Relative Density: CBSE Class 9 Physics

Relative density: Why do some objects float on the surface of the water while some sink? We all know that ice floats on the surface of the water. But heavy ice or the ice composed of heavy water (i.e. \({D_2}O\)) sinks in normal water! Because of varying densities of water in its different states and forms, we observe such different behaviour of ice. When we deal with liquids, it is not enough to just talk about the density of the liquid; at times, what is essential is to compare it with the density of another liquid, and that is when we talk about relative density.

Buoyancy, or the ability of an object to float in liquid or air, is closely related to the concept of specific gravity. A substance with lesser relative density than a fluid will float on that fluid, while a substance with greater relative density than that of fluid will sink. This is why helium-filled balloons rise in the air, oil forms a layer on water, and lead floats on mercury. The relative density of a substance is its identifying characteristic, and its value is the same for different samples of the same pure substance. Hence, we use it to identify unknown substances. To learn more about relative density, let us read further.

Density: Details

Density is the fundamental property of a substance. It can be defined as the ratio of the mass of the substance over the volume of the substance, or density is equal to mass per unit volume of a substance. Thus, it can be given as:

\({\rm{Density = }}\frac{{{\rm{ mass }}}}{{{\rm{ volume }}}}\)

The SI unit of mass is Kilogram, and the S.I. unit of volume is the cubic meter. Thus, the S.I. unit of density is Kilogram per meter cube or \({\rm{kg/}}{{\rm{m}}^{\rm{3}}}{\rm{.}}\) It is a scalar quantity. Density is the basic physical property of a substance that has a unique value for every substance, and it can be used with its other properties to characterize it. Different substances have different density values; this implies that different substances weigh different for equal volume. That is why the heavier substances tend to settle at the bottom, like in honey. But the lighter material like oil, they tend to float at the top.

Relative Density: Details

The relative density of a substance is also known as specific gravity. The relative density of a substance can be defined as the ratio of the density of the given substance to the density of the standard substance. The standard substance in liquids is water at \({{\rm{4}}^{\rm{o}}}{\rm{C}}\) and the standard substance of gases is air at room temperature or \({\rm{2}}{{\rm{0}}^{\rm{o}}}{\rm{C}}{\rm{.}}\) We use the value of density of water at \({{\rm{4}}^{\rm{o}}}{\rm{C}}\) because the density of water is maximum at that temperature. In terms of the S.I. units, the density of water is almost equal to \(1000\,{\rm{kg/}}{{\rm{m}}^{\rm{3}}}\) or \(1\,{\rm{kg/}}{{\rm{cm}}^{\rm{3}}}\) which makes relative density calculations very convenient. Thus, depending on the units, the density of the unknown object only needs to be divided by the factor of \(1000\) or \(1.\) Relative density plays a very important role in the petroleum industry. The petroleum products obtained are based on the measurements done according to the relative densities of the liquids. It is important here to remember that relative density is defined for highly incompressible aqueous solutions. The other incompressible substances like petroleum products that show variations in density caused by pressure are mostly neglected where we have to measure the apparent relative density.

Relative Density: Formula

We know, for a given substance, its density varies with the conditions of pressure and temperature.

Thus, whenever we deal with density, it becomes absolutely necessary to specify the values of temperature and pressure before calculating the values of mass and density of a given material. 

When we measure the standard density value, it is preferred to keep the pressure value at \(1\) atmosphere or \({\rm{101}}{\rm{.325}}\,{\rm{kPa}}\) ignoring the other variations caused by changing weather patterns and external affairs. 

