Every substance is composed of atoms and molecules. By definition, the amount of substance is expressed in moles. One mole of a substance contains 6.022 · 1023 constituent particles (Avogadro constant. This is not a dimensionless value, but a physical quantity with the unit mol-1). One mole is defined as the amount of substance of a system containing the same number of particles as there are atoms in 12 g of the carbon isotope 12C.
Under standard conditions, i.e. a pressure of 101.325 Pa and a temperature of 273.15 K (0°C), one mole of an ideal gas occupies a volume of 22.414 liters.
As early as 1664, Robert Boyle studied the effect of pressure on a given amount of air, which was confirmed by Mariotte in experiments. The results are stated in the Boyle-Mariotte law as:
Formula 1-4: Boyle's law
In words, the Boyle-Mariotte law states: for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume—the product of pressure and volume is constant.
More than a hundred years later, the relationship between the volume and temperature of a given amount of gas was also stated as: for a given amount of gas at constant pressure, volume is directly proportional to absolute temperature, i.e.
Formula 1-5: Gay-Lussac's law
For a given amount of gas the result of pressure and temperature changes is
This still applies to a given amount of gas.At a given temperature and pressure the gas volume is proportional to the amount of substance.We can therefore write:
The amount of substance can be determined by weighing.We can express the amount of gas as the ratio of mass to molar mass.The constant const. corresponds to 1 mole of gas in the equation, and it is called the gas constant R.Therefore, the ideal gas state can be described as a function of pressure、temperature and volume as follows:
Equation 1-6: General ideal gas equation of state
| P | Pressure | [Pa] |
| V | Volume | [m3] |
| M | Mass | [kg] |
| Molar mass | [kg kmol-1] | |
| R | General gas constant | [kJ kmol-1 K-1] |
| T | Absolute temperature | [K] |
The amount of substance can also be expressed as the number of molecules corresponding to the Avogadro constant.
Formula 1-7: Ideal Gas Equation of State I
| N | Number of particles | ||
| Na | Avogadro constant | = 6.022 · 1023 | [mol-1] |
| K | Boltzmann constant | = 1.381 · 10-23 | [J K-1] |
Dividing both sides of the equation by volume gives
Equation 1-8: Ideal Gas Equation of State II
Nparticle number density[m-3]
