The Mole Concept

The mole is the chemist's counting unit. It links the microscopic world of atoms and molecules to the macroscopic quantities we measure in the laboratory. This lesson covers the Avogadro constant, molar mass, and calculations involving moles of solids, liquids, solutions, and gases.

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The Avogadro Constant

One mole of any substance contains exactly 6.022 × 10²³ particles (atoms, molecules, ions, electrons, etc.). This number is called the Avogadro constant (Nₐ) or Avogadro's number.

Nₐ = 6.022 × 10²³ mol⁻¹

One mole of carbon-12 has a mass of exactly 12.00 g. One mole of any element has a mass in grams equal to its relative atomic mass.

Key Point: Always specify the type of particle when using moles. For example, "1 mole of water" means 6.022 × 10²³ water molecules, but it also contains 2 × 6.022 × 10²³ hydrogen atoms and 1 × 6.022 × 10²³ oxygen atoms.

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Molar Mass

The molar mass (M) of a substance is the mass of one mole of that substance, measured in g mol⁻¹. Numerically, it equals the relative formula mass (Mᵣ).

Substance	Formula	Mᵣ	Molar mass (g mol⁻¹)
Water	H₂O	18.0	18.0
Carbon dioxide	CO₂	44.0	44.0
Sodium chloride	NaCl	58.5	58.5
Sulfuric acid	H₂SO₄	98.1	98.1
Calcium carbonate	CaCO₃	100.1	100.1
Ethanol	C₂H₅OH	46.1	46.1

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Calculating Moles from Mass

The fundamental equation linking moles and mass is:

n = m / M

where:

• n = number of moles (mol)
• m = mass (g)
• M = molar mass (g mol⁻¹)

This can be rearranged to:

• m = n × M (to find mass)
• M = m / n (to find molar mass)

Worked Example 1: Moles from Mass

Calculate the number of moles in 11.0 g of carbon dioxide (CO₂).

M(CO₂) = 12.0 + (2 × 16.0) = 44.0 g mol⁻¹

n = m / M = 11.0 / 44.0 = 0.250 mol

Worked Example 2: Mass from Moles

Calculate the mass of 0.350 mol of sodium hydroxide (NaOH).

M(NaOH) = 23.0 + 16.0 + 1.0 = 40.0 g mol⁻¹

m = n × M = 0.350 × 40.0 = 14.0 g

Worked Example 3: Number of Particles

How many molecules are in 9.00 g of water?

M(H₂O) = 18.0 g mol⁻¹

n = 9.00 / 18.0 = 0.500 mol

Number of molecules = n × Nₐ = 0.500 × 6.022 × 10²³ = 3.01 × 10²³ molecules

How many atoms in total? Each water molecule has 3 atoms (2H + 1O).

Total atoms = 3.01 × 10²³ × 3 = 9.03 × 10²³ atoms

Exam Tip: If a question asks for the number of atoms rather than molecules, multiply by the number of atoms per molecule. This is a common source of error.

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Moles of Gases

Molar Volume at Room Temperature and Pressure (RTP)

At room temperature and pressure (approximately 298 K and 101.3 kPa), one mole of any gas occupies approximately 24.0 dm³ (or 24 000 cm³).

n = V / 24.0 (where V is in dm³)

n = V / 24 000 (where V is in cm³)

Worked Example 4: Volume of Gas at RTP

Calculate the volume of 0.150 mol of oxygen gas at RTP.

V = n × 24.0 = 0.150 × 24.0 = 3.60 dm³

Worked Example 5: Moles from Volume of Gas at RTP

Calculate the number of moles in 480 cm³ of ammonia gas at RTP.