The Mole Concept

A pairA pair = 2 items means 2two items. A dozenA dozen = 12 items means 12twelve items. Simple words for specific amounts.

But atoms are unimaginably small. A single drop of water contains more atoms than there are stars in the Milky Way. We need a counting word big enough for chemistry.

That word is the mole. One mole = exactly 6.0 × 10²³ particles. This number is called Avogadro's constantNₐ = 6.0 × 10²³ mol⁻¹. Named after Amedeo Avogadro. (Nₐ).

ParticlesAtoms (elements), molecules (covalent), formula units (ionic), or ions can be atoms, molecules, formula units, or ions — it depends on the substance.

Imagine you need to compare the weight of different fruits — but you have no scale. So you pick one fruit, call it your standard, and compare everything to it.

That's exactly what scientists did with atoms. They picked carbon-12 — one specific atom with 6 protons and 6 neutrons — and said: "This atom weighs exactly 1212 atomic mass units amuAtomic mass unit — the tiny unit for atomic-scale mass. 1 amu = exactly of a carbon-12 atom's mass.."

So 1 amuone-twelfth of carbon-12 = of a carbon-12 atom. Every other atom's mass is compared to this. Hydrogen is about 1 amu ( as heavy as carbon-12). Oxygen is about 16 amu ( times as heavy).

The relative atomic massAᵣ — the average mass of one atom compared to ¹⁄₁₂ of carbon-12. Found on the periodic table. No units — it's a ratio. (Aᵣ) of an element is found on the periodic table. It has no units — it's a ratio.

Tap an element to see its details. Try dragging one — it springs back:

For compounds, add the Aᵣ of every atom to get the relative molecular massMᵣ — the sum of all relative atomic masses in a formula. Used for covalent compounds. Relative formula mass is the same idea, used for ionic compounds. (Mᵣ). For water (H₂O): 18H×2 = 1×2 = 2
O×1 = 16×1 = 16
Total = 2 + 16 = 18.

In Mg(NO₃)₂, the 2multiplies everything inside the brackets outside the bracket multiplies both N and O₃. So: 1 Mg + 2 N + 6 O.

Here's the beautiful connection: the Aᵣ in amu is numerically equal to the molar massM — the mass of one mole of a substance, in g mol⁻¹. Numerically equals the relative atomic/molecular mass. in g mol⁻¹.

Carbon: Aᵣ = 12relative atomic mass (no units) → molar mass = 12 g mol⁻¹mass of 1 mole (in grams). Same number, different unit.

Slide to explore: 12 amu = 12 g mol⁻¹

To find how many moles, divide the mass by the molar mass.

To find the mass, multiply moles by the molar mass. The reverse of Step 8.

More moles = more particles. Multiply to go bigger.

Given particles, divide to get moles. The reverse of Step 10.

Now chain them together. The mole is your transfer station — every conversion passes through it.

Avogadro's LawEqual volumes of all gases, at the same T and P, contain the same number of molecules.: equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules.

This means 1 mole of any gas occupies the same volume at a given T and P.

The molar volumeVₘ — the volume occupied by one mole of gas. At STP = 22.4 dm³. At RTP = 24.0 dm³. depends on conditions:

The conversion map is now complete:

Find the mass of that element in one mole of the compound, divide by the total Mᵣ, multiply by 100. Example — % oxygen in H₂O: 88.9%O mass in 1 mol = 16
Mᵣ of H₂O = 18
16 ÷ 18 × 100 = 88.9%

The empirical formulaThe simplest whole-number ratio of atoms in a compound. Ionic compounds always use empirical formulas. gives the simplest whole-number mole ratio. To find it from mass data:

The molecular formulaShows the actual number of atoms in one molecule. May be a whole-number multiple of the empirical formula. shows actual atom counts. Find it by dividing the given Mᵣ by the empirical formula mass:

Then multiply the empirical formula by that ratio.

When a soluteThe substance that dissolves (e.g. NaOH, NaCl, sugar) dissolves in a solventThe liquid it dissolves in — usually water, you get a solution. How "strong" it is depends on the concentration — how much solute per unit of solution.

Mass concentration = mass of solute ÷ volume of solution:

Molar concentration = moles of solute ÷ volume of solution:

The two are linked: . And the most-used rearrangement:

Standard solutionA solution whose concentration is known accurately, made by dissolving a precise mass in a volumetric flask.: one whose concentration is known accurately — made with a precise mass and a volumetric flask.

In a balanced equation, coefficients = mole ratios. The 6-step method solves any reaction problem: