You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
The mole is the chemist's counting unit. Atoms and molecules are far too small to count individually, so chemists use a quantity called the mole to bridge the gap between the atomic scale and the laboratory scale. Understanding the mole concept is absolutely fundamental to everything that follows in quantitative chemistry.
A mole is defined as the amount of substance that contains exactly 6.022 × 10²³ particles. This number is called Avogadro's constant (symbol: Nₐ or L).
The particles can be atoms, molecules, ions, electrons, or any other specified entity. You must always state what the particles are — saying "one mole of oxygen" is ambiguous because it could mean one mole of oxygen atoms (O) or one mole of oxygen molecules (O₂).
The value 6.022 × 10²³ is an extraordinarily large number. To put it in perspective, if you had 6.022 × 10²³ grains of sand, they would cover the entire surface of the Earth to a depth of several metres.
The molar mass (symbol: M) of a substance is the mass of one mole of that substance, measured in g mol⁻¹. Numerically, the molar mass in g mol⁻¹ is equal to the relative atomic mass (Aᵣ) or relative molecular mass (Mᵣ) of the substance.
| Substance | Formula | Mᵣ | Molar mass (g mol⁻¹) |
|---|---|---|---|
| Carbon | C | 12.0 | 12.0 |
| Water | H₂O | 18.0 | 18.0 |
| Sodium chloride | NaCl | 58.5 | 58.5 |
| Sulfuric acid | H₂SO₄ | 98.0 | 98.0 |
| Calcium carbonate | CaCO₃ | 100.0 | 100.0 |
To find the molar mass of a compound, add up the relative atomic masses of all the atoms in the formula. For example, for H₂SO₄: (2 × 1.0) + 32.0 + (4 × 16.0) = 98.0 g mol⁻¹.
The relationship between mass, moles, and molar mass is given by:
n = m / M
Where:
This can be rearranged to:
Calculate the number of moles in 4.40 g of carbon dioxide (CO₂).
Step 1: Find the molar mass of CO₂. M = 12.0 + (2 × 16.0) = 44.0 g mol⁻¹
Step 2: Use n = m / M. n = 4.40 / 44.0 = 0.100 mol
Calculate the mass of 0.250 mol of sodium hydroxide (NaOH).
Step 1: Find the molar mass of NaOH. M = 23.0 + 16.0 + 1.0 = 40.0 g mol⁻¹
Step 2: Use m = n × M. m = 0.250 × 40.0 = 10.0 g
To convert between the number of moles and the number of particles, use:
Number of particles = n × Nₐ
Where Nₐ = 6.022 × 10²³ mol⁻¹.
How many molecules are present in 0.500 mol of water?
Number of molecules = 0.500 × 6.022 × 10²³ = 3.011 × 10²³ molecules
How many atoms are present in 0.500 mol of water?
Each water molecule (H₂O) contains 3 atoms (2 H + 1 O). Number of atoms = 0.500 × 6.022 × 10²³ × 3 = 9.033 × 10²³ atoms
This distinction between atoms and molecules is a common source of errors. Always read the question carefully.
To convert from mass to number of particles (or vice versa), you typically go through moles as an intermediate step:
Mass → Moles → Number of particles
How many atoms are in 6.40 g of sulfur (S₈)?
Step 1: Molar mass of S₈ = 8 × 32.0 = 256.0 g mol⁻¹
Step 2: Moles of S₈ = 6.40 / 256.0 = 0.0250 mol
Step 3: Number of S₈ molecules = 0.0250 × 6.022 × 10²³ = 1.506 × 10²²
Step 4: Each S₈ molecule contains 8 atoms, so number of atoms = 1.506 × 10²² × 8 = 1.204 × 10²³ atoms
The mole concept underpins all quantitative chemistry. Every calculation involving amounts of substance — from titrations to gas volumes to percentage yield — relies on being able to convert confidently between mass, moles, and number of particles.