Relative Density

Density

Density can simply be defined as the amount (mass) of substance per unit volume. It is often denoted using the Latin letter D or ρ; the lower-case Greek letter pronounced rho. The formula of density is given by ρ = m/v, where m is for the mass of the substance and v is for its volume present. From the equation, it is clear that density is directly proportional to mass and indirectly proportional to volume. Factors that affect the density values of a substance are pressure and temperature. Increasing the pressure and decreasing the temperature will bring up the density value of a substance as these changes reduce the volume. Similarly, by increasing the temperature and lowering the temperature, the density value can be reduced as the volume value goes up. Kg/m³ is the SI unit of density.

Relative Density

Relative density is a comparative measure of the density of a substance to the density of a reference substance. Usually, for liquids, the relative density is measured with respect to water at its densest form at a temperature of 4 0C/39.2 °F. For gaseous substances, relative density is measured with respect to air at room temperature, 20 °C or 68 °F. Specific gravity is another name for relative density. As in the case of density, temperature and pressure are the determining factors of relative density. So, temperature and pressure must be specified for both the sample and the reference. The relative density of a few substances at room conditions are given below.

• Rubbing alcohol – 0.79
• Baby oil – 0.83
• Water – 1.0 (since it is the standard)
• Milk – 1.03
• Honey – 1.42

Calculation of Relative Density

Relative density is commonly denoted by the symbols RD or SG (Specific Gravity), and its value is given by the formula ρ_sample/ ρ_H20. It does not have a unit as it is a ratio of two densities. So basically, relative density is a dimensionless physical quantity. If the relative density of material comes out to be less than 1, then that substance can be concluded to be less dense than the reference substance and vice versa. If it is exactly equal to 1, the densities of both the measured and reference substances are the same. If it is not explicitly mentioned, the reference material is understood to be water at 4 0C in the case of liquids and air at 20 0C if it is a gaseous substance. Relative density can be calculated using several approaches, as shown below.

Where,

g = local acceleration due to gravity

V = volume of the sample and water

ρ_sample = the density of the sample

ρ_H2O = the density of water

W_V represents the weight obtained in a vacuum

m_sample = mass of the sample

m_H2O = mass of water

Although the mass of a substance is generally easy to measure, that is not the case with volume because some substances do not have a regular shape. In situations like this, volume is measured by immersing the substance sample in a container containing a measured quantity of water and then measuring how much water is displaced by it. Since surface tension will affect the quantity of water that overflows, it is highly suggested to use a container with as small of a mouth as possible.

Uses of Relative Density

Relative density is usually used to calculate the concentration of a substance in a particular solution. Geologists also use it to figure out the mineral content of ore for extraction. Relative density can also be used to check the purity levels of materials.

Archimedes Principle

Perhaps the most popular story that revolves around density is the tale of Archimedes and his Eureka! Moment. The story is that once Archimedes of Syracuse was asked to prove that a new crown made by a blacksmith for the king Hieron was not made of pure gold. After brainstorming for hours together to no avail, he decided to take a bath and filled up his bathtub. But as he got in, he noticed that some water got displaced. He realized that the amount of water getting displaced was equal to his very own weight. Then he had the idea that if an amount of pure gold equal to the weight of the crown was immersed in water and if it failed to displace the same amount of water as the crown did, he could prove that the crown was not made of pure gold. Overflowing with sheer excitement, Archimedes ended up running through the streets of Syracuse to tell the king about his discovery, without realizing that he was not wearing any clothes.