In this explainer, we will learn how to define density, calculate the density of a substance, and predict whether it will float or sink in water.

Some materials are colorful, while others are colorless. Some have a strong taste or smell, and some are both flavorless and odorless. Scientists can separate substances according to difficult-to-measure properties like taste or smell. They can also separate them according to easier-to-measure properties like density.

Density is the amount of mass per unit volume and is, therefore, a measure of compactness. Materials with a high density are more compact than those with a lower density.

Density determines whether something floats or sinks in a liquid or gas. A substance floats in a liquid or gas of higher density. It sinks in a liquid or gas of lower density.

### Definition: Density

Density is the amount of mass per unit volume.

### Equation: Density

Water is a relatively compact substance, and it ordinarily has a density of
1 g/cm^{3}. Materials float on water if they have a density less than
1 g/cm^{3}
and sink if their density is greater than
1 g/cm^{3}. Cork floats on water because it has a very low density of about
0.2 g/cm^{3}. It is much less dense than water.

Wood is another material that floats on water since it is less dense than
1 g/cm^{3}. Most types of wood have a density of about
0.6 g/cm^{3}, but some can have a
density as low as 0.1 g/cm^{3}. Metals like aluminum are much denser than cork and wood. They ordinarily
sink in water, as their density is greater than
1 g/cm^{3}.

### Example 1: Understanding Why Some Objects Float on Water While Others Sink

The image below shows a tank of water into which various objects have been placed. Which of the following statements might explain what is observed?

- The ice cube and cork have densities greater than the density of water.
- The cork and stone have densities less than the density of water.
- The stone and iron nail have densities greater than the density of water.
- The piece of wood and iron nail have densities less than the density of water.
- The objects all have the same density as water.

### Answer

Density is a property of all materials and describes the compactness of a substance. A substance is compact if it has a high density and less compact if it has a lower density. Scientists determine density using the following equation:

A substance floats on water if it is less dense than water. Ice, wood, and cork all float on water because they have lower densities than water. Most types of stone and iron sink in water because they are denser than water.

The figure shows a stone and iron nail at the bottom of a tank of water. The stone and iron nail must have sunk to the bottom of the container because these objects are denser than water. So, choice C must be the answer to this question.

Let us use the density equation to calculate the density of
a medium-sized granite stone. We will first state that the
stone has a mass of
540.0 g and a volume of
200.0 cm^{3}. The first line shows that the stone measures
540.0 g:

The second line shows that the stone has a volume of
200.0 cm^{3}:

We can now write the density equation,
and make the mass and volume terms equal
540.0 g and
200.0 cm^{3}:

The result of this calculation shows that the granite stone has a
density of 2.7 g/cm^{3}:

Granite stones sink in water, as they are compact and denser than water.

### Example 2: Determining the Density of a Substance from Its Mass and Volume

A substance has a mass of 13.5 g
and occupies a volume of 5 cm^{3}. What is its density?

### Answer

The following equation shows how density depends on mass and volume:

The substance in question weighs 13.5 g
and has a volume of 5 cm^{3}. So, we can put these values into the density equation to determine the
density of this unidentified substance.

The following density equation has the mass and volume terms equal to
13.5 g and
5 cm^{3}:

The result of this calculation shows that the material in
question has a density of
2.7 g/cm^{3}:

So, the answer to this question is
2.7 g/cm^{3}.

We can do experiments to determine the density of a liquid and then figure out its name or composition using reference data. Let us imagine we are figuring out the name of an unidentified yellow liquid. We first measure the mass of an empty graduated cylinder as 80 g:

We then pour 100.0 cm^{3}
of the yellow liquid into the cylinder and find that the filled
cylinder measures 172 g:

So, the mass of the liquid in the graduated cylinder must be the difference between 172 g and 80 g:

The result of this calculation is on the following line:

Hence, the liquid has a mass of 92 g.

