Mole Concept

Summary

Mole: Mole is the measurement in chemistry. It is used to express the amount of a chemical substance.
One mole is defined as the amount of substance of a system which contains as many entities like, atoms, molecules and ions as there are atoms in 12 grams of carbon - 12".

Avogadro number: The number of the particles present in one mole of any substance is equal to 6.022x10²³. This is called avogadro’s number or avogadro’s constant.

Number of particles in 1 mole:
1 mole of hydrogen atoms represents 6.022 × 10²³hydrogen atoms.
1 mole of hydrogen molecules represents 6.022 × 10²³ hydrogen molecules.
1 mole of water molecules represents 6.022 × 10²³ water molecules.

The Video Tutorial:

Atomic mass: The atomic mass of an element is the mass of one atom of that element in atomic mass units or (u).

Atomic mass unit (amu): 1/12^th of the mass of an atom of carbon-12 is called atomic mass unit. It is a unit of mass used to express atomic masses and molecular masses.

Molar mass: The molar mass of an element is equal to the numerical value of the atomic mass. However, in case of molar mass, the units change from ‘u’ to ‘g’. The molar mass of an atom is also known as gram atomic mass.
For example, the atomic mass of carbon =12 atomic mass units. So, the gram atomic mass of carbon = 12 grams.

Molecular mass of the molecule: The sum of the atomic masses of all the atoms in a molecule of a substance is called the molecular mass of the molecule.

Molecular mass - calculation: Generally we use relative atomic masses of atoms for calculating the molecular mass of 1 mole of any molecular or ionic substances.
Example: Molecular mass of H₂SO₄
Atomic mass of Hydrogen = 1
Atomic mass of sulphur = 32
Atomic mass of oxygen = 16
Molecular mass of H₂SO4 = 2(Atomic mass of Hydrogen) + 1 (Atomic mass of sulphur) + 4 (Atomic mass of oxygen)
= 2×1 + 32 + 4× 16 = 98 u.

Calculation of molecular mass of hydrogen chloride:
Atomic mass of hydrogen + Atomic mass of chlorine = 1 + 35.5 = 36.5 u.

Formula unit mass: The formula unit mass of a substance is the sum of the atomic masses of all atoms in a formula unit of a compound. The term ‘formula unit’ is used for those substances which are made up of ions.
Formula unit mass of NaCl: 1 X Atomic mass of Na + 1 X Atomic mass of Cl
1x23 +1 x 35.5 = 58.5 atomic mass units.

Formula unit mass of ZnO:
= 1 X Atomic mass of Zn + 1 X Atomic mass O
= 1 X 65 + 1 X 16 = 81 u.

Avogadro's number, number of particles and moles - conversion formulae:

Number of moles (n) = Given number of particles (N) / Avogadro number (N₀)

Example: Find the number of moles present in 24.088X10²³particles of carbon dioxide
1 mole of carbon dioxide contains 6.022x10²³
Solution: The number of moles (n ) = Given number of particles (N) / Avogadro number (N₀).
= 24.088X10²³/ 6.022x10²³
= 4 moles.

Number of atoms (n) = Given mass (m) / Molar mass (M) x Avogadro number (N₀)

Example: Calculate the number of atoms in 48g of Mg
Solution: Number of atoms (n) = Given mass (m) / Molar mass (M) x Avogadro number (N₀).
= 48/24 X 6.022x10²³
= 12.04 X10²³atoms.

Number of molecules (n) = Given mass (m) / Molar mass (M) x Avogadro number (N₀)

Example: Calculate the number of molecules in 3.6 g of water
Solution: The molecular weight of H₂O = 18
18g of water - 6.022x10²³ molecules
3.6g of water - 6.022x10²³X 3.6/18
= 1.206 X 10²² molecules.

Number of particles (n) = Number of moles of particles (n) x Avogadro number (N₀)

Example: Calculate the number of atoms in 0.5 moles of carbon
Solution: Number of atoms = 0.5 X 6.022x10²³
= 3.0115 atoms

Extra problems:

1) Calculate the number of moles in 12g of oxygen gas
Ans: 32g of oxygen gas = 1 mole
12g of oxygen gas = ?
= 12 X 1 / 32 = 0.375 mole.

2) Calculate the number of moles present in 14g of carbon monoxide .
Ans: 28g of CO = 1 mole
14g of CO = ?
= 14 X 1 / 28 = 1/2 = 0.5 mole.

3) Find the mass of 5 moles of aluminium atoms?
Ans: Atomic mass of aluminium atom = 27g
5 moles of aluminium atoms = 5 X 27g = 135 g.

4) Calculate the molar mass of sulphur.
Ans: Sulphur is a poly atomic molecule. It is made up of 8 sulphur atoms.
Atomic mass sulphur atom = 32 g.
Molar mass of sulphur = 8 X 32 = 256 g.

5) Calculate the mass of 0.2 mole of water molecules.
Ans: 1 mole of water molecules = 18g
0.2 mole of water molecules = ?
= 0.2 X 18 / 1 = 3.6 g.

