm*10cm, one foot is 30.48cm which is 3.048 times greater than 10 cm.

This way, the volume in liters is `12.50 * 17.25 * 9.00*(3.048)^3,` and  the mass in grams is  `1.19 *12.50 * 17.25 * 9.00*(3.048)^3,` which is approximately `65393 (g)` (about 65kg). In megagrams, millions of grams, it will be million times less, i.e. `0.065393 Mg. approx 6.5*10^(-2) Mg.`

 

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