We then use this experimental data to determine the density of the yellow liquid. We first write the density equation on one line:

We then put the values 92 g
and 100.0 cm^{3}
into the density equation:

The result of the equation shows that the liquid has a density of
0.92 g/cm^{3}:

We can then compare the calculated density with reference data to help us determine the identity of the yellow liquid. The following table shows the density of some common liquid substances.

Liquid | Density (g/cm^{3}) |
---|---|

Petrol oil | 0.85–0.89 |

Vegetable oil | 0.91–0.93 |

Castor oil | 0.97 |

Gasoline | 0.66–0.69 |

Tap water | 1.00 |

Ethyl alcohol | 0.79 |

Orange juice | 1.05 |

Honey | 1.38–1.45 |

Milk | 1.03–1.04 |

Glycerin | 1.26 |

Mercury | 13.55 |

The liquid is yellow and has the density of vegetable oil. We can reasonably assume the unidentified substance is vegetable oil and later confirm this through one or two more scientific experiments. We should recognize from these calculations that vegetable oil floats above water since it is less dense than water.

### Example 3: Determining the Density of an Unidentified Liquid

A student wants to determine the density of a liquid. They first weigh a glass beaker and then add exactly
50 cm^{3}
of the liquid into the beaker. Finally, the
glass beaker is weighed again. The student records
their measurements in the table shown below. Using this information, what is the density of the
liquid to 1 decimal place?

Mass of Empty Glass Beaker (g) | Mass of Glass Beaker and Liquid (g) |
---|---|

67 | 112 |

### Answer

Let us first determine the mass of the liquid in the glass beaker as the difference between the mass of the empty glass beaker and the mass of the glass beaker and liquid:

The result of this calculation shows that the mass of the liquid is equal to 45 g:

We can now write the density equation to determine the answer. The density equation is

We can now put the values 45 g
and 50 cm^{3}
into the density equation:

The result of this calculation shows that the unidentified
liquid has a density of 0.9 g/cm^{3}:

This number is already written to one decimal place, so the answer to this question is
0.9 g/cm^{3}.

We can rearrange the density equation to determine the mass or volume of a substance.

The following equation shows how we can rearrange the density equation to determine a volume from known mass and density:

Similarly, the next equation shows how we rearrange the density equation for determining an unknown mass from known density and volume:

Let us imagine we find a 10 cm^{3}
pure gold nugget and want
to calculate its mass. We would first rearrange the density
equation to have volume and density on the right side of
the equals sign:

We would then replace volume with 10 cm^{3}:

Next, we would replace density with a value of
19.3 g/cm^{3},
as this is the density of gold:

The result of this calculation shows that the nugget is quite heavy, as its mass equals 193 g:

### Example 4: Determining the Mass of an Unidentified Liquid

An unknown liquid is claimed to have a density of
0.79 g/cm^{3}. If this claim is true, what would the mass of
40 cm^{3} of this liquid be?

### Answer

Let us first rearrange the density equation to have mass alone on the left side of the equals sign:

We can then multiply the values for the volume,
40 cm^{3},
and the density, 0.79 g/cm^{3}:

The result of this calculation shows that the liquid should have a mass of 31.6 g:

So, the answer to this question is 31.6 g.

Water is a relatively compact substance and is denser than petrol and oil. People do not use water for extinguishing petrol or oil fires because water sinks below the surface of these liquids. It then ends up being superheated and can explosively erupt outward. Water can make a petrol or oil fire many times more dangerous.

Balloons ordinarily contain gases of the elements hydrogen or helium, which are less dense than air. Hydrogen and helium balloons effectively float in air because they have such an incredibly low density. They are much less dense than air and will rise into the atmosphere if someone or something is not holding on to them.

Let us summarize what we have learned in this explainer.

### Key Points

- Density is the amount of mass per unit volume.
- We can calculate density using the following equation:
- Objects will tend to float on water if they are less dense than water.
- Objects will ordinarily sink in water if they are denser than water.
- We can often rearrange the density equation to determine an unknown volume or mass.
- Water is denser than petroleum and oil and is unsuitable for extinguishing petrol or oil fires.
- Balloons effectively float in air if they contain the low-density elements hydrogen or helium.