Density

Density describes how much mass is contained in a given volume. A substance with a greater density has more mass in the same volume.

Density is mass per unit volume. It is calculated by dividing the mass of a substance by the volume it occupies:

Here, $$\rho$$ (rho) is density, $$m$$ is mass and $$V$$ is volume.

Density units

Density is commonly expressed in kilograms per cubic metre, $$\mathrm{kg/m^3}$$, or grams per cubic centimetre, $$\mathrm{g/cm^3}$$. The mass and volume units must match the density unit: use kilograms and cubic metres for $$\mathrm{kg/m^3}$$, or grams and cubic centimetres for $$\mathrm{g/cm^3}$$.

For example, a substance with a mass of $$200\ \mathrm{g}$$ and a volume of $$100\ \mathrm{cm^3}$$ has a density of $$2\ \mathrm{g/cm^3}$$.

Finding mass or volume from density

The density equation can be rearranged to find mass when density and volume are known, or volume when mass and density are known:

Measuring Density

Density tells us how much mass is contained in a given volume. To determine it, measure the mass and volume of the substance, then divide the mass by the volume:

Here, $$\rho$$ is density, $$m$$ is mass and $$V$$ is volume. Use consistent units: mass in kilograms and volume in cubic metres give density in $$\mathrm{kg/m^3}$$; mass in grams and volume in cubic centimetres give density in $$\mathrm{g/cm^3}$$.

Measuring the density of a liquid

Measure the mass of an empty measuring cylinder with a balance. Pour the liquid into the cylinder, read its volume and measure the mass of the cylinder with the liquid. Subtract the empty cylinder’s mass from the combined mass to find the mass of the liquid. Divide this mass by the measured volume.

A cylinder may show volume in millilitres: $$1,\mathrm{mL} = 1,\mathrm{cm^3}$$, so a volume in millilitres can be used with a mass in grams to give density in $$\mathrm{g/cm^3}$$.

Measuring the density of a regular solid

Measure the solid’s mass with a balance. Measure its dimensions and use the appropriate geometric formula to calculate its volume. For example, the volume of a cuboid is $$V = \text{length} \times \text{width} \times \text{height}$$. Divide the measured mass by the calculated volume.

Measuring the density of an irregular solid

For an irregular solid that sinks, measure its mass with a balance. To find its volume, use displacement:

1. Pour enough liquid into a measuring cylinder to cover the solid and record the initial volume.
2. Fully immerse the solid in the liquid and record the new volume.
3. Subtract the initial volume from the new volume. The increase is the volume of liquid displaced, which equals the volume of the solid.

Divide the solid’s mass by this volume to find its density. Alternatively, collect the liquid displaced by the fully immersed solid and measure the collected liquid’s volume.

Floating and Density

An object’s overall density describes how much mass it has for its total volume. To predict whether it will float or sink, compare this density with the density of the liquid.

• If the object is less dense than the liquid, it floats at the surface.
• If the object is more dense than the liquid, it sinks.
• If the object and liquid have equal densities, the object can remain suspended within the liquid.

Overall density is the object’s total mass divided by its total volume. For a hollow object, the overall density includes the space enclosed by the object, not just the material from which it is made.

Comparing densities in the same units

Densities must be expressed in the same units before their numerical values are compared. For example, an object with a density of $$0.8\ \mathrm{g/cm^3}$$ has a density of $$800\ \mathrm{kg/m^3}$$. In a liquid with a density of $$1000\ \mathrm{kg/m^3}$$, the object floats because its density is lower.

Density of Immiscible Liquids

Some liquids do not mix to form a single uniform liquid. These liquids are immiscible and can settle into separate layers.

When two immiscible liquids have different densities, the less dense liquid floats above the more dense liquid. Density describes how much mass a substance has in a given volume: for equal volumes, the liquid with the greater mass is denser.

Comparing the densities of immiscible liquids

Densities must be expressed in the same units before their numerical values are compared. For example, a liquid with a density of $$0.80,\mathrm{g/cm^3}$$ has a density of $$800,\mathrm{kg/m^3}$$. If it is immiscible with a liquid of density $$1000,\mathrm{kg/m^3}$$, the first liquid settles above the second because it is less dense.

If two immiscible liquids have equal densities, density alone does not determine which liquid is above the other.