5.2: Density
14
Harper College Chemistry Department
We use the mass and volume of a substance to determine its density. Thus, the units of density are defined by the base units of mass and length.
The density of a substance is the ratio of the mass of a sample of the substance to its volume. The SI unit for density is the kilogram per cubic meter (kg/m 3 ). For many situations, however, this as an inconvenient unit, and we often use grams per cubic centimeter (g/cm 3 ) for the densities of solids and liquids, and grams per liter (g/L) for gases. Although there are exceptions, most liquids and solids have densities that range from about 0.7 g/cm 3 (the density of gasoline) to 19 g/cm 3 (the density of gold). The density of air is about 1.2 g/L. Table 1 shows the densities of some common substances.
| Densities of Common Substances | ||
|---|---|---|
| Solids | Liquids | Gases (at 25 °C and 1 atm) |
| ice (at 0 °C) 0.92 g/cm 3 | water 1.0 g/cm 3 | dry air 1.20 g/L |
| oak (wood) 0.60–0.90 g/cm 3 | ethanol 0.79 g/cm 3 | oxygen 1.31 g/L |
| iron 7.9 g/cm 3 | acetone 0.79 g/cm 3 | nitrogen 1.14 g/L |
| copper 9.0 g/cm 3 | glycerin 1.26 g/cm 3 | carbon dioxide 1.80 g/L |
| lead 11.3 g/cm 3 | olive oil 0.92 g/cm 3 | helium 0.16 g/L |
| silver 10.5 g/cm 3 | gasoline 0.70–0.77 g/cm 3 | neon 0.83 g/L |
| gold 19.3 g/cm 3 | mercury 13.6 g/cm 3 | radon 9.1 g/L |
While there are many ways to determine the density of an object, perhaps the most straightforward method involves separately finding the mass and volume of the object, and then dividing the mass of the sample by its volume.
\[\[ \text{density} = \frac{\text{mass}}{\text{volume}} \]\]
In the following example, the mass is found directly by weighing, but the volume is found indirectly through length measurements.
Calculation of Density Gold—in bricks, bars, and coins—has been a form of currency for centuries. In order to swindle people into paying for a brick of gold without actually investing in a brick of gold, people have considered filling the centers of hollow gold bricks with lead to fool buyers into thinking that the entire brick is gold. It does not work: Lead is a dense substance, but its density is not as great as that of gold, 19.3 g/cm 3 .
What is the density of lead if a cube of lead has an edge length of 2.00 cm and a mass of 90.7 g?
Solution The density of a substance can be calculated by dividing its mass by its volume. The volume of a cube is calculated by cubing the edge length.
\[\[\text{volume of lead cube}=2.00 \si{cm} \times 2.00 \si{cm} \times 2.00 \si{cm}=8.00 \si{cm^3} \] \[\text{density} = \frac{\text{mass}}{\text{volume}} = \frac{\text{90.7 g}}{8.00 \si{cm^3}}=\frac{11.3 \si{g}}{1.00 \si{cm^3}}=11.3 \si{g/cm^3} \]\]
(We will discuss the reason for rounding to the first decimal place in the next section.)
Check Your Learning
(a) To three decimal places, what is the volume of a cube (cm 3 ) with an edge length of 0.843 cm?
(b) If the cube in part (a) is copper and has a mass of 5.34 g, what is the density of copper to two decimal places?
To learn more about the relationship between mass, volume, and density, use this interactive simulator to explore the density of different materials, like wood, ice, brick, and aluminum.
Using Displacement of Water to Determine Density
This PhET simulation illustrates another way to determine density, using displacement of water. Determine the density of the red and yellow blocks.
Solution
When you open the density simulation and select Same Mass, you can choose from several 5.00-kg colored blocks that you can drop into a tank containing 100.00 L water. The yellow block floats (it is less dense than water), and the water level rises to 105.00 L. While floating, the yellow block displaces 5.00 L water, an amount equal to the weight of the block. The red block sinks (it is more dense than water, which has density = 1.00 kg/L), and the water level rises to 101.25 L.
The red block therefore displaces 1.25 L water, an amount equal to the volume of the block. The density of the red block is:
Experimental Determination of Density Using Water Displacement
A piece of rebar is weighed and then submerged in a graduated cylinder partially filled with water, with results as shown.
(a) Use these values to determine the density of this piece of rebar.
(b) Rebar is mostly iron. Does your result in (a) support this statement? How?
Solution
The volume of the piece of rebar is equal to the volume of the water displaced:
$\text{volume} = \SI{22.4}{mL} – \SI{13.5}{mL} = \SI{8.9}{mL} = \SI{8.9}{cm^3}$
(rounded to the nearest 0.1 mL, per the rule for addition and subtraction)
The density is the mass-to-volume ratio:
$\text{density} = \frac{\text{mass}}{\text{volume}} = \frac{\SI{69.658}{g}}{\SI{8.9}{cm^3}} = \SI{7.8}{g/cm^3}$
(rounded to two significant figures, per the rule for multiplication and division)
From [link] , the density of iron is 7.9 g/cm 3 , very close to that of rebar, which lends some support to the fact that rebar is mostly iron.
Check Your Learning
An irregularly shaped piece of a shiny yellowish material is weighed and then submerged in a graduated cylinder, with results as shown.
(a) Use these values to determine the density of this material.
(b) Do you have any reasonable guesses as to the identity of this material? Explain your reasoning.
Key Concepts and Summary
Measurements provide quantitative information that is critical in studying and practicing chemistry. Each measurement has an amount, a unit for comparison, and an uncertainty. Measurements can be represented in either decimal or scientific notation. Scientists primarily use the SI (International System) or metric systems. We use base SI units such as meters, seconds, and kilograms, as well as derived units, such as liters (for volume) and g/cm 3 (for density). In many cases, we find it convenient to use unit prefixes that yield fractional and multiple units, such as microseconds (10 −6 seconds) and megahertz (10 6 hertz), respectively.
Key Equations
- OpenStax Chemistry: Atom First , Chemistry: Atoms First. OpenStax CNX. Nov 13, 2018. Download for free at http://cnx.org/contents/4539ae23-1ccc-421e-9b25-843acbb6c4b0@9.17 . ↵