How can I use the density of a substance as a conversion factor?

Oct 14, 2016

Here's how you can do that.

Explanation:

The density of a substance tells you the mass of exactly one unit of volume of that substance.

This essentially means that density can be used as a conversion factor to go from the mass of a sample to the volume it occupies, or vice versa.

Now, density relates two quantities, mass and volume. To set density up as a conversion factor, simply arrange it by placing the quantity that is needed on top, i.e. as the numerator, and the quantity that is given on the bottom, i.e. as the denominator.

$\text{what you need goes on top"/"what is given to you goes on the bottom}$

So, for example, let's say that the density of an unknown substance is equal to ${\text{1.50 g mL}}^{- 1}$. This means that every milliliter of this substance has a mass of $\text{1.50 g}$.

$\text{1.50 g mL"^(-1) = 1.50 "g"/"mL" = "1.50 g"/"1 mL}$

Now, let's say that you are given $\text{25.0 g}$ of this substance and asked to find the volume of the sample.

Since you are given mass, place $\text{1.50 g}$ as the denominator. This will get you

25.0 color(red)(cancel(color(black)("g"))) * "1 mL"/(1.50color(red)(cancel(color(black)("g")))) = "16.7 mL"

Now let's say that your sample has a volume of $\text{112 mL}$ and you're interested in finding its mass.

Since you are given volume, place $\text{1 mL}$ as the denominator. This will get you

112 color(red)(cancel(color(black)("mL"))) * "1.50 g"/(1color(red)(cancel(color(black)("mL")))) = "168 g"

And there you have it. We've used the density of the substance to convert from mass to volume or vice versa.