How to Calculate Molarity Without Ruining the Solution

Two things go wrong with molarity, and neither is the arithmetic. The first is using the wrong molar mass, usually by forgetting water of crystallisation. The second is measuring the volume of the solvent instead of the volume of the finished solution. Both produce a solution that looks right and is not.

Moles first, then volume

Molarity, written M, is moles per litre. Getting to moles means dividing mass in grams by molar mass in grams per mole. Sodium chloride is 58.44 g/mol, so 5.844 g is exactly 0.1 mol. Dissolve that in enough water to reach one litre and you have a 0.1 M solution.

Weighing out a target concentration

Work backwards when you know what you want. To make 250 mL of 0.10 M NaCl, start with the moles: 0.250 L multiplied by 0.10 mol/L is 0.025 mol. Multiply by the molar mass and 0.025 × 58.44 gives 1.461 g. Weigh that, dissolve it, then top up to the 250 mL mark.

A second example with a heavier molecule shows how much the molar mass drives the answer. Glucose is 180.16 g/mol, so one litre of 0.25 M glucose needs 0.25 × 180.16, which is 45.04 g. A litre of sodium chloride at that same 0.25 M needs 0.25 × 58.44, or just 14.61 g. Identical concentration, three times the mass on the balance, purely because a mole of glucose weighs three times as much.

The volume in that formula is the volume of the solution, not the water you added. Adding 250 mL of water to 1.461 g of salt gives slightly more than 250 mL of liquid, and the concentration comes out low. Dissolve the solid in maybe half the target volume, then add water up to the graduation mark.

Dilutions and the C1V1 = C2V2 shortcut

Most lab work starts from a stock solution rather than from powder. The relationship is that concentration times volume before equals concentration times volume after, because diluting adds water without adding solute.

Suppose you have 2.0 M stock and need 500 mL at 0.15 M. Rearranging gives V1 = (0.15 × 500) / 2.0, which is 37.5 mL of stock. Add 462.5 mL of water and you are there. Notice that the units of volume only have to be consistent, so working in millilitres throughout is fine and saves a conversion step.

Using the molarity calculator

The calculator solves for whichever field you leave blank, so fill in the three you know. Enter mass in grams, volume in litres or millilitres (check which unit is selected, since this is where most wrong answers come from), and concentration in mol/L.

Where the molar mass comes from

Read it off the reagent bottle. Every supplier prints the formula weight on the label, and using that number avoids any dispute about which figure your textbook rounds to. If the bottle is missing or you are planning ahead, build it from the chemical formula with a molecular weight tool, and check whether the formula includes a dot followed by a number of waters. Copper sulfate pentahydrate weighs 249.68 g/mol against 159.61 for the anhydrous form, a 56% difference that will wreck a solution if you use the wrong one.

For percentage or mass-per-volume recipes, you will also need to relate mass to volume, which is where a density calculation comes in. Our roundup of free online math calculators lists the other conversion tools that tend to sit alongside this one.

Common questions

What is the difference between molarity and molality? Molarity is moles per litre of solution; molality is moles per kilogram of solvent. Molality does not change with temperature because mass does not expand, which is why it is preferred for freezing point and boiling point work.

Does temperature affect molarity? Slightly. Liquids expand when warmed, so the same moles occupy a larger volume and the concentration drops. It rarely matters at room temperature but does for precise work.

How do I convert a percentage solution to molarity? A 10% w/v solution means 10 g in 100 mL, which is 100 g per litre. Divide by the molar mass to get molarity. For NaCl that is 100 / 58.44, or about 1.71 M.

What does 1 N mean? Normality counts reactive equivalents rather than whole molecules. For an acid like HCl with one proton, 1 N equals 1 M. For sulfuric acid with two, 1 M is 2 N.