Relative molecular mass:
Relative molecular mass of a gas or vapour is the ratio between the mass of one molecule of gas or vapour to mass of one atom of hydrogen.
Relative molecular mass \(=\frac{\text { Mass of } 1 \text { molecule of a gas (or) vapour at STP }}{\text { Mass of } 1 \text { atom of hydrogen }}\)     .......(1)
Vapour density:
It is the ratio of the mass of a certain volume of a gas or vapour, to the mass of an equal volume of hydrogen, measured under the same conditions of temperature and pressure.
Vapour density (V.D) \(=\frac{\text { Mass of a given volume of gas(or) vapour at S.T.P }}{\text { Mass of the same volume of the hydrogen }}\)
According to Avogadro's law [Let the number of molecules in one volume = 'n']
Vapour density (V.D) \(=\frac{\text { Mass of 'n' molecules of a gas (or) vapour at S.T.P }}{\text { Mass of ' } n \text { 'molecules of a hydrogen }}\)
cancelling 'n' vapour density (V.D) \(=\frac{\text { Mass of } 1 \text { molecule of a gas or vapour at S.T.P }}{\text { Mass of } 1 \text { molecule of a hydrogen }}\)
Hydrogen is diatomic molecule, so
Vapour density \(=\frac{\text { Mass of } 1 \text { molecule of a gas or vapour at S.T.P }}{\text { Mass of } 2 \text { atoms of hydrogen }}\)
Vapour density \(=\frac{\text { mass of } 1 \text { molecule of a gas or vapour at S.T.P }}{2 \times \text { mass of 1atom of hydrogen }}\)
2 x Vapour density \(=\frac{\text { mass of } 1 \text { molecule of a gas (or) vapour at S.T.P }}{\text { mass of 1atom of hydrogen }}\)
From eqn (1)
2 x Vapour density = Relative molecular mass

(i) An atom is no longer indivisible.
(ii) Atoms of the same element may have different atomic masses (isotopes ₁₇Cl³⁵, ₁₇Cl³⁷)
(iii) Atoms of different elements may have the same atomic masses (isobars ₁₈Ar⁴⁰, ₁₇Ca⁴⁰)
(iv) Atoms of one element can be transmuted into atoms of other elements. So atom is no longer indestructible. It is called artificial transmutation.
(v) Atoms may not always combine in a simple whole number ratio [Eg: Glucose C₆H₁₂O₆, sucrose C₁₂H₂₂O₁₁)
(vi) Atom is the smallest particle that takes part in a chemical reaction.
(vii) The mass of an atom can be converted into energy (E = mc²).

Avogadro's law states that "equal volumes of all gases under similar conditions of temperature and pressure contain the equal number of molecules"

Ozone O₃

The molecules that consists of atoms of different elements are called heteroatomic molecule.
Examples: HCl, H₂O

The atomicity of an element can be derived using Avogadro's hypothesis. Let us consider the following equation

According to Avogadro's law, 1 volume of any gas occupy 'n' number of molecules.

if n = 1 then

(i) 1 molecule of hydrogen chloride gas is made up of \(\frac{1}{2}\) molecule of hydrogen and \(\frac{1}{2}\) molecule of chlorine
(ii) But 1 molecule of hydrogen chloride contains one atom of hydrogen and I atom of chlorine
(iii) Hence \(\frac{1}{2}\) molecule of hydrogen = 1 atom of hydrogen
(iv) Or 1 molecule of hydrogen = 2 atoms of hydrogen
(v) So the atomicity of hydrogen is 2, and molecular formula is H₂
Similarly,
\(\frac{1}{2}\) molecule of chlorine = 1 atom of chlorine 1molecule of chlorine = 2 atoms of chlorine So the atomicity of chlorine is 2, and its molecular formula is Cl₂

Applications of Avogadro's hypothesis
(i) It explains Gay-Lussac's law.
(ii) It helps in the determination of atomicity of gases.
(iii) Molecular formula of gases can be derived using Avogadro's law.
(iv) It determines the relation between molecular mass and vapour density.
(v) It helps to determine Gram molar volume of all gases (i.e. 22.4 lit at S.T.P)

Gram molecular of CO₂ = 44g
Number of molecules present in 44g of CO₂
= 6.023 X 10²³
∴ Number of molecules present in 11g of CO₂
= \(\frac{6.023\times{10}^{23}}{44}\)x 11
= 1.53 x 10²³ molecules.

Number of moles = \(\frac{Mass}{Atomic \ mass}\)
= \(\frac{81}{27}\) = 3 moles

Atomic masses of C= 12, O= 16
Gram molecular mass of CO₂ = 1(C) + 2(O) = 1(12) + 2(16) = 12 + 32 = 44
Gram molecular mass of CO₂ = 44g.