Molarity Is per Litre of Solution, Not per Litre of Water

Molarity moves with temperature; molality does not

The denominator is a volume, and volumes expand when warmed, so the same flask holds the same number of moles at a lower concentration once it is hot. That is why a volumetric flask carries a calibration temperature etched on the glass alongside its capacity — the mark is only exact at that temperature. Molality, defined as moles per kilogram of solvent, uses a mass instead and therefore does not move at all, which is why it is the quantity that appears in freezing-point and boiling-point work. For room-temperature bench chemistry the difference is usually below the other errors; for anything heated, refrigerated or precise, it is not.

Moles are the step people skip

Nothing is weighed in moles, so almost every real calculation begins with a mass and a molar mass before this tool is reached. Half a mole of sodium chloride is 29.22 grams, because its molar mass is about 58.44 grams per mole; the same 29.22 grams of glucose is far less than half a mole, because glucose is roughly three times heavier per mole. Getting the substance right matters more than getting the arithmetic right, and a hydrated salt is the usual trap — copper sulfate pentahydrate weighs considerably more per mole than the anhydrous form, and a recipe that names one while the shelf holds the other is out by a quarter or more.

Frequently asked questions

What does a capital M on a bottle mean?

Molar, meaning moles per litre — 2 M is 2 mol/L. A lower-case m is molal, moles per kilogram of solvent, and the two are different quantities that happen to be nearly equal for dilute aqueous solutions and diverge as concentration rises. An older label may also carry N for normal, a concentration expressed in equivalents rather than moles, which for an acid depends on how many protons it can donate: 1 M sulfuric acid is 2 N. Normality has largely fallen out of use precisely because the conversion is not a property of the bottle but of the reaction it is used in.

How do I dilute a stock solution to a lower molarity?

The number of moles does not change when you add solvent, so the starting concentration times the starting volume equals the final concentration times the final volume. To make 500 mL at 0.25 mol/L from a 1 mol/L stock, take 0.25 × 500 ÷ 1 = 125 mL of stock and make up to 500 mL. Note the last four words: make up to, not add 375 mL to. The relation holds for any pair of units as long as both concentrations are in the same one and both volumes are in the same one.