What molarity actually counts
Molarity (M) is moles of solute per litre of total solution — not per litre of solvent added. That distinction matters: when you dissolve something in water, the solute itself takes up some volume, so "1 mole in 1 litre of water" and "1 mole made up to 1 litre total" are two different concentrations. Every proper molarity calculation, and every volumetric flask marked to a fill line, is built around the second definition.
From molecular weight to a finished solution
Preparing a solution of known molarity comes down to three connected formulas:
Moles (n) = Molarity (M) × Volume (L)
Mass (g) = Moles (n) × Molecular Weight (g/mol)
Worked example: to make 0.5 L of a 1 M sodium chloride (NaCl) solution, first find moles needed: 1 mol/L × 0.5 L = 0.5 mol. NaCl has a molecular weight of about 58.44 g/mol, so the mass required is 0.5 mol × 58.44 g/mol = 29.22 g.
In practice: weigh out 29.22 g of NaCl, dissolve it in somewhat less than 500 mL of water, then add water up to the 500 mL mark in a volumetric flask — not the other way around, since dissolving the solid changes the total volume slightly.
If you don't already know a compound's molecular weight, the Molecular Weight Calculator works it out from a chemical formula.
Diluting a stock solution: M1V1 = M2V2
Diluting doesn't change how many moles of solute are present — it only spreads the same moles across more volume, which is exactly what M1V1 = M2V2 captures: initial molarity times initial volume equals final molarity times final volume.
Worked example: you have a 2 M stock solution and need 500 mL of a 0.5 M working solution. Rearranging for the unknown: V1 = (M2 × V2) ÷ M1 = (0.5 × 500) ÷ 2 = 125 mL. Measure out 125 mL of the stock solution, then add solvent until the total reaches 500 mL — meaning 375 mL of solvent gets added.
The units for both volumes need to match on either side of the equation, and it's the total final volume that matters, not just how much solvent gets added — a detail that trips people up if they add the full "missing" volume of solvent to a solution that already has some volume from the stock solution itself.
When molarity isn't the right unit
Because molarity is defined per litre of solution, it technically shifts a little with temperature — liquids expand slightly as they warm, so the same number of moles occupies more volume, nudging molarity down. For most lab work at room temperature that's negligible, but for precise physical chemistry, molality (moles per kilogram of solvent, unaffected by temperature) is the more stable choice. Outside the lab, everyday concentration is often expressed as a simple percentage by weight or volume instead, sidestepping moles entirely.