Atoms and Molecules

The gas laws

Ideal gasses all occupy the same volume per molecule (about 37 nm³) at the same temperature and pressure as each other. One mole of any gas occupies 22.414 litres; a volume equal to a cube with sides of 28 cm (11 inches) at standard pressure and temperature (STP; 0°C i.e. 273.15 K, and 1.0 atm pressure (in SI units 101,325 Pa).

Boyle's law.

Increasing the pressure (P), reduces the volume (V). P x V is constant. Therefore if the pressure is doubled the volume is halved.

Charles's law.

Increasing the (absolute) temperature (T) increases (expands) the volume (V). V is proportional to T. Doubling the absolute temperature will double the volume.

These laws can be combined into the ideal gas law:

PV =nRT

where    P is the pressure in pascal (1 atm = 101,325 Pa)
              V is the volume in cubic metres (m³ =1000 litres)
              T is the temperature in Kelvin (0K = -273.15°C)
              n is the number of moles of gas present
              R is the gas constant = 8.315 Pa.m³/(K.mol) = 8.315 J.K^-1.mol^-1) 

If different units are used for the pressure or volume then R must be used in the appropriate units. Thus if   P is the pressure in atm
              V is the volume in litres
              T is the temperature in Kelvin
              n is the number of moles of gas present
              R is the gas constant = 0.0821 L.atm.K^-1.mol^-1

 If the same amount of material is subjected to changes in pressure and/or temperature, n and R remain constant and the following equation may be used

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where the subscripts refer to the conditions at the beginning (1) and after (2) the change in conditions.

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This page was last updated by Martin Chaplin
on 10 February, 2005