# Relative Density.

Relative density is defined as the ratio of the density of a substance to the density of an equal volume of water.

Note: Density of pure water =1gcm-3 = 1000kgm-3 since density = mass ⁄ Volume, Then:

Note:

Relative density has no units.

Experiment: To determine the Relative density of a liquid using a density bottle.

The bottle contains exactly the same volume when the liquid level is at the hole.
mass of empty bottle M0

A dry density bottle with a stopper is weighed when empty using a balance.

Mass of bottle filled with the liquid M2

A dry density bottle with a stopper is weighed when filled with the liquid using a balance.
Mass of bottle filled with water M1

After removing the liquid and rinsing out the density bottle with water, the density bottle is filled with water and weighed again.

The measurements are recorded as below:

Mass of empty: =m0
Mass of bottle full of water: =m1
Mass of bottle full of liquid: =m2
Mass of liquid: =m2−m0
Mass of water: =m1−m0

Note:

The advantage of using a density bottle in measuring the relative density of a solid is that it is accurate compared to other methods.

Measurement of relative density of a solid

This can be found by weighing the solid in air and when fully immersed in water.

The solid immersed in water displaces an amount of water equal to its volume. The relative density is then calculated using;

Example 1

A density bottle was used to measure the density of mercury. The following measurements were taken:

Mass of empty bottle = 20g
Mass of bottle full of mercury = 360g
Mass of bottle full of water = 45g

Calculate the;
a. Relative density of mercury
b. Density of mercury

Solution

Example: 2

A density bottle has mass 75g when empty, 95g when full of water and 99g when full of a liquid.

Calculate the:
(i) Relative density of the liquid.
(ii) density of the liquid

Solution