Relative Density

Density is defined as the mass per unit volume of a substance. Different substances have different densities, which is why some materials float while others sink. For example, when liquids like oil, water, and honey are placed together, they form layers. This happens because each liquid has a different density; denser liquids settle at the bottom, while lighter ones float on top.

Relative density (also called specific gravity) is defined as the ratio of the density of a substance to the density of water (at 4°C).

Relative Density (RD)= \frac{\rho_{\text{substance}}}{\rho_{\text{water}}}

• It is a dimensionless quantity (no units)
• Helps determine whether a substance will float or sink
• If RD > 1 → substance sinks in water
• If RD < 1 → substance floats in water
• If RD = 1 → same density as water

To compare densities, we use the concept of relative density.

Unit of Relative Density

Relative density has no unit, because it is a ratio of two quantities with the same unit (density).

Properties of Relative Density

• Unitless quantity (dimensionless)
• Depends on temperature and pressure
• A characteristic property of a substance
• Useful in determining buoyancy
• Varies if physical conditions (like temperature) change

Factors Affecting Relative Density

1. Temperature
   An increase in temperature increases volume, which decreases density and then decreases relative density.
2. Pressure
   An increase in pressure decreases volume, which increases density and then increases relative density.
3. Nature of Substance
   Different materials naturally have different densities.
4. Porosity
   Materials with more empty spaces (voids) have lower density.

Relative Density of Some Common Substances

Methods to Determine Relative Density

Relative density can be measured using different experimental methods depending on whether the substance is a solid or a liquid and the level of accuracy required.

1. Buoyancy Method

This method is based on Archimedes’ Principle, which states that a body immersed in a fluid experiences an upward force equal to the weight of the fluid displaced.

The object is first weighed in air. Then it is weighed again when fully immersed in water. The loss in weight gives the buoyant force.

Relative Density = \frac{\text{Weight in air}}{\text{Loss of weight in water}}

Main Concept: Greater the loss in weight → greater the volume displaced → lower density.

2. Hydrometer

A hydrometer is an instrument used to measure the relative density of liquids. It consists of a bulb attached to a long narrow stem. It is placed in the liquid and allowed to float freely. The level to which it sinks indicates the density of the liquid.

Main Concept: In a denser liquid, the hydrometer floats higher; in a less dense liquid, it sinks deeper.

3. Hydrostatic Balance

This method is used mainly for solids and gives accurate results. The object is weighed in air. Then it is weighed when immersed in water. The difference in weight helps calculate relative density. Suitable for irregularly shaped objects

Relative Density= \frac{\text{Weight in air}}{\text{Weight in air − Weight in water}}

4. Pycnometer Method

A pycnometer is a special glass bottle used to determine the density of liquids precisely. The empty bottle is weighed. Then it is filled with water and weighed. Next, it is filled with the test liquid and weighed. Using these measurements, relative density is calculated.

5. Oscillating Densitometer

This technique is a modern and highly accurate method used in industries. A small tube filled with liquid is made to vibrate. The frequency of vibration depends on the density of the liquid. By comparing with a reference (like water), relative density is calculated. Difference between Density and Relative Density

Difference Between Density and Relative Density

Related Articles:

• Difference between density and specific gravity.
• Density of water
• Specific gravity formula

Solved Examples

Problem 1: It is given that the relative density of silver is 10.8. The density of water is 1000 kg/m³. What is the density of silver in SI units?

Solution: Given,
Relative density of silver = 10.8
Density of water = 1000 kgm^-3.
We know that,
Relative density =Density of silver/Density of water
Density of silver= Relative density \times Density of water
Density of silver= 10.8 x 10³kgm^-3.
Hence, the density of silver is 10800kgm^-3

Problem 2: It is given that the density of mercury is 13600 kg/m. The density of water is 1000 kg/m. What is the relative density of mercury in SI units?

Solution: Given,
Density of mercury = 13600kgm^-3
Density of water = 1000 kgm^-3.
We know that,
Relative density =Density of mercury/Density of water 
\therefore Relative density =13600/1000 = 13.6
Hence the relative density of mercury is 13.6.

Problem 3: It is given that the density of iron is 7800 kg/m³. The density of water is 1000 kg/m³. What is the relative density of iron in SI units? Is it greater than the relative density of mercury, which is 13.6? Will an iron rod sink in it or float?

Solution: Given,
Density of iron = 7800kgm^-3.
We know that,
Relative density =Density of mercury/Density of water
Relative density =\frac{7800}{1000 }= 7.8
Hence, the relative density of iron is 7.8.
As its relative density is lower than mercury it will float in it.

Problem 4: It is given that the density of diesel is 860 kg/m³. The density of water is 1000 kg/m³. What is the relative density of diesel in SI units?

Solution: Given,
Density of diesel = 860 kgm^-3
We know that,
Relative density =Density of diesel/Density of water
Relative density =\frac{860}{1000 } = 0.86
Hence the relative density of diesel is 0.86

Unsolved Problem

Problem 1: It is given that the density of gold is 19300 kg/m³. The density of water is 1000 kg/m³. What is the relative density of gold in SI units? Will it float in mercury with a relative density of 13.6 and in water with 1.0?

Problem 2. It is given that the density of copper is 8900 kg/m³. The density of water is 1000 kg/m³. What is the relative density of copper in SI units?

Problem 3: It is given that the density of iron is 7800 kg/m³. The density of water is 1000 kg/m³. What is the relative density of iron in SI units? Is it greater than the relative density of mercury, which is 13.6? Will an iron rod sink in it or float? What will happen with a rod made of gold with a density of 19300?