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 11.5 × 18.5 × 9.0 ft?

The mass in kilograms is 64.52

Explanation:

We know that density of a substance is an intensive property that can be calculated with following formula: " alt="density= \frac{mass}{volume}" />" />

Using the formula and using simple 3 rule, we can calculate the mass in the room.

First we calculate the volume of the room:

\\\\" alt="Volume=lenght*height*with" />\\\\" />

As density is given in grams/liters, we need to change unit measure feet3 to liters:

" alt="1 ft^{3} ---------28.32L\\ 1914.75ft^{3} -----------------------54225.72 L" />" />

Now we can use density formula isolating the mass, to get the value needed:

\\" alt="mass=density*volume" />\\" />

Following step is to replace density and volume with the data that we have:

" alt="mass=1.19g/L*54225.72L\\ mass=64528,60g" />" />

We know that 1000 g is 1Kg, so to obtain the value in Kg we need to divide the result.

" alt="mass=64.52Kg" />" />