# 11.2 Density

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## Learning objectives

By the end of this section, you will be able to:

• Define density.
• Calculate the mass of a reservoir from its density.
• Compare and contrast the densities of various substances.

The information presented in this section supports the following AP® learning objectives and science practices:

• 1.E.1.1 The student is able to predict the densities, differences in densities, or changes in densities under different conditions for natural phenomena and design an investigation to verify the prediction. (S.P. 6.2, 6.4)
• 1.E.1.2 The student is able to select from experimental data the information necessary to determine the density of an object and/or compare densities of several objects. (S.P. 4.1, 6.4)

Which weighs more, a ton of feathers or a ton of bricks? This old riddle plays with the distinction between mass and density. A ton is a ton, of course; but bricks have much greater density than feathers, and so we are tempted to think of them as heavier. (See [link] .)

Density , as you will see, is an important characteristic of substances. It is crucial, for example, in determining whether an object sinks or floats in a fluid. Density is the mass per unit volume of a substance or object. In equation form, density is defined as

$\rho =\frac{m}{V},$

where the Greek letter $\rho$ (rho) is the symbol for density, $m$ is the mass, and $V$ is the volume occupied by the substance.

## Density

Density is mass per unit volume.

$\rho =\frac{m}{V},$

where $\rho$ is the symbol for density, $m$ is the mass, and $V$ is the volume occupied by the substance.

In the riddle regarding the feathers and bricks, the masses are the same, but the volume occupied by the feathers is much greater, since their density is much lower. The SI unit of density is ${\text{kg/m}}^{3}$ , representative values are given in [link] . The metric system was originally devised so that water would have a density of $1\phantom{\rule{0.25em}{0ex}}{\text{g/cm}}^{3}$ , equivalent to ${\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}$ . Thus the basic mass unit, the kilogram, was first devised to be the mass of 1000 mL of water, which has a volume of 1000 cm 3 .

Densities of various substances
Substance $\rho \left({\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}\text{g/mL}\right)$ Substance $\rho \left({\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}\text{g/mL}\right)$ Substance $\rho \left({\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}\text{g/mL}\right)$
Solids Liquids Gases
Aluminum 2.7 Water (4ºC) 1.000 Air $1\text{.}\text{29}×{\text{10}}^{-3}$
Brass 8.44 Blood 1.05 Carbon dioxide $1\text{.}\text{98}×{\text{10}}^{-3}$
Copper (average) 8.8 Sea water 1.025 Carbon monoxide $1\text{.}\text{25}×{\text{10}}^{-3}$
Gold 19.32 Mercury 13.6 Hydrogen $0\text{.}\text{090}×{\text{10}}^{-3}$
Iron or steel 7.8 Ethyl alcohol 0.79 Helium $0\text{.}\text{18}×{\text{10}}^{-3}$
Lead 11.3 Petrol 0.68 Methane $0\text{.}\text{72}×{\text{10}}^{-3}$
Polystyrene 0.10 Glycerin 1.26 Nitrogen $1\text{.}\text{25}×{\text{10}}^{-3}$
Tungsten 19.30 Olive oil 0.92 Nitrous oxide $1\text{.}\text{98}×{\text{10}}^{-3}$
Uranium 18.70 Oxygen $1\text{.}\text{43}×{\text{10}}^{-3}$
Concrete 2.30–3.0 Steam $\left(\text{100º C}\right)$ $0\text{.}\text{60}×{\text{10}}^{-3}$
Cork 0.24
Glass, common (average) 2.6
Granite 2.7
Earth's crust 3.3
Wood 0.3–0.9
Ice (0°C) 0.917
Bone 1.7–2.0

As you can see by examining [link] , the density of an object may help identify its composition. The density of gold, for example, is about 2.5 times the density of iron, which is about 2.5 times the density of aluminum. Density also reveals something about the phase of the matter and its substructure. Notice that the densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. The densities of gases are much less than those of liquids and solids, because the atoms in gases are separated by large amounts of empty space.

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