The concept of Mole and Related Calculations

What is a mole?

A mole is a unit of measurement used to express amounts of a substance, just like other units such as a pair, dozen, or gross.

1 mole = 6.02 × 10²³ particles (Avogadro's constant)

A mole refers to the amount of substance containing exactly 6.02 × 10²³ elementary entities (atoms, molecules, ions, or electrons).

Example:

1 mole of water (H₂O) contains 6.02 × 10²³ molecules.

1 mole of sodium (Na) contains 6.02 × 10²³ atoms.

1 mole of CuCl₂ contains 6.02 × 10²³ ions.

1 mole of iron (Fe) contains 6.02 × 10²³ electrons.

Molar mass of a substance

The molar mass is the mass of 1 mole of any substance, measured in g/mol. It is denoted by M.

Example:

The molar mass of sodium (Na) = 23 g/mol.

The molar mass of sodium chloride (NaCl) = 58.5 g/mol.

The molar mass of sodium sulfate (Na₂SO₄) = 142 g/mol (calculated as 23 × 2 + 32 + 16 × 4).

Relative molar mass (Mr)

The relative molar mass is the mass of one molecule of a compound compared to the mass of one atom of carbon-12. It has no units.

Molar mass (M) = Relative molecular mass (Mr).

Molar mass of an element = Relative atomic mass (Ar).

Examples:

M of Na = 23 g/mol, Ar of Na = 23.

M of CH₄ = 16 g/mol, Mr of CH₄ = 16.

M of H₂O = 18 g/mol, Mr of H₂O = 18.

Calculating molar mass

To calculate the molar mass of a compound, sum the masses of its constituent atoms.

Example: Calculating the molar mass of (NH₄)₂CO₃:

N = 14, H = 1, C = 12, O = 16.

Solution: (NH₄)₂CO₃ = (14g × 2) + (1g × 8) + 12g + (16g × 3) = 28g/mol + 8g/mol + 12g/mol + 48g/mol = 96 g/mol

Amount of a substance (number of moles, n)

The number of moles, n, is the mass of a substance divided by its molar mass.

Formula:

Where:

m is the mass of the substance in grams.

M is the molar mass in g/mol.

Example:

For 180g of carbon: $n = \frac{180\text{g}}{12\text{ g}}$

For 180g of CO₂: n = 4.09 mol

Number of particles in a given amount of substance

To find the number of particles in a given amount of substance, we use the formula:

Number of particle = number of moles × Avogadro's number.

Where:

n = number of moles.

N = number of particles.

L = Avogadro's number (6.02 × 10²³ mol⁻¹).

Example:

For 20g of calcium (Ca):

n = 0.5 mol

N = 0.5 mol × 6.02 × 10²³ mol⁻¹ = 3.01 × 10²³ particles.

Molar volume (Vm)

The molar volume is the volume occupied by 1 mole of a gas at standard temperature and pressure (STP).

STP:

Temperature = 0°C (273 K).

Pressure = 1 atm (760 mm Hg).

The molar volume at STP is 22.4 dm³ or 22.4 L.