Establish the ideal gas equation - QS Study

## The ideal gas equation:

Let pressure, volume and temperature of a fixed mass of gas be P, V and T respectively.

Boyle’s LawAt constant temperature, the volume of a fixed mass of gas is inversely proportional to its applied pressure.

Mathematical form:   when T is constant ……………………… (1)

Charle’s Law: At constant pressure, the volume of a given definite mass of a gas increases or decreases by 1/273th part of his volume at 0°C for each degree Celsius rise or fall in temperature.

Alternative form: The volume of a given mass of gas directly proportional to its absolute temperature when pressure remains constant.

Mathematical form: V  T  when P is constant ……………………… (2)

Avogadro’s Hypothesis: At same temperature and pressure, the equal volume of all gases [elemental or compound] contains the equal number of molecules. It can also be stated as volume of gases at constant temperature and pressure is directly proportional to their number of moles.

Mathematical form: V  N when P and T are fixed.

..V  n ………………………(3)

Again, n  N    where n=number of moles and N=number of molecules

From equation (i), (ii) and (iii) we get,

This is the ideal gas equation.