This topic is fundamental to all of the mathematical aspects of chemistry. Central to chemical calculations is the mole – the amount of a substance that contains the Avogadro number of particles. Essential laws and definitions include the ideal gas equation, the Avogadro constant, Avogadro’s law, relative atomic mass, and the use of the mass spectrometer.

Definitions and Laws

The definitions and laws that need to be known and understood are:

- Stp (standard temperature and pressure)
- Ideal gas (see note 1)
- The ideal gas equation (see note 2)
- Avogadro’s law (see note 3)
- Relative atomic mass
- Relative molecular mass
- Avogadro constant (see note 4)
- Mole (see note 4)
- Molar volume (see note 5)
- Graham’s law of diffusion
- Empirical formula
- Molecular formula

1. An ideal gas is one which obeys the gas laws (Boyle’s and Charles’) at all temperatures and pressures. In reality no such gas actually exists, but the concept is a useful one. At high pressures and low temperatures real gases cease to obey the gas laws exactly. The gases that come nearest to being ideal are those that have very low boiling points, and in general, these are the ones of small molecular mass. In particular, hydrogen and helium are nearest to being ideal gases in behaviour.

2. Remember when using this equation, that all quantities must be in their correct units, specifically that pressure is expressed in pascals and volume in metres cubed and temperature in Kelvin.

3. The most useful application of Avogadro’s Law is that for gaseous reactions, a mole reacting ratio can be replaced by the volume reacting ratio. For example, if 1 mole of gas X reacts with 3 moles of gas Y, then 1 volume (e.g., 1 litre) of gas X will react with 3 volumes (3 litres) of gas Y.

4. It is important to understand that the mole is defined in terms of the Avogadro Constant, not the other way round. The Avogadro Constant cannot therefore be defined as the number of particles in a mole.

5. The molar volume of a gas is the volume occupied by one mole of the gas. It is equal to 22.4 litres at s.t.p. and about 24 litres at room temperature. Room temperature is taken to be about 20°C, and for this temperature, the 22.4 litres has expanded to 24 litres.

Units and conversions

Errors are often made in the conversion of units

K = °C + 273

1000 cm^{3} = 1 litre (dm^{3}); 1000 litres = 1 m^{3}; 106 cm^{3} = 1 m^{3}

To convert cm^{3} to m^{3}, divide by 10^{6} (or multiply by 10^{-6} — which is the same thing).

1 kilopascal (kPa) = 1000 pascals, hence 101 kPa = 101 X 10^{3} Pa

Stoichiometry (chemical calculations)

The relevant equation for the reaction is the starting point for chemical calculations. From the moles ratio between the different substances, the mass ratio or the volume ratio (for gases) can be worked out.