The density of air at ordinary atmospheric pressure and 25^∘ C is 1.19 g / L. What is the mass,

The density of air at ordinary atmospheric pressure and 25^∘...

The density of air at ordinary atmospheric pressure and $25^{\circ} \mathrm{C}$ is $1.19 \mathrm{~g} / \mathrm{L}$. What is the mass, in kilograms, of the air in a room that measures $4.5 \mathrm{~m} \times 5.0 \mathrm{~m} \times 2.5 \mathrm{~m} ?$

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Key Concepts

Unit Conversion

Unit conversion involves changing one set of units to another while maintaining the same quantity. In physics and chemistry, it's common to convert between differing measurement systems, such as from grams per liter to kilograms per cubic meter, to ensure consistency across calculations.

Volume Calculation

Volume calculation is the process of determining the amount of space occupied by an object or region. For geometric shapes like rectangular prisms, the volume is calculated by multiplying the lengths of its three dimensions. This concept is crucial when determining the total volume in which a physical property such as density is applied.

Density

Density is a fundamental physical property defined as the mass per unit volume of a substance. It provides a relationship between the amount of matter and the space it occupies, which is essential in calculations where either mass or volume needs to be determined given the other quantity.

Transcript

00:01 Here we're going to be talking about density and density by definition is known as a mass over volume.

00:08 And so here we have stated that the density of air at 25 degrees celsius is equal to 1 .19 grams per liter.

00:18 And we have a room here with these dimensions.

00:21 It measures 4 .5 by 2 .0 by 5 .0 meters.

00:27 And so if we want to go ahead and determine the mass of a room, of the air in the room, what we're going to do? well, we already know the density of that room at that specific type of temperature.

00:41 And what we have dimensions of that room.

00:43 So what we can do is go ahead and determine the volume of that room.

00:47 And once we determine the volume, we can multiply the volume by the density in order to get the mass.

00:52 So if you want to just go ahead and find the volume in which we know volume is length.

00:57 Times width times height.

00:59 So we can do 5 .0 times 2 .0 times 4 .5 meters.

01:07 We can add the unit later.

01:09 When we do that in our calculator, we're going to get 56 .25 meters cubed.

01:18 So this is our volume.

01:19 Our 56 .25 meters cube.

01:21 So let's go ahead and just for emphasis, put that it equals v.

01:27 That's going to be our volume.

01:29 And so now if you want to just go ahead and play, plug everything into our equation here for density...

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