We explain what density is, its formula, how to calculate it, the types that exist and we give several examples.

**What is density?**

The **density** The mass of a substance is the quotient between the mass of the sample and the volume it occupies, its unit of measurement being kg/m3 in the International System of Units. The Greek letter ρ (rho) is often used to denote it.

The density of water, which is the universal fluid, is 1000 kg/m3 or 1 g/cm3 at 25°C, since the density undergoes changes with temperature and pressure.

Many times objects with the same dimensions are found, and yet some are lighter and others heavier, this is due to differences in density. The lighter object has less density than the heavier one.

Density is an intensive property of matter, which does not depend on the amount of mass of the sample that is examined, since it is the mass/volume ratio that remains constant for the same substance. This makes it possible to differentiate one substance from another.

Materials have a wide range of densities, the lowest being those of gases, so the unit kg/m3 is very large and grams/liter or g/L is preferred. Other frequently used units are grams/milliliter or grams/cubic centimeter.

The concept of density is especially useful when working with continuous media such as fluids, whether they are gases or liquids.

**density formula**

According to the given definition, density has a mathematical formula given by:

Where the density is ρ, m is the mass and V the volume.

**How is density measured?**

The density of an object can be calculated if its mass and volume are previously measured. The latter is not always easy, since the sample can be irregular, however there are several methods.

**geometric method**

If the sample has a regular geometric shape, there are formulas that allow the volume to be calculated based on its dimensions. As for the mass, this can be obtained with the help of a scale.

**Test tube method: volume displacement**

If the object is not regular, its volume can be determined by measuring the volume displaced by completely immersing it in a fluid such as water.

For this, a graduated container is used and filled with an exact volume of water V1, then the object is completely submerged and the new volume V2 is measured. The volume of the object is equal to the difference V2 – V1.

To use this method, the substance in the sample must not dissolve in the water and a graduated container of the appropriate size must be available.

**Density using Archimedes’ principle**

Archimedes’ principle can be used to find out the density of a solid sample. The principle states that a body partially or totally submerged in a fluid experiences an upward force called thrust, the magnitude of which is equal to the weight of the fluid displaced by placing the body.

To determine the density of an object using Archimedes’ principle, follow these steps:

Determine the mass mc of the object using a balance.

Fill a container with a fluid whose density is known, which is usually distilled water. This value is called m1.

Completely submerge the solid object in the container with water, taking care that it does not touch the walls. It is observed that the fluid exerts a push **AND** on the solid upwards, and this in turn, by Newton’s third law, exerts a reaction of the same magnitude on the water, but in the opposite direction.

When weighing the set, the value obtained, called m2, will be that of the container filled with water plus this reaction.

From the equation for density, the volume V of the body can be expressed, which is equivalent to the volume of fluid displaced:

where mc and ρc are the mass and density of the body, respectively, while mf and ρc are the mass and density of the displaced fluid. From this expression the density of the body ρc is cleared:

The mass of the displaced fluid mf is simply:

mf = m2 −m1

Therefore:

**types of density**

**absolute density **

It is the density as previously defined: the quotient between the mass and the volume of the sample.

**Relative density**

also called *specific gravity*, is the density of a substance with respect to another that is taken as a reference. For solids and liquids this reference substance is water at 4ºC and 1 atm of pressure and for gases it is dry air. It is calculated by:

Relative density = material density / water density

Both the density of the material and that of the water must be measured under identical conditions of pressure and temperature, and expressed in the same units.

The following image shows the relative densities of steel and wood.

Since the density of steel is 7800 kg/m3 and that of water is 1000 kg/m3, the relative density of steel, denoted sg, is:

sg = 7800 / 1000 = 7.8

For its part, the relative density of wood is:

sg = 500 / 1000 = 0.5

Objects whose relative density is less than 1 float on water, while those whose relative density is greater than 1 sink.

**Apparent density**

It is calculated by the ratio between the mass of the sample and its volume, including pores and air spaces:

Bulk density = Mass / Volume = (Particle mass + Air mass)/ (Particle volume + Air volume)

**examples of density**

The lightest metal of all is lithium, with a density of 530 kg/m3 The density of blood is 1060 kg/m3 Osmium is the densest metal known, with a density of 22570 kg/m3 Plasma quarks have a density of 1×1019kg/m3

**solved exercises**

**Exercise 1**

Calculate the density of the cork, knowing that a cube made of this material, which measures 1.5 cm on a side, has a mass of 1 g.

The volume of a cube is:

V = ℓ3 = (1.5 cm)3 = 3.375 cm3

The statement indicates that the mass m of the cube is m = 1 g, therefore, substituting values into the density equation:

ρ = m/V = 1g / 3.375 cm3 = 0.296 g/cm3

**Exercise 2**

What is the mass of a sphere made of osmium with a radius of 15 cm?

Starting from the density equation:

The mass is cleared as:

m = ρ∙V

It is necessary to calculate the volume of the sphere, which is given by the formula:

where r is the radius of the sphere. Since the density of osmium is 22570 kg/m3, it is convenient to express the 15 cm in meters:

r = 15 cm = 15 × 10−2 m

V = (4/3)π×(15 × 10−2 m)3 = 0.01414 m3

This value is substituted in the mass clearance:

m = ρ∙V = 22570 kg/m3 × 0.01414 m3 = 319.1 kg

**References**

Chang, R. 2013. Chemistry. 11th Edition. McGraw Hill Education.

Giancoli, D. 2006. Physics: Principles with Applications. 6th. Ed Prentice Hall.

Shipman, J. 2009. An Introduction to Physical Science. Twelfth edition. Brooks/Cole, Cengage Editions.

Tippens, P. 2011. Physics: Concepts and Applications. 7th Edition. McGraw Hill.

University of Antioquia. Density of the solids. Retrieved from: docencia.udea.edu.co.