Density and Its Uses
Density is an intrinsic property of matter. We define density (d) as the mass or volume of a substance at a given temperature. We write d = m/v where d is density, m is mass, and v is volume. If we know two of the variables in this equation, we can solve for the third algebraically. The units for density are a mass unit divided by a volume unit. The units used to describe density often differ for the phases of matter: solids (g/cm3), liquids (g/mL), and gases (g/L).
After you read this section, try the practice problem examples 1 and 2.
Most of us have long understood that oil is lighter than water, or that iron is heavier than sugar. But in making such statements, we are implicitly comparing equal volumes of these substances: after all, we know that a cup of sugar will weigh more than a single ordinary steel nail.
Mass and volume, as we learned in the previous unit, are measures of the quantity of a substance, and as such are defined as extensive properties of matter.
You will recall that the ratio of two extensive properties is
always an intensive property – one that characterizes a particular kind of matter, independently of its size or mass. It is this ratio, (mass ÷ volume), that we are concerned with in this lesson.
These plots show how the masses of three liquids vary with their volumes. Notice that
- the plots all have the same origin of (0,0): if the mass is zero, so is the volume;
- the plots are all straight lines, which signify direct proportionality.
The only difference between these plots is their slopes. Denoting mass and volume by m and V respectively, we can write the equation of each line as m = ρV, where the slope ρ (Greek lower-case rho) is the proportionality constant that relates mass to volume. This quantity ρ is known as the density, which is usually defined as the mass per unit volume: ρ = m/V.
The volume units milliliter (mL) and cubic centimeter (cm3) are almost identical and are commonly used interchangeably.
The general meaning of density is the amount of anything per unit volume. What we conventionally call the density is more precisely known as the mass density.
Density can be expressed in any combination of mass and volume units; the most commonly seen units are grams per mL (g mL–1, g cm–3), or kilograms per liter.
1 kg m–3 = 1 g L–1 = .0624 lb ft–3