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The mole and the Avogadro constant

The IUPAC traditionally defines mole as “SI base unit for the amount of substance (symbol: mol). The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. 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”.

As can be seen from the definition, the mole is defined in terms of another SI base unit, the kilogram. Hence, also assumes the mass of 12C to be fixed at 12g/mol. The other important factor that needs to be considered is the term “amount of substance”. The definition of substance, especially in the wake of quantum mechanics is something that is ambiguous.

As a consequence of the above-mentioned ambiguity in the traditional definition of mole, the new definition is based on the Avogadro’s constant.

The mole is the amount of substance of a system which corresponds to 6.022141 79 x 1023 elementary entities.”

The IUPAC also defines the Avogadro’s constant: “Fundamental physical constant (symbols: L, NA) representing the molar number of entities: 6.02214179 x 1023 mol-1”.

These two definitions establish a relationship between the terms that is fundamental to study of modern chemistry.

Applications of the mole concept

To apply the mole concept to the chemical reactions, we need to have a look at the concept of atomic mass and atomic weight. Atomic mass is defined as the mass of one individual atom of an isotope of an element. Its mass is defined in terms of the mass of a single atom of carbon-12 which is exactly equal to 12 atomic mass units (amu). All the other isotopes of all elements are determined using the mass of carbon-12 as the benchmark. Atomic weight, on the other hand, means the weighted average of all the isotopes of an element in proportions of their natural abundance. The practical approach to using this definition lies in identifying how the mass of one atom of carbon-12 is related to the weights we measure while keeping the stoichiometry of reactions.

Mass of one atom of C-12 = 1.99265 x 10-23 g

Hence, Mass of 1 mole (6.022141 79 x 1023 atoms) of C-12 = 1.99265 x 10-23 x 6.022141 79 x 1023 = 12 g.

The same formula applied to the atomic weight leads us to the mass of 1 mole of naturally abundant carbon. In a similar fashion, all the elements can be assigned to have a molar mass that is the mass of 1 mole of that element.

In this context, we must remember a few important points:

  1. Weight and mass are not the same thing, although, for earth, these have roughly equal value and the chemical reactions can be carried out by measuring the weights of reactants (in grams/ Kg).

  2. Atomic weight is actually measure of mass (not weight, it’s not a force but average of atomic masses of different isotopes).

  3. Atomic weight (and atomic mass) are not same as molar mass. Although, for practical purposes of weighing reactants and products in a chemical reaction, the idea “1 mole of an element has the mass (in grams) that is numerically equal to its atomic weight as given in the periodic table” can be useful. But, it must be remembered that this is not actually true. It works because the number of reacting atoms or molecules is huge (remember how large Avogadro’s number is!) and a few atoms or molecules more or less won’t significantly alter the course of the reaction.

Conversion of moles to mass:

Let’s say we have 10 moles of pure Ca metal. We want to know what is the mass (in practice, weight, when found out by weighing balance) of this much Ca.

The first thing is to look up the periodic table to see the atomic weight (in lieu of molar mass) of Ca (40.078 amu).

The next step is to multiply the number of moles by the atomic weight (in lieu of molar mass) which equals 10 x 40.078 = 400.78 g of Ca.

Conversion of mass to moles:

Let’s say we have 23 g of Na metal.

Again, the first thing is to look up the periodic table to see the atomic weight (in lieu of molar mass) of Na (22.989 amu).

The next step is to divide the number of mass of Na by the atomic weight (in lieu of molar mass) which equals 23/22.989 = 1.00047 moles of Na

All of the concepts above, can be applied to molecules, ions and other particles, taking 1 mole as the Avogadro's number of molecules/ ions/ other particles, respectively.

References:

  1. https://goldbook.iupac.org/html/M/M03980.html

  2. https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Atomic_Theory/The_Mole_and_Avogadro%27s_Constant

  3. https://www.iupac.org/publications/ci/2009/3102/1_mills.html

  4. https://goldbook.iupac.org/html/A/A00543.html

  5. https://www.iupac.org/publications/ci/2010/3201/2a_jeannin.html

  6. https://www.iupac.org/publications/ci/2010/3201/2_lorimer.html

  7. https://www.khanacademy.org/science/chemistry/atomic-structure-and-properties/introduction-to-the-atom/v/the-mole-and-avogadro-s-number