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1 Atomic Structure and Properties 2 Compound Structure and Properties 3 Properties of Substances and Mixtures 4 Chemical Reactions 5 Kinetics 6 Thermochemistry 7 Equilibrium 8 Acids and Bases 9 Thermodynamics and Electrochemistry

1 Atomic Structure

1.1 Moles and Molar Mass 1.2 Mass Spectra of Elements 1.3 Elemental Composition of Pure Substances 1.4 Composition of Mixtures 1.5 Atomic Structure and Electron Configuration 1.6 Photoelectron Spectroscopy 1.7 Periodic Trends 1.8 Valence Electrons and Ionic Compounds

The Mole

Learning Objective 1.1.A Calculate quantities of a substance or its relative number of particles using dimensional analysis and the mole concept.
Covers AP LO 1.1.A (1.1.A.1–1.1.A.3)

Quick Notes

  • Atoms and molecules are too small to count individually — we use the mole as a unit to count particles in bulk.
  • 1 mole = 6.022 × 1023 particles (Avogadro’s number)
  • The molar mass of a substance (in g/mol) is numerically equal to the average mass of one particle in atomic mass units (amu).
  • We use dimensional analysis to convert between:
    • Mass (g) and moles (mol)
    • Moles (mol) and particles (atoms, molecules, formula units)
  • Key conversions:
    • particles = moles × 6.022 × 1023
    • mass (g) = moles × molar mass (g/mol)
    • moles = mass (g) ÷ molar mass (g/mol)
    • moles = particles ÷ 6.022 × 1023

Full Notes

In chemistry, we deal with incredibly small particles such as atoms, ions, and molecules. These particles are far too small to count individually in the lab. To connect the amount of a substance we can measure (mass) with the number of particles it contains, we use a unit called the mole.

The Mole as a Counting Unit

A mole is defined as 6.022 × 1023 particles. This is known as Avogadro’s number.

Just like 1 dozen = 12 things, 1 mole = 6.022 × 1023 things. These could be atoms, molecules, or formula units, depending on the substance.

Photo of Matt
Matt’s Exam Tip

Always be specific about what you're counting. For elements like copper or iron, you're counting atoms. For covalent compounds like water, you're counting molecules. For ionic compounds like NaCl, you're counting formula units. This will become clearer later in the course.

Why the Mole Is Useful

While we cannot count atoms directly, we can measure the mass of a substance in grams. The mole allows us to link mass with the number of particles.

The molar mass of a substance (in g/mol) is the mass of one mole of its particles.

The numerical value of the molar mass (in g/mol) is the same as the average mass of a single particle (in amu).

Diagram showing that 12.01 g of carbon contains one mole, i.e., 6.022 × 10^23 carbon atoms

ExampleCarbon has an average atomic mass of 12.01 amu, so its molar mass is 12.01 g/mol. This means that 12.01 g of carbon contains 1 mole of atoms, or 6.022 × 1023 atoms.

Dimensional Analysis

Dimensional analysis is a method for converting between different units using conversion factors. It is essential for solving problems involving mass, moles, and particle numbers.

Core conversions:

If we know that

Formula banner: moles (n) equals mass in grams divided by molar mass in g mol⁻¹

Then we can rearrange this form of the expression

And if we know

Equation banner: number of particles = moles × Avogadro constant Nₐ

Then we can rearrange this form of the expression


Worked Example

Question: How many molecules are in 9.00 g of water (H2O)?

  1. Find the molar mass of H2O
    H: 1.01 × 2 = 2.02
    O: 16.00
    Molar mass = 18.02 g/mol
  2. Convert grams to moles
    moles = 9.00 g ÷ 18.02 g/mol = 0.499 mol
  3. Convert moles to molecules
    particles = 0.499 mol × 6.022 × 1023 = 3.00 × 1023 molecules

Answer: 3.00 × 1023 molecules of water.

Summary

The mole is a fundamental concept in chemistry that connects the measurable mass of a substance to the number of atoms, molecules, or formula units it contains. By using Avogadro’s number and molar mass, we can convert between mass, moles, and particles using simple mathematical relationships. This allows chemists to understand and predict how much of each substance is involved in a chemical reaction.

Key conversions to remember: