Density is defined as the amount of mass in a unit volume of matter, for every substance has a different density. Here, we will cover what relative density is, calculations related to relative density, and the density of various substances.
Observe how the different liquids form different layers. The different substance poses a different density, meaning that for the same volume different substances weigh different, so the heavier substances tend to settle at the bottom, like in the case of honey and in the case of lighter material like oil, they tend to float at the top.
What is Relative Density?
Relative density (also known as specific gravity) is the ratio of the density of a substance to the density of a reference substance, typically water. It is a dimensionless quantity because it compares two densities, and the unit cancels out.
- It helps determine whether an object will float or sink in a fluid.
- Relative density is unitless because it is a ratio of densities.
- A relative density of 1 means the substance has the same density as water, and if it's greater than 1, the substance will sink in water.
Example:
- Relative Density of Water = 1.
- Relative Density of Lead = 11.34, meaning lead is 11.34 times denser than water.
Relative Density Formula,
The formula for Relative Density (RD) is:
Relative Density (RD)=Density of water/ Density of the substance
Where:
- Density of the substance is the mass per unit volume of the substance.
- Density of water is typically 1000 kg/m3 at 4°C (where water is densest).
RD=ρsubstance/ ρwater
Unit of Relative Density
Relative Density (RD) is dimensionless. This means it has no units, as it is the ratio of two densities, and the units cancel each other out.
For example:
- The density of the substance might be in kg/m³.
- The density of water is also in kg/m³.
Since both the numerator and denominator have the same units, they cancel out, leaving the Relative Density as a pure number (unitless).
Properties of Relative Density
- Dimensionless Quantity: Relative density is a unitless ratio of the density of a substance to the density of water, meaning it has no units.
- Depends on Temperature: Relative density varies with temperature, as changes in temperature affect the volume of a substance, thus altering its density.
- Characteristic of Material: It is a unique property for each substance at a given temperature and pressure, making it useful for identifying materials.
- Helps Determine Buoyancy: A relative density greater than 1 indicates that a substance will sink in water, while a relative density less than 1 means the substance will float.
Relative Density of different materials
Following is the table showing different density of materials:
| Substance | Density(kgm-3) |
| WATER | 1000 |
| DIESEL | 860 |
| GASOLINE | 725 |
| SILVER | 10500 |
| GOLD | 19300 |
| AIR | 1.18 |
| MERCURY | 13600 |
| BLOOD | 1600 |
| COPPER | 8900 |
As we can observe from the table different materials are having different density values. It is to be noted that these measurements are made based on a certain temperature and pressure. Because changing the physical conditions may give a different value of density each time as the density is dependent upon that factors.
Factors affecting Relative Density
As stated above the relative density is a ratio of the density of a substance with respect to the density of water. Hence, any change in the density of either substance or water will influence the relative density ratio therefore following are the factors that affect the density of any substance and indirectly affect relative density.
- Temperature– The density is mass per unit volume it will change if the volume changes as the mass doesn’t change until we add some more of the same material to it. Increasing the volume of substance will decrease the density and vice versa is also true. We can change the volume if we heat or cool the substance. It will accordingly change its density therefore volume is inversely proportional to density. And so the temperature increase is also inversely proportional to the density as it increases the volume if the temperature is increased.
- Pressure- For instance imagine we take a glass of water from earth to space, where it vaporizes as soon as possible due to the absence of pressure. However, its density decreases since the volume has increased. As we go on increasing the pressure the density also increases proportionally as the force of attraction between the molecules strengthens and the intermolecular spaces become less hence increasing its density. So we can say pressure is directly proportional to the density of the material.
- Nature of substance- As from the formula it is clear that density is a characteristic property of any material and hence the relative density is totally dependent upon the nature of substance as well as of water at a certain temperature.
- Porosity- Porosity refers to the presence of empty spaces or voids within a material. A substance with high porosity will have lower density since the voids reduce the amount of material in a given volume. Therefore, materials with higher porosity tend to have lower relative density compared to those with lower porosity.
Different ways to calculate Relative Density
- Buoyancy Method
- Hydrometer
- Hydrostatic Balance
- Immersed Body Method
- Pycnometer Method
- Air Comparison Pycnometer Method for Solids
- Oscillating Densitometer
Buoyancy Method
This method utilizes the principle of buoyancy, which states that an object submerged in a fluid experiences an upward force equal to the weight of the fluid displaced. To determine the relative density of a substance, it is submerged in a fluid (usually water), and the buoyant force is measured. The relative density is calculated by comparing the weight of the substance in air to the apparent weight when submerged in water.
Hydrometer
The relative density of any liquid is taken out using a hydrometer. A bulb is completely attached to a stalk of constant cross-sectional area. The hydrometer is first floated in the reference liquid (in light blue), and the displacement (the level of the liquid in stalk) is marked (with a blue line). The reference could be in practice water.
