Density

Introduction

Instinctively (or as a by product of your everyday interactions with the world) you'll know that certain materials are heavier than others. For example, if someone was to ask you : are stone bricks or styrofoam bricks heavier? you'd probably say 'stone bricks' - and you'd be correct, but only if under the assumption that the bricks are the same shape, and thus volume.

What is Density?

Density is a measure of how much 'stuff' is within a fixed volume of a substance - be it a solid, liquid or gas. And the way to measure how much 'stuff' is in something is to measure its mass. Because everything is made up of molecules, and the molecules' mass is made up primarily of their protons and neutrons, measuring the density of something means you're able to compare how tightly packed it is with protons and neutrons. The denser something is, the more protons and neutrons are packed within it. Cool right? This explains why styrofoam is less dense (also known as lighter) than stone - it has lots of air pockets in its design.

Another way of thinking about density is that it is a way of working out how much a fixed volume of the substance weighs (or more accurately, what its mass is). For example, the density of liquid water at 30 degrees is 0.995 g/cm3. This tells us that every cubic centimeter of water (also known as 1 milliliter) has a mass of 0.995 grams.

Why is Density a useful measurement?

Different materials have different physical properties. Some of these different properties include strength, pliability, elasticity, conductivity and density. Measuring and categorizing substances by their physical properties allows us to design products with substances that have the most compatible physical properties. For example, we use aluminium to make planes because of its physical properties: it's strong, durable and it has a low density, which makes it light. This keeps the plane's structural weight to a minimum, and improves its fuel efficiency.

Having a catalog of substances' physical properties is also useful to consult with when we're trying to identify what an unknown sample is, or if we want to know if the sample in front of us is pure (e.g. gold vs. fool's gold).

How do we Calculate Density?

The formula we use to calculate density is below:

or

ρ = m / v

Where

• ρ (the Greek letter pho) represents density, in kg/m3 (or g/cm3),
• m represents mass, in kg (or g), and
• v represents volume, in m3 (or cm3).

Let's look at an example.

An Example
The volume of substance B below has a mass of 30 kg. What is its density?

We already have the mass of the substance (i.e. 30 kg), but before we can use the formula above, we need to work out its volume. The volume of a cuboidal container is given by multiplying its height by its depth by its width.

Volume = height x depth x width
Volume = 1 m x 2 m x 3m
Volume = 6 m3

The density of the substance can therefore be calculated as below:
Density = mass / volume
Density = 30 kg / 6 m3
Density = 5 kg/m3

Some Extra Points

A couple of points to also know about density:

• When you have two liquids that don't mix, like oil and water, the one with the lower density will float to the top. The densities of olive oil and water at room temperature are 0.920 kg/m3 and 0.995 kg/m3 respectively. Which one will float if the two are put into the same glass?

• The density of a substance will change based on its state. The density of water in its three different states is 0.960 kg/m3, 0.995 kg/m3 and 0.1000 kg/m3. Which density do you think relates to its solid state, liquid state, and gas state? Hint: The particles in a gas are further apart than they are in a solid. This means that there will be less molecules (and more empty space) within a fixed volume of gas compared to the same volume of liquid or solid.