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Deduction of Avogadro number

 sanjiv %2829%29

↪ It is deduced from Avogadro law that 1 g molecular mass of each of the ideal gases occupies same volume at NTP which is 22.4 L.
↪ This volume is molar volume.

↪ Avogadro hypothesis states that equal volumes of all the gases contain same number of molecules at the same temperature and pressure.
↪ A molar volume contains same number of molecules and this constant number is Avogadro number.

 Deduction of Avogadro number

Consider H2 gas to deduce the number.
Molecular mass of H2 = 2 and 1 g molecular mass of H2 = 2 g.
Let w - mass of H atom and 2w is the mass of H2 molecule.

i.e. 2 wg contain 1 molecules of H2
2 g contain 1/w molecules of H2 

i.e., 1 g mol of H2 contains 1/w molecules of H2 and it is constant number not only for H2 but for all gases.

This constant number of molecules is Avogadro number, which is calculated as,

i.e., molar volume of 1 g mol of any gas contains Avogadro number of molecules
6.023 x 1023 molecules.


 Molecular of a Compound from its Volumetric Composition

↪ The molecular formula of some compound gases can be deduced from the law.

Let us deduce the formula of steam.

Consider: Hydrogen + Oxygen = Steam

It is observed by experiment that 

↪ 2 volumes of Hydrogen + 1 volume of Oxygen = 2 volumes of steam
Let, 1 Volume of gas contain n molecules of it. Then by Avogadro's hypothesis:
2n molecules of H2 + n molecules of O2 = 2n molecules of steam
or, 1 molecule of H2 + 1/2 molecule of O2 = 1 molecule of steam

It has been deduced with reference to hydrogen that elementary gases are diatomic.
↪ 1 molecule of hydrogen contains 2 atoms of hydrogen and 1/2 molecule of oxygen contains 1 atom of oxygen.

Therefore, simple formula for steam is H2O and the molecular formula (H2O)n where n is small integer.

The vapor density of steam is 9, hence its molecular weight is 18.
Therefore, for 
(H2O)n ⇒ (2+16)n = 18 and n=1.

Hence, molecular formula for steam is H2O.