The mole stops being a formula triangle

moles = mass ÷ Mr. Sometimes moles = concentration × volume and moles of gas = volume ÷ 24 dm³ at RTP. Taught as three formula triangles. Higher-tier only on many specs.

The mole is the SI unit of amount of substance, defined by the Avogadro constant (Structure 1.4.1). It is the bridge between the mass you can weigh and the particles that react. IB adds: molar concentration in mol dm⁻³ with careful volume-unit discipline (1.4.5); Avogadro's law and the ideal gas equation PV = nRT (1.5.3–1.5.4), which replaces the memorised 24 dm³ with something that works at any T and p; partial-pressure-free but temperature-general reasoning; limiting reactant and theoretical yield (Reactivity 2.1.3), percentage yield (2.1.4), and atom economy (2.1.5). Empirical vs molecular formula (1.4.4) is treated rigorously, including from combustion data.

Volume of a specific reagent stops being the answer and becomes an input; the limiting reagent concept means you can no longer just pick the number in the question and divide. Gas problems require unit conversion into SI (Pa, m³, K) or careful use of a consistent set — a notorious source of error. And every calculation is now multi-step: mass → mol → mol (via ratio) → mass/volume/concentration.

RTP molar volume is a legitimate shortcut at a fixed condition; formula triangles get answers out of 15-year-olds.

Using 24 dm³ at 100 °C; forgetting cm³ → dm³ (divide by 1000); ignoring the limiting reagent and using the wrong reactant's moles; carrying the wrong number of significant figures; and — most damaging — being slow. Mole calculations must become automatic, because in HL they are a sub-step inside harder questions (titration → Ka; calorimetry → ΔH; electrolysis → charge), not the question itself.