How can I use the density of a substance as a conversion factor?
Here's how you can do that.
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
#"1.50 g mL"^(-1) = 1.50 "g"/"mL" = "1.50 g"/"1 mL"#
Now, let's say that you are given
Since you are given mass, place
#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
#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.