Find the mass of air inhaled during a deep breath. Use a value of two point zero liters for the volume of the air in a value of one point two nine kilograms per meter cubed for the density of air.
So in this exercise, we want to solve for a mass — Let’s call that 𝑚 — of air that’s inhaled during a deep breath, and we’ve heard that two point zero zero liters the volume of the air that is being inhaled in this breath.
So we have a mass; we have a volume; and then finally we’re given a density, the density of air, as one point two nine kilograms per meter cubed. So again we’re looking for mass. We’ve been given a volume — we’ll call it capital 𝑉 — two point zero zero liters. And we’re given a density; we’ll call it the Greek letter 𝜌.
And that is equal to one point two nine kilograms per cubic meter. Now you may recall the definition that says that density is equal to mass divided by volume. We can use this relationship and rearrange it to solve for the mass 𝑚, which is what we’re after in this case.
If we start with the equation in its symbol form, which says that 𝜌 equals 𝑚 over 𝑉, or density equals mass over volume, then you can see we will want to multiply both sides by capital 𝑉, the volume, to isolate the mass.
When we do that, the volume on the right-hand side of the equation cancels out and we’re left with an expression that reads 𝑚 equals 𝑉 times 𝜌 or mass equals volume times density.
So let’s plug in the values for 𝑉 and 𝜌 we’ve been given here. 𝑉 is two point zero zero liters, and 𝜌 is one point two nine kilograms per meter cubed. Now before we multiply these two terms together, you may see you that we’ll need to do a little bit of unit conversion so that our volumes are using the same unit bases. Right now we have a volume in liters on our left term and a volume in cubic meters in our right. So I’ll want to get those to agree with one another.
To do that, let’s recall the definition that one cubic meter is equal to 1000 liters. This definition means that we can replace the meters cubed in the denominator of our density with 1000 L or 1000 liters.
When we do that, you can see that the liters unit cancels out and we’re left with a final unit of kilograms, which is the unit of mass, so this is a very good sign we’re gonna get an answer in terms of the units that we want.
Now to finish off, we multiply through two point zero zero times one point two nine divided by 1000. And we get an answer of two point five eight times ten to the negative third kilograms, which is the same as two point five eight grams.
That is the mass of air that is inhaled during a deep breath when the volume of our lungs is two point zero zero liters and the density of air is one point two nine kilograms per meter cubed.