\({\rm{Relative}}{\mkern 1mu} {\rm{Density}} = \frac{{{\rm{Density}}\,{\rm{of}}\,{\rm{substance}}}}{{{\rm{density}}\,{\rm{of}}\,{\rm{waterat}}\,{4^{\rm{o}}}{\rm{C}}}} = \frac{{\frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{a}}\,{\rm{substance}}}}{{{\rm{volume}}\,{\rm{of}}\,{\rm{the}}\,{\rm{substance}}}}}}{{\frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{waterat}}\,{4^{\rm{o}}}{\rm{C}}}}{{{\rm{Volume}}\,{\rm{of}}\,{\rm{water}}}}}}\,\)

If we take equal volumes of the substance and the water, 

\( \Rightarrow {\rm{Relative}}{\mkern 1mu} \,{\rm{Density}} = \frac{{{\rm{Mass}}\,{\rm{of a}}\,{\rm{substance}}\,{\rm{of}}\,{\rm{any}}\,{\rm{volume}}}}{{{\rm{Mass}}\,{\rm{of}}\,{\rm{an}}\,{\rm{equal}}\,{\rm{valume}}\,{\rm{of}}\,{\rm{waterat}}\,{4^{\rm{o}}}{\rm{C}}}}\)

Thus, relative density is the ratio of the mass of a substance to that of a reference substance of equal volume.

Since relative density is a ratio of two similar quantities, it is a dimensionless quantity. For example, in the case of honey, the density of honey equals \(1.42\;{\rm{grams}}/{\rm{c}}{{\rm{m}}^3}.\) So its specific gravity would be \({\rm{1}}{\rm{.42}}\;{\rm{grams/c}}{{\rm{m}}^{\rm{3}}}/1\;{\rm{grams/c}}{{\rm{m}}^{\rm{3}}}{\rm{ = 1}}{\rm{.42}}{\rm{.}}\)  We can see that specific gravity is a ratio. Therefore the units in the numerator and denominator get canceled, and specific gravity does not have a unit, and hence specific gravity is a dimensionless physical quantity.

If a substance has less than \(1\) relative density, it is less dense than a reference substance. If the value of relative density is greater than \(1\) then it is denser than the reference substance. If the relative density comes out to be precisely \(1,\) then the densities are equal. The formula to calculate the relative density of solids can be given as:

\({\rm{Relative}}\,{\mkern 1mu} {\rm{Density}} = \frac{{{\rm{Loss}}\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{solid}}\,{\rm{in}}\,{\rm{air}}}}{{{\rm{Loss}}\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{solid}}\,{\rm{in}}\,{\rm{water}}}}\)

The specific gravity of a substance will let us know if it will float or sink; it gives us an idea about relative mass or relative density. For the given substance, If the value of specific gravity is less than \(1,\) it will float on water, and if it is greater than \(1\) it will sink in water.

Factors Impacting the Value of Relative Density

Size of the impurity sample: A sample whose substantial volume is immersed in the fluid will increase the fluid level within the container it is immersed in, affecting the volume, hence the density of the fluid.

Nature of the sample: The density of a substance is a characteristic property of its nature; thus, so is the relative density of the substance.

Temperature variation: According to the Archimedes Principle, the temperature is considered while determining the density of a solid or a liquid. The temperature changes affect liquids and cause changes in the density of about \(0.1 – 1\,{\rm{g}}/{\rm{c}}{{\rm{m}}^3}\) per \(^{\rm{o}}{\rm{C}}.\) Although, Solids are generally not affected by temperature changes, the corresponding density changes are not relevant. 

Diameter of bubbles: The presence of air bubbles in a fluid when we measure the density of a solid can affect our calculations. A small bubble of diameter \(1\,{\rm{mm}}\) can lead to a \(0.5\,{\rm{mg}}\) increase, and those with a diameter of \(2\,{\rm{mm}}\) can result in a \(4\,{\rm{mg}}\) increase. Thus, it is ensured that there are no air bubbles in the liquid as we measure masses.

Pressure of the surroundings: As the pressure increases, the density also increases. The force of attraction between the molecules strengthens, and the intermolecular spaces between the molecules decreases, increasing their density. Thus, pressure is directly proportional to the density of the material and hence will affect the relative density.

