Question

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?

Answer 1

The mass in kilograms is 64.52

Step-by-step explanation:

We know that density of a substance is an intensive property that can be calculated with following formula:
`[tex]density= (mass)/(volume)`[/tex]

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

First we calculate the volume of the room:

`[tex]Volume=lenght*height*with`\\
`Volume=11.5 feet * 18.5 feet *9.0 feet`\\
`Volume=1914.75 feet^(3)`[/tex]

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

`[tex]1 ft^(3) ---------28.32L\\ 1914.75ft^(3) -----------------------54225.72 L`[/tex]

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

`[tex]mass=density*volume`\\[/tex]

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

`[tex]mass=1.19g/L*54225.72L\\ mass=64528,60g`[/tex]

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

`[tex]mass=64.52Kg`[/tex]