# Relative Density

## Relative Density Measurement

Density is one of the basic physical properties of a substance which can be used along with its other unique properties to characterize it.
The relative density of solids or liquids is the ratio between the mass of a volume of a substance to be examined, determined at 20 °C, and the mass of the same volume of water, determined at 4 °C. The relative density has no dimension. The density, r, of a substance is the quotient of the mass, m, and its volume, v. The density, r, is given, in SI units, in kg/m3.

One of the major applications of the determination of relative density is in the petroleum industry where the products obtained are based on the measurements done according to the relative densities of the liquids under process. Heavy molecular weight hydrocarbons are converted to the low molecular weight hydrocarbons such as gasoline, jet fuel and diesel based on the chemical processes involving the measurements based on relative densities of compounds. Relative density in this industry is particularly carried at high temperatures ranging between 40 to 100°C. This is important to provide data which is required for the conversion of kinematic viscosities to their corresponding dynamic viscosities.
Methods used for the determination of Relative density

There are broadly four classes of methods which are used to determine the relative density of any substance based upon its type. These methods are discussed as follows:

• 1. Buoyancy methods

• This method employs the application of Archimedes principle which states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid.

• Hydrometer (for liquid substances)

• A hydrometer is an instrument of uniform mass which is used to measure the relative density of unknown liquids. They make use of reference liquids (whose relative densities are already known in literature or experimentally). Any hydrometer can be used over a limited density range as the hydrometer must float in the studied liquid and the level of the hydrometer must be sufficiently submerged to obtain a reading on the scale. It is possible to calibrate hydrometers in g / ml or some other density unit. The floating hydrometers can obtain sufficiently accurate and rapid density determinations that allow the density of a liquid to be deduced by reading a graduated scale from the depth of immersion.

For determining relative density by this method, clean and dry a hydrometer. Then to this add approximately 30ml of liquid to your weighed hydrometer without bothering to measuring out the liquid accurately. Now carefully read and record whatever amount of liquid crosses the hydrometer's scale. Weigh the hydrometer and liquid, and then calculate the density of the liquid. Repeat this procedure thrice to find the density of any liquid

• Hydrostatic balance (for liquid and solid substances)

• This method is based on the principle that the relative difference obtained when a sample's mass is measured with respect to air and water (or any other suitable liquid) can be used to measure its density. The measured density for solids is only representative of the specific sample used. A body of known volume, v, is weighed first in air and then in liquid to determine liquid density.

In this method, an instrument of suitable construction is used by placing it on a horizontal support. The plummet (diver) is then suspended on a thin wire, made preferably of platinum. In order to first calibrate the instrument, the plummet is equilibrated in the air, then immersed into the cylinder filled with water and then equilibrated again by placing suitable riders (weights) at appropriate notches along the beam. The plummet should swim freely in the liquid. Then the cylinder is filled with the test liquid and the measurement is carried out in a similar way. While taking the measurement, care should be taken that the length of the immersed portion of the suspending wire is similar in all measurements. The weight to be added in order to obtain the balance in the test liquid (or to be subtracted in the case of density liquids below that of water) directly gives the measurement of its relative density.

• Immersed body method (for solid substances)

• The density of a solid is determined in this method by the difference between the results of weighing the liquid before and after a body of known volume is immersed in the sample liquid. This method is generally used for solids which are available in irregular shapes. A volume of liquid as small as 0.4 mL can be used as a sample in this method to determine the relative density of a small solid. This method is very quick and accurate. In this method, the test solid material is transferred to a container containing any sample liquid of known volume and density.
The volume of the sample liquid before immersing the solid material and the volume of the liquid after immersing the solid material are noted down. The difference between both these values gives the volume of the solid substance. The mass of the solid substance is a property which can be easily measured using any weighing balance. Hence, now the relative density of the sample can be easily calculated by taking the ratio of its mass and volume.

• 2. Pycnometer methods

• Pycnometers of different shapes and with known volumes can be used for solids or liquids. The density is calculated from the weight difference between the pycnometer and its known volume.

In this method, a pycnometer of suitable form and of a capacity of not less than 5 mL is used. The empty pycnometer is first washed properly, dried and then weighed accurately. Then it is filled with the test liquid which should already be preheated to a temperature of about 20 °C. Then the filled pycnometer is held at a temperature of 20 ± 1 °C for about 30 minutes and the liquid is adjusted to the mark using, if necessary, a small strip of filter-paper to remove the excess and to wipe the inlet from the inside and is then weighed accurately. Then the weight of the liquid in the pycnometer is noted down. The liquid is then removed and, the pycnometer is then cleaned and dried again to repeat the measurement with carbon-dioxide-free water, also at 20 ± 1 °C, and the weight of water in the pycnometer is calculated. The relative density is given by the weight ratio of the test liquid and water.

• Air comparison pycnometer (for solids)

• With the gas comparison pycnometer, the density of a solid in any form can be measured at room temperature. The volume of a substance is measured in a variable calibrated volume cylinder in the air or in an inert gas. After the volume measurement has been completed, one mass measurement is taken for density calculation.

To calculate the relative density using this method, the procedure is almost similar as described above in the pycnometer methods section. The only difference is that water used in the previous method is replaced with gas in this method.

• Oscillating densitometer

• An oscillating densitometer can be used to measure the density of a liquid. At the resonance frequency of the oscillator which depends on its mass, a mechanical oscillator constructed in the form of a U - tube is vibrated. The introduction of a sample changes the oscillator's resonance frequency. Two liquid substances of known densities must calibrate the device. These substances should preferably be chosen to span the range to be measured by their densities.

Factors Influencing Measurement of Relative Density

• • Air bubbles: A small bubble with a diameter of 1 mm yields a 0.5 mg increase, while those with 2 mm yield a 4 mg increase. Therefore, make sure that the solid object or sinker immersed in the liquid is not adhered to by air bubbles.

• • Solid matter sample: A sample with too large a volume immersed in the fluid will result in an increase in the level of fluid within the pitcher of the glass. As a result, part of the sample dish's suspension bracket will also be immersed, resulting in increased buoyancy. As a result, the specimen's weight in the fluid will decrease. Samples changing the volume or assimilating fluid are inappropriate for measurement.

• • Temperature: Solids are generally not sensitive to temperature changes so that the corresponding density changes are not relevant. However, since, according to the Archimedes Principle while determining the density of a liquid or a solid, its temperature is taken into account. The temperature change effects liquids greater and causes changes in the density in the order of 0.1 to 1 ‰ per °C. Hereby, the third digit after the decimal point is affected.