The hydrometer is then floated in a liquid of unknown density. The change in displacement is then noted. In the example depicted, the hydrometer has dropped in the green liquid; therefore its density is lower than that of the reference liquid. It is important that the hydrometer floats in both liquids. The application of simple physical principles like the change in displacement can help determine the relative density.
Hydrostatic Balance
The hydrostatic balance method involves measuring the weight of a substance in both air and water. The weight of the substance in air is subtracted from its weight in water, and the relative density is calculated by comparing the loss in weight to the weight of an equal volume of water. This method is highly accurate for solids.
Immersed Body Method
The immersed body method is similar to the buoyancy method. In this approach, the body is completely immersed in a liquid, and the loss in weight is measured. The relative density is determined by comparing the mass of the body to the weight of the displaced liquid. This method is commonly used for determining the relative density of irregularly shaped objects.
Pycnometer Method
A Pycnometer is used to determine the density of a liquid. It is usually made of glass, with a fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus. It enables a liquid's density to be calculated by reference to an appropriate working fluid, such as water or mercury.
If the flask is empty, full of water, and full of a liquid whose relative density is needed, the relative density can easily be calculated. The particle density is also calculated with a Pycnometer. The Pycnometer is filled with a liquid of known density, in which the powder of known weight is completely insoluble and Hence, the relative density of the powder can be calculated by dividing the weight of the displaced liquid by the weight of an equal volume of water.".
Air Comparison Pycnometer Method for Solids
This method is an advanced version of the pycnometer method, designed specifically for solids. The air comparison pycnometer works by measuring the volume of a solid by comparing its weight in air with its weight in a vacuum. This method is highly accurate for materials with low porosity and is often used for precise measurements in scientific research.
Oscillating Densitometer
An oscillating densitometer is an instrument that measures the density of liquids by analyzing the frequency of oscillation of a vibrating element in the liquid. The oscillation frequency is affected by the density of the liquid, and by comparing the frequency in the sample liquid to that in a reference liquid, the relative density can be calculated. This method is often used in industrial applications for continuous monitoring of liquid densities.
Each of these methods provides a different level of accuracy and is chosen based on the type of material and the conditions of the measurement.
Difference between Density and Relative Density
Density | Relative Density |
|---|
Density is the mass per unit volume of a substance. | Relative density is the ratio of the density of a substance to the density of water. |
Density has units, typically kg/m³ or g/cm³. | Relative density is unitless (dimensionless). |
Density does not depend on the density of water or any reference substance. | Relative density is always calculated with respect to water or another reference substance. |
Density can change with temperature or pressure. | Relative density varies with the density of water at a given temperature but not the substance’s nature. |
Solved Examples
Example 1: It is given that the relative density of silver is 10.8. The density of water is1000 kgm-3. What is the density of silver in SI unit?
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
Example 2: It is given that the density of mercury is 13600 kgm3. The density of water is1000 kgm3. What is the relative density of mercury in SI unit?
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.
Example 3: It is given that density of iron is 7800 kgm-3. The density of water is1000 kgm-3. What is the relative density of iron in SI unit? Is it greater than 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.
Example 4: It is given that density of diesel is 860 kgm-3. The density of water is 1000 kgm-3. What is the relative density of diesel in SI unit?
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
Example 5: It is given that density of gold is 19300 kgm-3. The density of water is 1000 kgm-3. What is the relative density of gold in SI unit? Will it float in mercury with a relative density of 13.6 and in water with 1?
Solution:
Given,
Density of gold = 19300kgm-3
We know that,
Relative density =Density of gold/Density of water
Relative density =\frac{19300}{1000 } = 19.3
Hence the relative density of gold is 19.3.
So it will not float in both mercury and water as it has a greater density.
Example 6. It is given that density of copper is 8900 kgm-3. The density of water is1000 kgm-3. What is the relative density of copper in SI unit?
Solution:
Given,
Density of copper = 8900 kgm-3
We know that,
Relative density =Density of copper/Density of water
Relative density =\frac{8900}{1000 }=8.9
Hence the relative density of iron is 8.9
Example 7 : It is given that density of iron is 7800 kgm-3. The density of water is1000 kgm-3. What is the relative density of iron in SI unit? Is it greater than 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 density of 19300?
Solution:
Given,
Density of iron = 7800kgm-3
Density of gold = 19300kgm-3
We know that,
Relative density =\frac{Density of gold}{Density of water }
Relative density =\frac{19300}{1000 } = 19.3
Hence the relative density of gold is 19.3.
Also the relative density of mercury can be found.
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 iron has a relative density that is lower than mercury it will float in it and the rod of gold will sink as it has a greater relative density.
Conclusion
Relative density, also known as specific gravity, is a dimensionless quantity that compares the density of a substance to the density of a reference substance, typically water at 4°C. Unlike density, which is an absolute property with units (kg/m³ or g/cm³), specific gravity has no units as it is a ratio. While density refers to the mass per unit volume of a substance, specific gravity helps determine whether a substance will float or sink in a given fluid, especially water.
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