Molar mass cheat sheet

Everything you need to compute molar mass by hand, from Hill-notation rules to benchtop MW values.

Atomic weights — IUPAC 2021 conventional values

Values are the IUPAC 2021 “conventional atomic weights” (single-value form). Where an element has a natural-abundance range, IUPAC publishes a bracket — the conventional value is what you use for stoichiometry unless you’re doing high-precision mass-spec.

Hill notation — the ordering rules

The Hill system orders element symbols in a molecular formula so any two chemists write the same compound the same way:

1. Carbon first (if present), then hydrogen, then every other element in alphabetical order by symbol.
2. If no carbon, all elements go in alphabetical order (H included).
3. Group multipliers apply to everything inside their parentheses; nested groups multiply through.
4. Hydrates use a middot (·), asterisk (*), or period (.) as a separator: CuSO4·5H2O.

Examples:

• Ethanol → C2H6O (C, then H, then O).
• Water → H2O (no C; H before O alphabetically).
• Ammonium sulfate → (NH4)2SO4 — parentheses group the two NH₄⁺ before the SO₄.
• Copper(II) sulfate pentahydrate → CuSO4·5H2O — the middot separates the salt from the waters of crystallization.

Common polyatomic ion masses

Sum of atomic weights, no charge assumed (charges are ignored in mass sums):

Common reagent MWs

Hydrates — never forget the waters

A hydrate is a salt that carries a fixed number of water molecules in its crystal lattice. The bottle mass is the hydrated mass; the anhydrous formula ignores the waters.

$\text{MW}(\text{X}\cdot n\text{H}_2\text{O}) = \text{MW}(\text{X}) + n \cdot 18.015$

Common bench hydrates:

Rule. Read the label on the bottle. Use the MW that matches the formula on the label — never assume anhydrous.

Common mistakes

1. Using the anhydrous MW for a hydrate. Weighing 159.60 g of “CuSO₄” from a pentahydrate bottle delivers only 159.60/249.68 ≈ 64 % of the copper you meant. Ratios shift accordingly.
2. Missing a group multiplier through nested parentheses. K3[Fe(CN)6] has 6 carbons and 6 nitrogens, not 1 of each. The Hill parser walks parentheses recursively — you must too when doing this by hand.
3. Rounding atomic weights too aggressively. IUPAC 2021 gives S = 32.06 and Cl = 35.45. Using 32 and 35.5 introduces ~0.5 % error on small molecules — rarely important, but stacks up on high-MW ligands.