Calculating Density

Density is a measure of the mass of material in a given volume, it is the property of a material that combines the molecular mass of the atoms in the material and how closely packed the molecules are.

Identical sized objects with different densities will have different mass.

Density, figure 1

Calculating Density

Density, figure 2

Density is a fixed property of a material, cutting a material in two will chance the volume and the mass but not the density.

Example calculations

  1. What is the density of a 2 m3 block of brass with a mass of 16,960 kg?

Density, figure 3

  1. What is the mass of a 4 ㎤ block of copper with a density of 8.79 g/cm3?

Density, figure 4

Note that although the SI unit of density is the kg/m3, a cubic meter of many materials is a very large amount and, therefore, the units of g/cm3 (grams per cubic centimeter) is frequently used.

For a liquid or a gas density can be given in kg/l or g/ml.

Density of States of Matter

As a material changes from a solid to a liquid and then to a gas, the particles of the material spread out. As the particles themselves are not changing their mass, this results in the density of a material reducing as it changes from a solid into a liquid then into a gas.

Density, figure 1

Each particle has the same mass in each state of matter, but as a solid has more particles per cubic metre than a gas, the solid has a higher density than the gas.

As liquids and gasses heat up the particles move faster and spread out more, thus they become

less and less dense the hotter they become, this is the principle that a hot air balloon uses to fly.

Solids, however, do not show noticeable changes in their density with temperature, as the lattice structure increases its vibrational energy, but the particles do not spread out from the lattice until the solid melts. .

An exception to prove the rule!

There is one important and notable exception to the general rule that density decreases as you move from a solid to a liquid: Ice and water.

Density of ice = 0.917 g/cm3

Density of water = 1 g/cm3 (at 5℃ and 1 atmosphere of pressure)

The reason for this is that the molecules of water have a positive and negative end, so when they form ice they push each other away slightly making them spread out and become less dense.

Ice is less dense than water and this is why it will float. If this were not true then ice as it formed would sink to the bottom on a lake, eventually the lake would freeze completely killing all the life in the lake.

Measuring Density

Finding the density of any object requires measuring the mass and the volume of the object, then using the formula for density:

Density, figure 1

For a solid object with a regular shape this is straightforward.

Measuring the density of a regular shaped solid

  1. Measure the three dimension, height, width and breadth
  2. Multiplethe dimensions to find volume
  3. Use a balance to find the mass
  4. Use the formula to find the density

Measuring the density of an irregular shaped solid

Measuring the mass is done in the same way as above, however, it is not possible to measure the dimensions in the same way. Instead the volume is found by using Archimedes Principle.

Archimedes discovered that if an object is fully immersed in water, the water is displaced by the same volume as the object. This is why the water level rises when someone get into a bath for example. If the object can be immersed in a measuring cylinder of water, then the increase in the volume of the water in the cylinder is equal to the volume of the object.

Density, figure 2

Measuring the density of a liquid

Place a container on a top pan balance and re-set the scale to zero using the tare function. Add a known volume of the liquid into the container and record the mass. The formula can be used in the same way as for a solid object, the units might be changed to g per ml.

Explain why liquid oxygen is more dense than oxygen in its gaseous form.
Your answer should include: molecules / closer
Explanation: The oxygen molecules will be closer together in the liquid phase compared to the gaseous phase, due to the increases in the kinetic energy of the gas. This results in less molecules per unit volume in the gas compared to the liquid and, therefore, to a lower density.