Density as a Conversion Factor

Suppose you wanted to know how much space a particular mass of a certain substance would occupy. To convert mass to volume (or vice versa), you must know the relationship between the mass and volume and that relationship is density. (The following examples are also in your workbook in Example 20.)

Quick review: This example shows you how to calculate density. You've already done that. You divide the mass by the volume and that gives you the density.

Mass = 5.0 g Volume = 2.0 mL
What is the density?
Density =	5.0 g 2.0 mL	= 2.5 g/mL

Now that we know the density for this material, we can calculate how much 6.0 milliliters of it would weigh as asked for here. Take the 6.0 milliliters and then use the density 2.5 grams per milliliter as a conversion factor. The 2.5 goes on top with the grams and the one milliliter goes on the bottom because you want to cancel out milliliters and end up with grams. The result is 15 grams.

How much would 6.0 mL weigh?
6.0 mL x	2.5 g 1 mL	= 15 g

Here we are asked how much volume would four grams of this material occupy? You start with 4.0 grams and multiply by one milliliter over 2.5 grams and you come up with the answer of 1.6 milliliters.

How much volume would 4.0 g take up?
4.0 g x	1 mL 2.5 g	= 1.6 mL

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E-mail instructor: Eden Francis