What molarity actually measures
Molarity is the number of moles of solute per litre of solution — not per litre of solvent, and not per litre of water you add. That distinction is the single most common source of lab error: dissolving 1 mol in 500 mL of water and topping up to 1 L is not 1 M, because the final volume is not 1 L until you make it so.
M (mol/L) = n (mol) ÷ V (L)
Solving for the other two:
n = M × V and V (L) = n ÷ M
To go from grams to moles you need the molar mass, which you get from the molar mass calculator:
n (mol) = m (g) ÷ M (g/mol)
Worked example
You need 250 mL of a 0.25 mol/L solution and you are making it from a solid with a molar mass of 70 g/mol.
Volume in litres: 0.250 L. Moles required: 0.25 × 0.250 = 0.0625 mol. Mass: 0.0625 × 70 = 4.375 g.
The practical sequence matters as much as the arithmetic: dissolve in less than 250 mL of water, transfer to a 250 mL volumetric flask, rinse the beaker into the flask, top up to the mark, then invert to mix. Adding 250 mL of water to 4.375 g of solid gives a slightly less concentrated solution than intended, and the difference is the reason volumetric flasks exist.
Molarity, molality and normality are not the same
- Molarity (M) — mol per litre of solution. Changes with temperature, because volume does.
- Molality (m) — mol per kilogram of solvent. Does not change with temperature, which is why colligative properties (freezing point depression, boiling point rise) are defined in terms of it.
- Normality (N) — mol of reactive units per litre. 1 M HCl is 1 N HCl, but 1 M H₂SO₄ is 2 N because it supplies two protons.
Using molality where molarity was specified is a frequent exam and lab error, and the two diverge more the more concentrated the solution is.
Diluting a stock solution
Serial dilutions follow the same relationship as the dilution calculator, expressed in concentration rather than volume:
C₁V₁ = C₂V₂
To make 100 mL of 1 mmol/L from a 1 mol/L stock: V₁ = (0.001 × 100) ÷ 1 = 0.1 mL. That is not pipettable, which is exactly why serial dilution exists — a 1:100 step repeated twice gives 100 µL, which is. Writing the step factor down is the habit that prevents a factor-of-ten drift somewhere in the middle of a series.