What is solution concentration?
A solution is a homogeneous mixture: the solute (salt) dissolved molecule-by-molecule in the solvent (water). Concentration answers the only question that then matters chemically — how crowded is it? — because reactions happen particle-to-particle, and a crowded solution reacts at a different pace than a sparse one. Every concentration unit ever invented is just a fraction: something-per-something. Read the two somethings carefully and no unit will ever surprise you.
The one rule to remember: check the numerator and the denominator. Moles-per-liter-of-solution (M) and moles-per-kilogram-of-solvent (m) differ by more than a letter — the denominators measure different things.
Molarity, molality, normality: three denominators
Molarity (M) is moles of solute per liter of solution — the lab workhorse, because pipettes and volumetric flasks measure volume. Its weakness: volume expands with temperature, so 1.0000 M at 20 °C is not 1.0000 M at 40 °C. Molality (m) divides by kilograms of solvent, which heat does not change — which is why colligative work (freezing-point depression, boiling-point elevation) insists on it. Normality (N) counts equivalents per liter instead of moles: one mole of H2SO4 delivers two acid equivalents, so 0.5 M H2SO4 is 1 N — the panel's equivalents field (H2SO4 = 2, HCl = 1, H3PO4 = 3) is exactly that conversion. To prepare 1 L of 0.1 M NaCl: weigh 5.844 g, dissolve in less than a liter, then bring to exactly 1.000 L in a volumetric flask — final volume, not water added.
Dilution: the moles you start with are the moles you keep
Diluting adds solvent, never solute, so moles are conserved: C1V1 = C2V2 is nothing but “moles before = moles after” with the volume divided out. The Dilution panel's sample: 10 M stock, 50 mL taken, diluted to 250 mL — the five-fold volume increase cuts the concentration exactly five-fold, C2 = 2.0000 M with a 5.0× dilution factor. The same bookkeeping, run in reverse, tells you how much stock to measure for a target concentration — the daily bread of buffer preparation.
Percent and PPM: concentration for everyday speech
Percent solutions are ratios per hundred, in three flavors that must never be confused: w/v (grams of solid per 100 mL of solution — the default in biology labs), v/v (mL per 100 mL, used for liquid-in-liquid like ethanol), and w/w (grams per 100 g, immune to volume contraction). The percent panel's sample: 5 g dissolved to 100 mL is 5% (w/v) = 50 g/L. For very dilute aqueous solutions, PPM takes over — defined for water as mg/L because a liter of dilute solution weighs essentially a kilogram. The PPM panel converts one sample everywhere: 1 ppm = 1000 ppb = 106 ppt = 0.0001% = 1 mg/L.
The molar-mass bridge
Concentrations are stated in moles but bottles and balances speak grams, and the translation between them is the molar mass. NaCl weighs 58.440 g/mol (the panel computes it from the same atomic masses as the Molar Mass page), so dissolving 58.440 g and diluting to exactly 1 L gives 1.0000 M — that is the entire recipe for a standard solution. The Molarity panel accepts either a formula (mass computed from the built-in parser) or a plain mass, then reports moles, molarity, normality, or ppm side by side.
Common misconceptions
- M and m are the same unit. Liter-of-solution versus kilogram-of-solvent: for dilute water at room temperature they nearly coincide, which is precisely why the panel labels its molality output as an approximation.
- PPM means the same thing everywhere. mg/L is a water-specific shortcut. In gas mixtures and solids, ppm is strictly a mass/mass (or mole/mole) ratio.
- Diluting changes the amount of solute. Only the concentration. The sample's 50 mL of 10 M stock and its 250 mL of 2 M product contain the identical 0.50 mol.
- Volumes are additive. 50 mL of ethanol + 50 mL of water yield about 97 mL — mixing contracts. This is why v/v percentages specify “dilute to volume” rather than “add”.
Related tools: Molar Mass (the grams↔moles translator), Equation Balancer (stoichiometry on these moles), and Acid-Base (where concentrations become pH).
