Avogadro number

What is One Mole and How many Particles are in a Mole?

The Mole and the Number of Particles

1. One mole is defined as the amount of substance that contains as many particles as the number of atoms in exactly 12 g of carbon-12, which is 6.02 × 10²³ particles. The symbol of mole is mol.
2. In chemistry, we use the unit ‘mole’ to represent the amount of substance containing 6.02 × 10²³ particles.
   1 mole of copper
   = 6.02 × 10²³ copper atoms
   2 moles of copper
   = 2 × 6.02 × 10²³ copper atoms
3. The number of particles per mole (6.02 × 10²³ mol^-1) is determined experimentally and is known as the Avogadro constant or the Avogadro number.
   The Avogadro constant (N_A) is defined as the number of particles in one mole of a substance.
4. The particles in the substances can be atoms, molecules or ions. (Refer to the below table)
   

   Type of substance	Examples
   Atomic substances (consist of atoms)	All metal elements such as copper and zinc.
   	All noble gases such as helium and argon.
   	Certain non-metal elements such as carbon and silicon.
   Molecular substances (consist of molecules)	Ail covalent compounds such as water and carbon dioxide.
   	Certain non-metal elements such as hydrogen (H2), oxygen (O2), nitrogen (N2), fluorine (F2), chlorine (Cl2), bromine (Br2), iodine (I2), sulphur (S8) and phosphorus (P4).
   Ionic substances (consist of ions)	All ionic compounds such as sodium chloride and zinc bromide.

5. Therefore, the type of particles needs to be specified carefully.
   (a) 1 mole of atomic substances contains 6.02 × 10²³ atoms. For example, 1 mole of zinc contains 6.02 × 10²³ zinc atoms.
   (b) 1 mole of molecular substances contains 6.02 × 10²³ molecules. For example, 1 mole of water contains 6.02 × 10²³ H₂O molecules.
   (c) 1 mole of ionic substances contains 6.02 × 10²³ formula units. For example, 1 mole of sodium oxide contains 6.02 × 10²³ formula units of Na₂O.
6. We can find the number of particles in any number of moles of substances and vice versa using the following relationship.
   

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The Mole and the Number of Particles Problems with Solutions

1. Find the number of atoms in
(a) 0.4 mole of iron.
(b) 0.1 mole of oxygen gas.
Solution:
(a) Iron, Fe is an atomic substance.
Given the number of moles of iron = 0.4 mol
Number of iron atoms = number of moles × N_A
= 0.4 × 6.02 × 10²³
= 2.408 × 10²³ atoms

(b) Oxygen gas, O₂ is a molecular substance.
Given the number of moles of oxygen gas = 0.1 mol
Number of oxygen molecules = number of moles × N_A
= 0.1 × 6.02 × 10²³
= 6.02 × 10²² molecules
Based on its formula O₂, each oxygen molecule contains two oxygen atoms.
So, 6.02 × 10²² oxygen molecules contain 2 × 6.02 × 10²² oxygen atoms, that is 1.204 × 10²³ oxygen atoms.

2. How many moles ofwater contain 3.01 × 10²² water molecules?
Solution:

3. 0.3 mole of zinc bromide, ZnBr₂ is dissolved in a beaker of water. Calculate the total number of ions present in the beaker.
Solution:
Zinc bromide, ZnBr₂ is an ionic substance.
Given the number of moles of ZnBr₂ = 0.3 mol
The number of formula units of ZnBr₂ in the beaker
= number of moles × N_A
= 0.3 × 6.02 × 10²³
= 1.806 × 10²³ formula units
Based on its formula, each formula unit of ZnBr₂ consists of three ions, which are one zinc ion and two bromide ions.
Therefore, the total number of ions in the beaker
= 3 × number of formula units of ZnBr₂,
= 3 × 1.806 × 10²³
= 5.418 × 10²³ ions

4. Which of the following contains 6.02 x 10²³ atoms?
(A) 1 mol of nitrogen gas
(B) 1 mol of bromine gas
(C) 1 mol of carbon dioxide
(D) 1 mol of neon
Solution: D
6.02 x 10²³ atoms is equivalent to 1 mol of atoms.
1 mol of nitrogen gas, N₂ contains 2 mol of atoms.
1 mol of bromine gas, Br₂ contains 2 mol of atoms.
1 mol of carbon dioxide, CO₂ contains 3 mol of atoms.
1 mol of neon, Ne contains 1 mol of atoms Neon is a noble gas.
It is a monoatomic gas, unlike nitrogen, bromine and carbon dioxide gases.
Thus, 1 mol of neon contains 1 mol of atoms.