Density Calculations

Key Concepts

• Density is defined as mass per unit volume.

• Density can be calculated using the formula:
  d = m ÷ v

  where d = density, m = mass, v = volume

• The greater the density, the more mass per unit volume.

• The unit of density derived from SI units is kilograms per cubic meter, kg/m³ or kgm^-3.

• More commonly, densities are given in g/mL (gmL^-1) or g/cm³ (gcm^-3 or g/cc).

• Density is a characteristic property of pure substances so density can help identify a particular pure substance.

Densities of Some Pure Substances

Pure Substance State Density (g/mL) at 25oC and 1atm gold solid 19.3 mercury liquid 13.6 lead solid 11.4 silver solid 10.5 copper solid 9.0 zinc solid 7.1 aluminium solid 2.7 carbon (graphite) solid 2.3 sulfur solid 2.0 phosphorus solid 1.8 ethanoic acid (acetic acid) liquid 1.04 water liquid 1.0 ethanol liquid 0.79 chlorine gas 0.0029 oxygen gas 0.0013

In general metals are more dense than non-metals*. For example, at 25oC the density of metallic lead is 11.4g/mL while the density of non-metallic sulfur is only 2.0g/mL. The mass of 1mL of lead would be 11.4g, while the mass of 1mL of sulfur is only 2.0g In general, solids are more dense than liquids which are more dense than gases**. For example, at 25oC, solid sulfur has a density of 2.0g/mL, liquid water has a density of 1.0g/mL and gaseous oxygen has a density of 0.0013g/mL.

^* There are quite a few exceptions, especially the Group I (alkali metals) which have unusually low densities compared with other metals.
^**Note that mercury is an exception, it is a very dense liquid.

Density Calculations

This equation can be re-arranged in order to calculate mass or volume given the density of a substance:

Check for consistency in units:
If density is given in g/mL then the mass must be in grams and the volume in milliltres.
If the density is given in g/cm³ then the mass must be in grams and the volume in cubic centimetres.

Examples of Calculations Using Densities

1. Calculate the density of a ruby which has a volume of 1.6 cm³ and a mass of 6.7g.

   density = mass ÷ volume
   density = 6.7 ÷ 1.6 = 4.2 g/cm³

2. Calculate the density of a liquid which has a volume of 28mL and a mass of 26.4g

   density = mass ÷ volume
   density = 26.4 ÷ 28 = 0.94 g/mL

3. Beeswax has a density of 0.96 g/cm³ at 25^oC and 1atm pressure.
   Calculate the mass of 5 cm³ of beeswax.

   density = mass ÷ volume
   So mass = density x volume
   mass = 0.96 x 5 = 4.8g

4. Milk has a density of 1.03 g/mL at 25^o and 1atm pressure.
   Calculate the mass of 1L of milk.

   density = mass ÷ volume
   So mass = density x volume
   Convert 1L to millilitres: volume = 1L x 1000mL/L = 1000mL
   mass = 1.03g/mL x 1000mL = 1030g (=1.030kg)

5. At 25^o and 1atm pressure, diamond has a density of 3.5 g/cm³.
   Calculate the volume of 0.5g of diamond.

   density = mass ÷ volume
   So, volume = mass ÷ density
   volume = 0.5g ÷ 3.5g/cm³ = 0.14cm³

6. At 25^oC and 1atm pressure, ethylene glycol has a density of 1.11g/mL.
   Calculate the volume of 0.025kg of ethylene glycol.

   density = mass ÷ volume
   So, volume = mass ÷ density
   Convert 0.025kg to g: mass = 0.025kg x 1000g/kg = 25g
   volume = 25g ÷ 1.11g/mL = 22.5mL

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