Density (mass per unit volume) is not a fundamental property of nature but a so-called derived unit, which is a quantity that cannot be measured directly with any device (i.e., common lab instrument). One can't measure density of a substance with a ruler, scale or bucket. Instead we must measure the substance's mass, then measure its volume, so that we can calculate the density by dividing the mass by the volume.

## Understanding Density

Consider two unit cubes, each having the same volume. If the ball in each cube has the same mass, which box would weigh more? And why?

The box that has more balls has more mass per unit volume (i.e., it has a higher density). Thus, density is a property of matter, and the density of a material helps to distinguish it from other materials. Different materials have different densities (Table 1). There are two factors that contribute to the density of an object.

1. The mass of the atoms or molecules that makes up the material.
2. The volume or amount of space the material occupies. If the molecules or atoms are “packed” in more closely, the object will be denser.

Table 1.  Density of common substances

 Substance Density, 103 kg/m3 Air 0.0012 Aluminum 2.70 Copper 8.92 Gold 19.3 Iron 7.86 Lead 11.3 Magnesium 1.75 Osmium a 22.61 Uranium 18.7 Water 1.00

## Definition and Units

The density of a substance is the relationship between the mass of the substance and how much space it takes up (i.e., its volume). The higher an object's density, the higher its mass per unit volume. The average density of an object equals its total mass divided by its total volume. A denser object (such as iron) will have less volume than an equal mass of some less-dense substance (such as water).

Since mass is usually expressed in grams and volume in cubic centimeters, density is typically expressed in grams/cubic centimeter (g/cm3) or g/cc. In the SI system of units, however, density is designated in kg/m3 (kilogram per cubic meter). The unit conversion is shown in Equation 1.

(1) 1 kg/m3 = 1,000 g/1,000cm3 = 1 kg/L

## Relative Density

Relative density (formerly called specific gravity) is a dimensionless quantity defined as the density of a substance divided by the density of a given reference material (in most cases this usually means with respect to the density of water, which is 1 at standard temperature and pressure). If a substance's relative density is less than 1, then it is less dense than the material it is being referenced to; if greater than 1, then it is denser. If the relative density is exactly 1, then the densities are equal (i.e., equal volumes of the two substances have the same mass).

## Calculating Density

We can calculate density using a simple formula (Equation 2).

(2) Density = Mass ÷ Volume

Note that density is the relation of mass and volume, not weight and volume.

Next Time: The difference between mass and volume and weight and volume is further explained in our next blog.