Methods used for Measuring the Relative Density

1. Pycnometer Method: A Pycnometer is a device that is used to measure the density of a liquid. The device is made of glass, with a fitting ground glass stopper with a capillary tube passing through it, allowing the air bubbles to escape from the apparatus. Thus, we can calculate a liquid’s density by referencing an appropriate working fluid, such as water or mercury. 
2. Hydrometer: The hydrometer is first floated in the reference liquid, and the displacement is marked. The reference could be in practice water.  Then, the hydrometer is floated in a liquid of unknown density. The change in displacement is then noted. Thus, using simple physical principles of change in displacement, we can measure the relative density.
3. Hydrostatic Balance: These are based on Pascal’s Principle; according to this principle, the pressure difference between two points within a vertical column of any liquid or fluid is proportional to the vertical distance between the two given points, the density of the fluid, and the gravitational force.
   Other methods include Buoyancy Method, Immersed Body Method, Air Comparison Pycnometer Method for Solids, and an Oscillating Densitometer are used to calculate the relative density of the given materials.

Applications of Relative Density

1. The concept of relative density is used for determining the density of an unknown substance from the known density of another substance.
2. Geologists also use it to find out the nature and type of the rock.
3. The products obtained in the petroleum industry are mostly based on the measurements done according to the relative densities of the liquids under process.
4. Based on the chemical processes involving the measurements based on relative densities of the compounds, heavy molecular weight hydrocarbons can be converted to low molecular weight hydrocarbons such as gasoline, jet fuel, and diesel.
5. Relative density is used for testing the purity of a substance, for example, gold and silver.
6. Mineralogists often use relative density to help determine the mineral content of a rock or other sample.
7. Gemologists use it as an aid in the identification of gemstones.
   Relative density is measured in terms of water density because it is the simplest way to measure it in the field. Density is defined as the mass of a sample divided by its volume. It can be challenging to measure accurately the volume of an irregularly shaped rock. The perfect way to measure the density of an object is to put it in a water-filled graduated cylinder and measure the amount of water displaced. But there can be inaccuracies in this method since water can get spilled accidentally during the experiment. So it is better to suspend the sample from a spring scale and weigh it underwater.

Summary

The relative density of a substance is also known as specific gravity. The relative density of a substance can be defined as the ratio of the density of the given substance to the density of the standard substance. Relative density is the ratio of the mass of a substance to that of a reference substance. Its formula can be given as \({\rm{Relative}}\,{\rm{Density}} = \frac{{{\rm{Density}}\,{\rm{of}}\,{\mkern 1mu} {\rm{substance}}}}{{{\rm{density}}\,{\mkern 1mu} {\rm{of}}\,{\rm{water}}\,{\rm{at}}\,{\mkern 1mu} {4^{\rm{o}}}{\rm{C}}}}.\) Since relative density is a ratio of two similar quantities, it is a dimensionless quantity. For the given substance, If the value of specific gravity is less than \(1,\) it will float, and if it is greater than \(1\) it will sink in water.

Frequently Asked Questions on Relative Density

Frequently asked questions related to relative density is listed as follows:

Q.1. Define density.
Ans: The density of a material can be defined as the ratio of mass over the volume of the given material.

Q.2. What is relative density?
Ans: Relative density is the ratio of the given substance’s density to the standard substance’s density.

Q.3. What is the S.I. unit of relative density?
Ans: Relative density is a dimensionless quantity, and it has no units.

Q.4. If the density of a substance is greater than the density of a fluid, would it sink or float in that fluid?
Ans: If the density of a substance is greater than the density of a fluid, its relative density w.r.t fluid will be greater than \(1;\) it will sink.

Q.5. Give the formula for the relative density of a solid.
Ans: The formula for the relative density of a solid can be given as:
\({\rm{Relative}}{\mkern 1mu} \,{\rm{Density}} = \frac{{({\rm{Loss}}\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{solid}}\,{\rm{in}}\,{\rm{air}})}}{{{\rm{Loss}}\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{solid}}\,{\rm{in}}\,{\rm{water}}}}.\)

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