What is Mole Concept? – Introduction, Importance and Formulae

Introduction

The structure of matter can be one of the following –
atoms → molecules → bulk compound or element
atoms → bulk element
atoms → ions → bulk ionic compound

It clearly shows that the masses that are measured in the laboratory are masses corresponding to large numbers of tiny atoms or molecules. Logically atoms that are heavier (e.g. oxygen atom is heavier than the hydrogen atom.) will register larger masses for equal numbers of atoms.

Relative atomic mass

If one carbon atom has a mass of 12 atomic mass units and one magnesium atom has a mass of 24 atomic mass units, then a magnesium atom is twice as heavy as a carbon atom. It follows that this ratio will be maintained for any number of atoms.
On the atomic mass scale the carbon 12 isotope is designated a value of 12 atomic mass units and all other masses are measured relative to this (relative atomic mass).

Why is it more convenient to refer to the quantity of a substance in terms of the number of its molecules or atoms, rather than their masses?
When we mix two substances, we get one or more new substance(s). For example, the reaction of hydrogen and oxygen to form a new substance water. This can be represented in the form of an equation as –

2H₂ (g) + O₂ (g) → 2H₂O (l)
In above equation, 2 molecules (4 atoms or 4 u) of hydrogen react with 1 molecule (2 atoms or 32 u) of oxygen and give two molecules (36 u) of water. It means, the quantity of a substance can be given by –
(a) its mass or
(b) the number of the molecules.
But, an equation of a chemical reaction only shows directly the number of atoms / molecules of a particular substance that would react with atoms / molecules of another substance. Therefore, it is more convenient to refer to the quantity of a substance in terms of the number of its molecules or atoms, rather than their masses.

What is the need of Mole Concept?
Atoms / molecules are microscopic particles. They cannot be counted as such. So, a new chemical counting unit ‘mole’ was introduced to link the mass of an element or compound to the number of atoms / molecules present in them. The word mole was apparently introduced in about 1896 by Wilhelm Ostwald who derived the term from the Latin word ‘moles’ meaning a ‘heap’ or ‘pile’. The mole whose symbol is ‘mole’ is the SI base unit for measuring amount of substance.

What is Mole Concept?
As standard, it is convenient to consider the number of atoms needed to make 12g of carbon and for this number to be given a name – one mole of carbon atoms.

A mole is the amount of pure substance that contains as many particles (atoms, molecules, or other fundamental units) as there are atoms in exactly 0.012 kg or 12 g of C-12 isotope’.

In simple words, a mole is the number of atoms in exactly 0.012 kg (12 grams) of C-12. It should be noted that although mole is defined in terms of carbon atoms but the unit is applicable to any substance just as 1 dozen means 12 (1 dozen pen or 1 dozen banana) or one gross means 144 of anything. Mole is a scientist’s counting unit like dozen or gross. By using mole, scientists count atoms and molecules in a given substance.

Avogadro’s number

It is experimentally found that the number of atoms contained in exactly 12 grams of C-12 is 602,200, 000, 000, 000, 000, 000, 000 or 6.022×10²³.
Avogadro’s number = 6.022 x 10²³
This number (6.022×10²³) is called Avogadro constant in honour of Amedeo Avogadro an Italian physicist and is denoted by symbol, N_A. This allows us to talk about relative quantities of substances in the macroscopic world and to know the relative number of atoms (or smallest particles) in each bulk substance.

We know that –

atomic mass of Carbon = 12 u

atomic mass of Helium = 4 u

We can see that one atom of carbon is three times as heavy as one atom of helium. On the same logic 100 atoms of carbon are three times as heavy as 100 atoms of helium.
Similarly,
6.022×10²³ atoms of carbon = 3 x 6.022 × 10²³ atoms of helium.

But 6.022×10²³ atoms of carbon weigh 12g, therefore 6.022×10²³ atoms of helium will weigh
1/3 × 12g = 4g.

Molar Mass

Numerically, mass of one mole atoms of the element is equal to its atomic mass expressed in gram.

Mass of one mole of a substance is called its molar mass.

For example –
(i) mass of one mole atoms of oxygen (O) is 16 g and mass of one mole of fluorine is 9 g.
(ii) mass of one mole molecule of oxygen (O₂) is 32 g as there are two atoms in a molecule of oxygen (O₂).
Note that if it is not mention atom or molecule before mole, it always means one mole of that substance in its natural form. For example, one mole of oxygen means one mole molecule of oxygen as oxygen occurs in nature as molecular oxygen.
(iii) mass of one mole molecule of a compound is equal to its molecular mass. For example, mass of one mole molecule of water will be 18 g as molecular mass of water is 18u.
1 mole of atoms = 6.022×10²³ atoms = Relative mass in grams
1 mole of molecules = 6.022×10²³ molecules = Relative mass in grams

Molar mass is always expressed as grams per mole or g /mol or g mol^-1.
For example,

Molar mass of oxygen (O₂) = 32 g mol^-1 Molar mass of lead (Pb) = 207 g mol^-1
Molar mass of water (H₂O) = 18 g mol^-1

Formulae in brief –

Mass = Molar mass x Number of moles
Number of moles = Given number of particles / Avogadro number
Number of particles = (Given mass / molar mass) x Avogadro number (from 1 and 2)
If one carbon atom has a mass of 12 atomic mass units and one magnesium atom has a mass of 24 atomic mass units, then as a magnesium atom is twice as heavy as a carbon atom. It follows that this ratio will be maintained for any number of atoms.
Equal masses of carbon and magnesium contain different numbers of atoms.

6 g of carbon contains 6 / 12 moles of carbon = 0.5 moles
6 g of magnesium contains 6 / 24 moles of magnesium =0.25 moles

1 mole = 6.022 x 10²³atoms or molecules or formula units of that substance.

1 mole of water (H₂O)contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms. It is a simple matter of multiplying the moles of the compound by the atoms or ions that make it up.

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Problems / Numericals based on Mole Concept

What is Mole Concept? – Introduction, Importance and Formulae

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