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Density and Relative Density

Density

Density is defined as the mass of a unit volume of any substance. If a substance has “m” mass and “V” volume, the density of that substance can be written as follows.

Density and relative density eq 01

SI unit of density is kg m-3 (kilograms per cubic meter).

Density is constant for each substance. It only depends on the type of the substance. So density is an intensive property.

Examples of density test questions

Examples of density test questions - Question 01

At 4℃, the density of pure water is 1000 kg m-3. Express the density of water in grams per cubic meter (g cm-3)

  • Solution
Density and relative density eq 02

Examples of density test questions - Question 02

Find the mass of 500 cm3 of pure water at 4℃.

  • Solution
Density and relative density eq 03

Examples of density test questions - Question 03

The densities of two liquids A and B are 1000 kg m-3 and 1200 kg m-3 respectively. A homogeneous mixture is obtained by mixing A and B. The final mixture has a density of 1150 kg m-3. By considering there is no volume change when mixing, find the mass and volume ratios between A and B in the mixture.

  • Solution

Mass ratio

Let's take the masses of A and B are m1 and m2 respectively.

Density and relative density eq 04

Let's apply the equation for density for the mixture.

Density and relative density eq 05

Volume ratio

Let's take the volumes of A and B are V1 and V2 respectively.

Density and relative density eq 06

Relative density

The ratio between the density of any substance, to the density of water is called the “Relative density”. Relative density is a unitless and dimensionless quantity.

Density and relative density eq 07

Examples of relative density test questions

Examples of relative density test questions - Question 01

Find the relative density of coconut oil. (The density of coconut oil is 890 kg m-3 and the density of water is 1000 kg m-3)

Density and relative density eq 08

Density and relative density of some materials

MaterialState of the materialDensity (kg m-3)Relative density
(Also equal to density in g cm-3)
Water (at 40C)Liquid10001.000
Water (at 00C)Liquid999.80.9998
Water (at 200C)Liquid9980.998
Hydrogen (at STP*)Gas8.99 x 10-28.99 x 10-5
Nitrogen (at STP)Gas1.2510.001251 (1.251 x 10-3)
Air (dry air at STP)Gas1.2750.001275 (1.275 x 10-3)
Ice (at 00C)Solid9170.917
Sea waterLiquid1020 - 10351.02 - 1.035
Blood
(at 370C - average human body temperature)
Liquid1050.61.0506
DiamondSolid35153.515
MagnesiumSolid (metal)17381.738
AluminumSolid (metal)27002.700
IronSolid (metal)78747.874
LeadSolid (metal)1134011.34
MercuryLiquid (metal)1353413.534
GoldSolid (metal)1930019.3
PlatinumSolid (metal)2145021.45
The core of the Earth9820 - 133009.82 - 13.3
Neutron starSolid3.7 x 1017 -
5.9 x 1017
3.7 x 1014 -
5.9 x 1014
The nucleus of an atom (average)2.3 x 10162.3 x 1013
Sun (average)14081.408
Table 01: Density and relative density of some materials and objects
*STP = Standard temperature and pressure (According to IUPAC standard temperature is 273.15 K (00C) and the standard pressure is 105 Pa (1 bar)).
**There could be some inaccuracies in the data included here.

How to calculate the density of a gas?

Also to calculate the density of a gas you can use 'The ideal gas equation'.

Density and relative density eq 20

Where,

  • P = Pressure of the gas (Pa)
  • V = Volume (m3)
  • n = Number of moles (mol)
  • R = Universal gas constant (8.314 J mol- K-)
  • T = Temperature (K)
  • m = Mass of the gas (kg)
  • M = Molar mass of the gas (kg mol-)
  • d = Density of the gas (kg m-3)

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References and Attributes

Table 01: Some data were referred from WolframAlpha.com

Figures:

The cover image was created using an image by Zaccaria Boschetti from Pixabay


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