6) Which has greater number of atoms, 100g of sodium or 100g of iron?
Atomic mass of Na = 23 u, Fe = 56 u.
Ans: 1 mole of substance contains the number of particles = Avagadro's constant.
1 mole of Na = 23g
23g of Na contains - 6.023 X 10²³ atoms
100g of Na Contains - ?
= 100 X 6.023 X 10²³/23
= 4.3 X 6.023 X 10²³atoms.
1 mole of Fe = 56g
56g of Fe contains - 6.023 X 10²³ atoms
100g of Fe contains - ?
= 100 X 6.023 X 10²³/ 56
= 1.78 X 6.023 X 10²³ atoms
Therefore, 100g of Na has greater number of atoms than 100 g of Fe.

7) How many atoms of oxygen are present in 300 grams of CaCO3?
Ans: Molecular mass of calcium carbonate = 40 + 12 + 3 X 16 = 40 + 12 + 48 = 100g
1 mole of Calcium carbonate contains – 3 mole of oxygen atoms.
100 g of calcium carbonate contains - 3 X 6.023 X 10²³ atoms
300g of calcium carbonate contains - ?
= 300 X 3 X 6.023 X 10²³/100
= 54.207 X 10²³oxygen atoms.

8) The mass of one atom of an element 'A' is 2.65 X10^-23 g. Calculate its atomic mass and name the element.
Ans: The mass of one atom of an element A = 2.65 X10^-23g
We know that 1 mole of an atom = 6.023 x 10²³ atoms
1 mole of an atom = Its atomic weight
Mass of one atom of an element = 2.65X10^-23g
Mass of 6.023 x 10²³ atoms of an element A = 2.65X10^-23X6.023 x 10²³
= 15.69 g

The element is oxygen.

9) Calculate the number moles of magnesium in 0.478g of magnesium ?

Ans: Molecular weight of magnesium =24g

24g of magnesium = 1 mole

0.478g of magnesium = ?

= 0.478 X 1/24 = 0.019 mole.

10) In which of the following cases the number of hydrogen atoms is more ? Two moles of HCl or one mole of NH₃.

Ans: Calculation of number of hydrogen atoms present in 2 moles of HCl
1 mole of HCl contains 6.023X10²³ molecules of HCl
2 moles of HCl contains 2 X 6.023X10²³= 12.046X10²³ molecules of HCl
1 molecule of HCl contains 1 hydrogen atom
12.046X10²³molecules of HCl contains12.046X10²³ hydrogen atoms
Calculation of number of hydrogen atoms present in 1 mole of NH₃
1 mole NH₃ Contains 6.023X10²³molecules of NH₃
1 molecule of NH₃contains 3 atoms of hydrogen
6.023X10²³molecules of NH₃contains 3X 6.023X10²³ atoms of hydrogen
= 18.069 X10²³ atoms of hydrogen
Number of hydrogen atoms present in 2 moles of HCl = 12.046X10²³
Number of hydrogen atoms present in 1 mole of NH₃= 18.069 X10²³
Therefore, numbers of hydrogen atoms are more in 1 mole of NH_3.

11) Find the number of oxygen atoms in 88g of CO₂?

Ans: Molar mass of CO₂ = 44 g/mol
Number of moles of CO₂ present in 88g of CO₂ = 88g/44g mol^-1
= 2 moles
1 mole of CO₂contains 2 moles of Oxygen atoms.
2 moles of CO₂ contains 4 moles of Oxygen atoms
1 mole of oxygen contains 6.023 X 10²³ atoms of oxygen
4 moles of oxygen contains = 4 X 6.023 X 10²³
= 24.092 X 10²³
= 2.4092 X 10²⁴atoms of oxygen

Therefore, 88g of CO₂ Contains 2.4092 X 10²⁴atoms of oxygen.

12) Calculate the number of water molecules contained in a drop of water weighing 0.06g ?

Ans: 18g of water = 1 mole
0.06 g = ?
= 0.06/18 = 3.33 X 10^-3 mole of water
1 mole of water contains - 6.022X10²³ molecules of water
3.33 X 10^-3mole of water contains -----?
= 6.022X10²³X 3.33 X 10^-3
= 2 X 10²⁰ molecule of water
∴ 0.06g of water contains 2 X 10²⁰ molecules of water.

13) Find the number of aluminium ions present in 0.051g of aluminium oxide(Al₂O₃).

(Atomic masses: Al= 27u;O= 16u)

Ans: Molecular weight of Al₂O₃ = 102 g
102 g of Al₂O₃ contains 6.022X10²³ molecules
0.051g of Al₂O₃ contain X number of molecules
X = 0.051 X 6.022X10²³/102 = 0.003 X 10²⁰
X = 3 X 10²⁰
1 molecule of Al₂O₃contains – 2 Al⁺³ions
3 X 10²⁰molecules contains – 2 X 3 X 10²⁰
= 6 X 10²⁰Al⁺³ ions
∴ 0.051 g of Al₂O₃ contains 6 X 10²⁰Al⁺³ ions.