What is Density?

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.

How are Density and Matter Related?

Density is one of the most important and easily measured physical properties of matter. It is widely used to identify pure substances as they have unique density values and to characterize the composition of various kinds of mixtures. The density of a substance can be measured without altering its chemical identity.

It expresses a mass-to-volume relationship. We know that mass and volume are extensive properties of matter that determine a substance’s quantity. The more mass an object contains in a certain space, the denser it is. The relationship does not solely depend on the closely packed atoms of any substance or compound.

For example, how can one distinguish one metric ton (1000 kg) of feathers and one metric ton of bricks?

The mass of both these objects will be same, i.e., one metric ton. However, a metric ton of feathers will occupy a very large volume of the order of $102 \mathrm{million} {\mathrm{cm}}^3$. Whereas, a metric ton of bricks will occupy around half a million cm3. The bricks will be denser because their mass is packed into a smaller volume than that of bricks. Thus, the relationship between mass and volume of any substance is what defines the property of density.

Density  is usually defined as the ratio of an object’s mass (m) to its volume (V) or the mass per unit volume. The ratio of two extensive properties is always an intensive property which means that the value of density does not depends on the quantity of matter present. It is denoted by a Greek letter  (rho) and is given as,

$\rho =mv$

Though, conventionally we call it density, but more precisely it is known as ‘mass density’. The units of density are commonly expressed as gram per cubic meter $\mathrm{g} {\mathrm{cm}}^{-3}$ for solids, gram per millilitre $\mathrm{g} {\mathrm{ml}}^{-1}$ for liquids and gram per litre $\mathrm{g} {\mathrm{L}}^{-1}$ for gases.

Specific Gravity

A concept closely related to density is specific gravity (SG) or even more appropriately known as the relative density of a material. It is simply the ratio of the material’s density to the density of water. If the specific gravity of an object is less than one (SG < 1), it will float in water and if it is greater than one (SG > 1), the object will sink in water.

The density of water at room temperature 25°C is exactly $1 \mathrm{g} {\mathrm{ml}}^{-1}$ (or equivalent to $1 \mathrm{kg} {\mathrm{L}}^{-1}$). This is due to the very definition for 1 Litre in SI system which states that 1 L is the amount of water that has a mass of 1 kg. Unlike density, SG is a unitless quantity as it is just the ratio of two similar quantities (densities).

Here, the question arises as to "why is there a need to divide the density of an object by 1?" Well, the answer is explained in the next section.

Affect of Temperature on Density

On heating, all substances tend to expand resulting in the same mass to occupy a larger volume. Consequently, this leads to a decrease in the density of the substance. Although most solids expand relatively less than liquids, this fact cannot be neglected. The expansion in a liquid is far greater than that of solids. On the other hand, the volume of any gas is highly temperature-sensitive and hence its density.

The answer to the question from the previous section will be that the density of water and other materials varies with temperature and even within the ranges of room temperature. Even the density of water will not be precisely $1 \mathrm{g} {\mathrm{mL}}^{-1}$with certain temperature variations . For accurate measurements, this variation must be taken into account because the value of density is temperature-dependent. It is important to divide the density of  by 1 or the nearest value of 1 while calculating the specific gravity of a particular substance.

What is the Cause of Thermal Expansion?

When the atoms or the molecules of any matter are heated, they acquire thermal energy and move around more energetically. Usually, in solids and liquids, the motion of the molecules is quite irregular which causes the average molecular distance between them to increase. As a result, the volume increases and the density decreases.

Calculation of Density in Solids

Hydrostatic weighing is one of the most preferred methods to calculate how dense a solid material will be. In general, the solids of interest are not in the form of ordered geometrical shapes. Their volumes are calculated indirectly. The volume of a regular solid is measured using mathematical formulae whereas the volume of irregular solids is measured by how much liquid it displaces in a measuring cylinder. The mass of a substance is determined by weighing it on an electronic balance.

For example, a small solid cylinder of iron is weighed in both air and water (for simplicity). The mass of the cylinder is 800 g and it displaces 700 mL of water when it is immersed in the measuring cylinder for weighing. In order to calculate the density of the iron cylinder, the mass is divided by the volume displaced. Mathematically,

$\rho =800 \mathrm{g} 700 \mathrm{mL} = 1.14 \mathrm{g} {\mathrm{mL}}^{-1}$

In this case, the iron cylinder will sink and a portion of it will stick out of the water as its density is greater than that of water.

Determination of Composite Density of Solids

There are times when a solid contains more than one kind of material. Consider a mysterious solid object which is made up of two types of materials-one rocky and the other gel-like. The sample of this solid has a known volume ratio of these two materials. The density of the composite solid ρS is determined using the following equation,

${\rho }_S={\rho }_R{V}_R+{\rho }_G{V}_G$

Where, ${\rho }_R$ is the density of the rocky material, ${\rho }_G$ is the density of the gel-like material, $V_R$ is the volume of the rocky material and $V_G$ is the volume of the gel-like material.

Common Mistakes

Density and mass are often confused with weight for a simple reason. Given two solid objects of the same size, the one with a higher density will have more mass and hence more weight. It is important to remember that density is the relationship between the mass and the volume and not the volume or the mass alone.
While solving problems, it should be ensured that the units of all the physical quantities should be the same - either in the SI system or the CGS system.

Formulas

• The density, ρ of any substance is given by, $\rho =mV$ where m is the mass and V is the volume of the given substance.
• According to Archimedes principle, the buoyant force FB is equal to the weight (W) of the liquid displaced and is written as$FB=W$.
• The density of the composite solid ${\rho }_C$ is determined using the equation, ${\rho }_C={\rho }_1{V}_1+{\rho }_2{V}_2$ where ${\rho }_1$ and ${\rho }_2$ are the densities of the individual components of the composite and $V_1$ and $V_2$ are the volume fractions of these components.

Context and Applications

This topic is significant in the professional exams for undergraduate courses especially for

Bachelor of Science in Chemistry

Bachelor of Science in Physics

It is also used for quality control in

Petrochemical industry

Production of cosmetic and personal care products

Related Concepts

Mass and weight

Volume

Gravitational Force

Practice Problems

Q1: The volumetric mass density is more precisely known as,

(a) Specific gravity

(b) Specific mass

(c) Specific volume

(d) Specific pressure

Correct option: (a)

Q2: Suppose the density of a solid is d and it is dropped in a liquid of density D. If D<d then,

(a) Solid will partially float

(b) Solid will partially sink

(c) Solid will completely sink

(d) None of the above

Correct option: (c)

Q3: The density of a substance can be defined as,

(a) Mass per unit pressure

(b) Mass per unit area

(c) Mass unit weight

(d) Mass per unit volume

Correct option: (d)

Q4: The density of gases is,

(a) Greater than density of solids

(b) Less than density of liquids

(c) Greater than the density of liquids

(d) Equal to the density of solids

Correct option: (b)

Q5. What is the density of a cube of side 2 m and mass 10 kg? 

(a) $1.25 \mathrm{kg} {\mathrm{m}}^{-3}$

(b) $0.25 \mathrm{kg} {\mathrm{m}}^{-3}$

(c) $2.25 \mathrm{kg} {\mathrm{m}}^{-3}$

(d) $3.25 \mathrm{kg} {\mathrm{m}}^{-3}$

Correct option: (a)

Explanation: The density is defined as the mass per unit volume, and the volume of a cube is given as cube of its side. Hence, density in the given question will be equal to m divided by cube of length. After substituting the given values, the answer will come out to be (a).