In 1811, a scientist Avogadro’s established a relationship between the volume and number of molecules of the gas, which is known as Avogadro’s law

### Statement

The Volume of a gas is directly proportional to the number of molecules of the gas at constant temperature & pressure

#### Mathematic Expression:

Mathematically it may be written as
V ∞ n
OR
V = K n
On the basis of the above statement we can say that
1 dm3 of O2 gas will contain the same number of molecules as 1 dm3 of H2 or N2 or any other gas at same temperature and pressure.
It was also observed that 22.4 dm3 of any gas at S.T.P contain 1 mole of that gas, so 22.4 dm3 volume at S.T.P is called as molar volume or the volume of 1 mole of the gas and the mass present in 22.4 dm3 of any gas will be equal to its molar mass or molecular mass.

#### Explanation:

It means that, if we take different sample of different gases at same temperature and pressure, then if the volume of each gas sample is equal, the no. of molecules of each sample will be also equal evidently, if we increase the volume of gas sample, the no, of molecules will be also increase. Avogadro’s also found that at the some condition of temperature and pressure, the one mole of any gas occupies always 22.4dm3 volume, this volume is called molar gas volume. Also, this volume contain always constant no. of particles of gas, and its value is 6.02 x 1023. This value is called Avagadro’s number.

### Determination of Unknown Molecular Mass of a Gas With the Help of Avogadro’s Law

Suppose we have two gases (i) Oxygen (ii) CO
The volume of these two gases are equal which are 1 dm3.
The mass of 1 dm3 of oxygen is 1.43 gm
The mass of 1 dm3 of Co is 1.25 gm
According to Avogadro’s law we know that 1 dm3 of CO at S.T.P contain the same number of molecules as 1 dm3 of O2 under similar condition. Hence a molecule of CO has 1.25 / 1.43 times as much as a molecule of O2 and we know that the molecular mass of oxygen is 32 so the molecular mass of CO would be
1.25 / 1.43 x 32 = 28 g / mole