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

##### 1 Answer

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*.

#"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 **every milliliter** of this substance has a mass of

#"1.50 g mL"^(-1) = 1.50 "g"/"mL" = "1.50 g"/"1 mL"#

Now, let's say that you are given **volume** of the sample.

Since you are given **mass**, place *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

Since you are given **volume**, place *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.