# Mole Concept

In chemistry, scientists link the mass of an element or compound to the number of atoms or molecules present in them. this is done through the ‘mole’. So, the scientists count the atoms and molecules by weighing them. It has been found by experiments that if we weigh an element equal to its atomic mass in grams, then it contains 6.022 x 1023 atoms of the element. This concept is called mole concept.

Now both, the gram atomic mass of the element as well as 6.022 x 1023 atoms of the element, represent one mole of the element. Similarly, if we weigh a compound equal to its molecular mass in grams, then it contains 6.022 x 1023 molecules of the compound. Thus, mole is a link between the mass of atoms (or molecular) and the number of atoms (or molecules).

### Gram atomic mass and gram molecular mass –

The amount of substance whose mass in grams is numerically equal to its atomic mass, is called gram atomic mass of that substance. The atomic mass of a substance expressed in grams is called its gram atomic mass. To write the gram atomic mass of a substance we simply write its atomic mass and replace atomic mass unit ‘u’ with ‘grams’.

The gram atomic mass of a substance represents the mass of 1 mole of atoms (6.022 x 1023  atoms) of that substance.The number of atoms present in 1 gram atomic mass of any substance is 6.022 x 1023 atoms.

The amount of a substance whose mass in grams is numerically equal to its molecular mass, is called gram molecular mass of that substance. In other words, the molecular mass of a substance expressed in grams is called its gram molecular mass. To write the gram molecular mass of a substance, we write its molecular mass and then replace the unit ‘u’ by ‘grams’.

The gram molecular mass of a substance represents the mass of 1 mole of molecules (6.022 x 1023  molecules) of that substance. So, the number of molecules present in 1 gram molecular mass of any substance is 6.022 x 1023 molecules.

Molar mass –

The molar mass of a substance is the mass of 1 mole of that substance. The unit of molar mass is grams per mole (g/mol). The molar mass can be of an element or of a molecular compound. The molar mass of an element is numerically equal to the atomic mass expressed in g/mol. And the molar mass of a molecular substance is numerically equal to its molecular mass expressed in the units g/mol.

The molar mass can also be used in the place of gram molecular mass. Since, molar mass is the mass of 1 mole of a substance, therefore, it has 6.022 x 1023 entities of substance in its 1 unit.

When we are dealing with the atoms of an element, we have to use its ‘gram atomic mass’ or molar mass of element. But when we are dealing with the molecules of a substance, then we have to use its ‘gram molecular mass’ or molar mass of a molecule.

Avogadro number –

The gram atomic mass of carbon element is 12 grams. When a scientist is performing an experiment or weighing12 grams of carbon, he knows that he is dealing with 6.022 x 1023 atoms of carbon. In other words, he is working with 1 mole of carbon atoms. The gram molecular mass of water is 18 grams. When a scientist is using 18 grams of water in his experiment, he knows that he is carrying out the reaction by using 6.022 x 1023 molecules of water. In other words, the scientist is working with 1 mole of water. So, we consider a collection of 6.022 x 1023 particles of a substance as one mole.

A group of 6.022 x 1023 particles (atoms, molecules or ions) of a substance is called one mole of that substance. This number, 6.022 x 1023 , which represents one mole, is called Avogadro Number (NA).

A mole of a substance is that amount of the substance which contains the same number of particles (atoms, molecules or ions) as there are carbon atoms in 12 grams of carbon-12 element. Since 12 grams of carbon-12 element contains 6.022 x 1023 atoms of carbon, we can also say that: A mole of a substance is tat amount of the substance which contains 6.022 x 1023 particles of that substance.

### Formulae based on mole concept –

We have just seen that

1 mole of atoms of an element = gram atomic mass of that element = 6.022 x 1023 atoms

So, there are 3 relations that can help us in converting amount of a substance into mass and number of particles

• 1 mole of atoms = gram atomic mass
• 1 mole of atoms = 6.022 x 1023 atoms
• Gram atomic mass = 6.022 x 1023 atoms

For molecules,

• 1 mole of molecules = gram molecular mass
• 1 mole of molecules = 6.022 x 1023 molecules
• Gram molecular mass = 6.022 x 1023 molecules

### Questions related to mole concept from NCERT textbook –

Page 42

Question 1:-

If one mole of carbon atom weighs 12 grams, what is the mass (in grams) of 1 atom of carbon?

Answer 1:-

Mass of 1 mole carbon atom = 12 gram

Mass of 6.022 x 1023 atoms = 12 gram

Mass of 1 atom = (12)/(6.022 x 1023) = 1.99 x 10-23 gram

Question 2:-

Which has more number of atoms, 100 grams of sodium or 100 grams of iron ?

