## The ideal gas equation:

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

**Boyle’s Law: **At 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.