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The definition of mole was given by the National Institute of Standards and Testing, in the year 1971. A mole is defined as the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. Its symbol is “mol”. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Avogadro’s constant.

A single atom of an element has an extremely small mass. For example an atom of carbon-12 has a mass of 1.993 × 10-23g. This is far too small to weigh. A more convenient amount to weigh is 12.00 g. 12.00 g of carbon-12 contains    6.02 × 1023 atoms of carbon-12. This number is known as Avogadro’s Constant (NA or L).

Chemists measure the amounts of substances in moles. A mole is the amount of substance that contains L particles of that substance. The mass of one mole of any substance is known as the molar mass and has the symbol M.  For example, hydrogen atoms have 1/12th of mass of carbon-12 atoms so a mole of hydrogen atoms contains 6.02 × 1023 hydrogen atoms and has a mass of 1.01g. In reality elements are made up of a mixture of isotopes.

The relative atomic mass of an element At is the weighted mean of all the naturally occurring isotopes of the element relative to Carbon-12. This explains why the relative atomic masses given for the elements above are not whole numbers. The units of molar mass are g mol^-1 but are relative molar masses Mt have no units. For molecules relative molecular mass is used. For example, the Mt of Glucose, C₆H₁₂O₆ = (6 × 12.01) + (12 × 1.01) + (6 × 16.00) = 180.18. For ionic compounds the term relative formula mass is used.

Avogadro’s constant states that under conditions of constant temperature and pressure, equal volumes of different gases contain equal number of molecules.
If the initial temperature and volume are same as the final temperature and pressure, then the relationship between the number of molecules, N, and the volume, V is,
                                                     V_f/ V_i = N_f / N_i

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