Final answer:
The density of a substance, calculated by mass divided by volume, shows that density and volume are inversely proportional: if volume increases, density decreases, and vice versa.
Step-by-step explanation:
The density formula, which is density (d) equals mass (m) divided by volume (V), or d = m/V, shows that density and volume are inversely proportional to each other. This means that if the volume of a substance increases, keeping the mass constant, the density decreases. Conversely, if the volume decreases, the density increases. For instance, if a sample of iron has a mass of 23.4 grams and a volume of 3.00 cm³, its density would be calculated as 23.4 grams divided by 3.00 cm³, which gives a density value. This relationship also explains why gases, which have atoms and molecules separated by more space, have lower densities compared to solids and liquids where atoms and molecules are packed closer together.
When the distance between atoms and molecules in a substance increases significantly, the volume increases by the cube of the factor of increase while the density decreases proportionally.