Answer 2:-

Moles of sodium = given mass/gram atomic mass = 100/23 = 4.34

Moles of iron = given mass/gram atomic mass = 100/56 = 1.78

One mole contains equal number of atoms. Since, number of moles of sodium is greater than number of moles of iron, therefore, sodium contains more number of atoms.

Page 43 and 44

Question 6:-

Calculate the molar masses of the following substances :-

(a) Ethyne, C2H2
(b) Sulphur molecule, S8
(c) Phosphorous molecule, P4
(d) Hydrochloric acid, HCl
(e) Nitric acid, HNO3

Answer 6:-

(a) Molar mass of ethyne = (2×12 + 2×1) g/mol = 26 g/mol
(b) Molar mass of Sulphur = (8×32) g/mol = 256 g/mol
(c) Molar mass of phosphorous molecule = (4×31) g/mol = 124 g/mol
(d) Molar mass of hydrochloric acid = (1 + 35.5) g/mol = 5 g/mol
(e) Molar mass of nitric acid = (1 + 14 + 3×16) = 63 g/mol

Question 7:-

What is the mass of:-

(a) 1 mole of nitrogen atoms
(b) 4 moles of aluminium atoms
(c) 10 moles of sodium sulphite (Na2SO3)

(atomic masses : N=14u, Al=27u, Na=23u, S=32u  and O=16u)

Answer 7:-

(a) mass of 1 mole nitrogen = 14 g

(b) mass of 4 moles of aluminium
= (4x molar mass of aluminium)
= (4×27)
= 108 g

(c) mass of 1 mole of sodium sulphite
= molecular mass of sodium sulphite
= (2×23 + 32 + 3×16) = 126 grams
mass of 10 moles of sodium sulphite
= 126 x 10
= 1260 g

Question 8:-

Convert into moles :

(a) 12g of oxygen gas
(b) 20g of water
(c) 22g of carbon dioxide

(Atomic masses : O=16u, H=1u, C=12u)

Answer 8:-

(a) 1 mole of oxygen gas = (2×16)g = 32g
If 32 g oxygen gas = 1 mole
Then, 12 g of oxygen gas = (1×12)/32 = 0.375 mole

(b) 1 mole of water = 18g
If 18g of water = 1 mole
Then, 20g of water = (1×20)/18 = 1.11 mole

(c) 1 mole of carbon dioxide = 44g
If 44g of carbon dioxide = 1 mole
Then, 22g of carbon dioxide = (1×22)/44 = 0.5 mole

Question 9:-

What is the mass of :

(a) 2 mole of oxygen atoms
(b) 5 mole of water molecules

Answer 9:-

(a) 1 mole of oxygen atoms = 16g
mole of oxygen atoms = 16×0.2 = 2g

(b) 1 mole of water molecules = 18g
0.5 mole of water molecules = 18×0.5 = 9g

Question 10:-

Calculate the number of molecules of Sulphur (S8) present in 16g of solid Sulphur. (Atomic mass of S=32u)

Answer 10:-

Molecular mass of Sulphur molecule = (8×32)u = 256u
256g of Sulphur = 1 mole
16g of Sulphur = (1×16)/256 = 0.0625 mole
Molecules in 1 mole = 6.022 x 1023
Molecules in 0.0625 mole = 0.0625 x 6.022×1023 = 3.76 x 1023

Question 11:-

Calculate the number of aluminium ions present in 0.051g of aluminium oxide. (Hint : The mass of an ion is the same as that of an atom of the same element. Atomic mass of Al=27u)

Answer 11:-

Chemical formula of aluminium oxide = Al2O3
Mass of 1 mole of aluminium oxide = (2×27 + 3×16) = 102g
102g of aluminium oxide = 1 mole
0.051g of aluminium oxide = (1×0.051)/102 = 0.0005 mole
Molecules in 1 mole = 6.022×1023
Molecules in 0.0005 mole = 6.022×1023 x 0.0005 = 0.003011 x 1023
Aluminium ions in 1 molecule = 2
Aluminium ions in 0.003011 x 1023 molecules = 2 x 0.003011 x 1023 = 6.022 x 1020

ConclusionMole concept is an approach developed to link the number of atoms or molecules to the amount of substance. One mole of substance is that amount of the substance which contains the same number of particles as there are carbon atoms in 12 grams of carbon-12 elements. One mole of any substance contains 6.022 x 1023 particles in it. The number 6.022 x 1023 is called Avogadro Number.