How to Calculate Molar Mass, Including Parentheses and Hydrates

The three cases the arithmetic has to handle

A plain subscript is the easy case: it counts the atoms of the element immediately before it, and an element with no subscript counts once. C6H12O6 is six carbons, twelve hydrogens and six oxygens, giving 180.156 g/mol. Nothing here catches anyone out, which is why textbooks stop there and students then meet a real formula.

The bracket case is where marks are lost. In Ca(NO3)2 the group NO3 appears twice, so the formula holds two nitrogens and six oxygens, and the six is the number people forget. The hydrate case is different again: the dot in CuSO4·5H2O is not multiplication of the copper sulfate, it is an instruction to add five separate water molecules. The anhydrous salt is 159.602 g/mol, the five waters are 90.075 g/mol, and the pentahydrate is their sum, 249.677 g/mol — which means more than a third of the crystal you weigh out is water.

Molar mass, molecular mass and formula mass

The three names describe the same arithmetic with different units attached. Relative molecular mass is a ratio and therefore carries no unit: water is 18.015, full stop. Molar mass is the mass of one mole and carries g/mol: water is 18.015 g/mol. Formula mass is the term used when the substance has no discrete molecules, as with an ionic solid like NaCl, where CaCO3 or NaCl describes the repeating ratio in a lattice rather than a particle you could isolate.

The numbers coincide because of how the mole is defined. Since the 2019 revision of the SI, a mole is exactly 6.02214076 × 10^23 entities, a fixed count rather than a mass of carbon-12. The consequence is subtle but worth knowing: the gram per mole is no longer exactly tied to the carbon-12 scale, so the molar mass constant is now an experimental quantity that happens to equal 1 g/mol to within about one part in a billion. For every calculation you will ever do by hand, treating the two as identical is exact enough.

Where the answer goes wrong

Capitalisation is a chemical statement, not a typing preference. CO is carbon monoxide at 28.010 g/mol; Co is cobalt at 58.933. Any parser worth using will refuse an unknown symbol rather than guess, which is why a formula that returns an error is usually a lowercase letter that should have been a capital, or a capital that should have been lowercase in a two-letter symbol.

The second recurring error is rounding at the start rather than the end. Atomic weights are published to three or four decimals for a reason, and truncating them before multiplying by a large subscript compounds the loss. Round once, at the end, and to the precision the question actually needs: two decimals is right for almost every school problem, four when a molar mass feeds a titration or a gravimetric result you will later subtract from another number of similar size.

Frequently asked questions

Why do two sources give slightly different molar masses?

Because standard atomic weights are averages over natural isotopic abundance, and that abundance varies slightly between geological sources. IUPAC now publishes intervals rather than single values for a dozen elements, including hydrogen, carbon, oxygen and sulfur, and different tables pick different conventional values from within those intervals. The disagreement lands in the third or fourth decimal and never changes an answer at school precision.

Is molar mass the same as molecular weight?

Numerically yes, dimensionally no. Molecular weight is the older name for relative molecular mass, a pure number with no unit; molar mass is that same number expressed in g/mol. Since they agree to every digit you will use, the distinction only bites when a question asks for units, or when you are cancelling units in a longer calculation and need g/mol to make the grams disappear.

Does the hydrate water count when I weigh out a reagent?

It counts entirely, and forgetting it is the classic way to prepare a solution roughly a third too dilute. Say you need one mole of copper sulfate, look up the anhydrous value of 159.602 g/mol and weigh that much out of a bottle of the pentahydrate: you have taken only 159.602 divided by 249.677, or 0.639 mol — 36 percent short, which is exactly the water fraction of the crystal. Check which form the bottle contains before converting a mass into moles; the label carries the dot or it does not, and for this purpose they are different substances.