Concentration: wt%, g/L and molarity
Three ways to state how strong a solution is — mass fraction, mass concentration, molarity — and why crossing from one to another needs the solution density.
The idea
Three units state the strength of a solution, and the move that trips people is crossing between a mass-basis unit and a volume-basis one. Get the bridge right and the rest is arithmetic.
The three units
Weight percent is mass fraction times a hundred: the mass of solute over the mass of the whole solution. It carries no hidden assumption — it is the same number whether you have a drum or a tanker, at any temperature — which is why it is the unit of sale and storage.
Grams per litre is mass concentration: solute mass per litre of solution. It is the unit of a flowing circuit, because plants meter volume.
Molarity is moles of solute per litre of solution, the unit of stoichiometry, and to reach it you need the molar mass of the solute as well.
The density bridge
The bridge between wt% and g/L is the solution density, and it is not optional. One litre of a real process solution does not weigh one kilogram; a strong liquor is denser, a sub-zero brine denser still. The relation is g/L = wt% × ρ ÷ 100 with ρ in kg/m³, or equivalently mass concentration = mass fraction × density. Skip the density and substitute 1000 kg/m³ and you are quietly assuming pure water — fine for a dilute trace, wrong by tens of percent for a concentrated reagent. This is why the substance hubs on this site tabulate density against concentration and temperature: the bridge is a measured property, not a constant.
Molarity adds one more step and one more place to slip. Molarity = g/L ÷ molar mass. The slip is using the molar mass of the wrong species — the anhydrous salt where the solution was made up from a hydrate, or the acid where you meant the ion. For stoichiometry the species has to be the one in the reaction, so the molar mass has to match it.
A practical habit settles all of this: write the unit on every number and name the basis. "243 g/L NaOH" and "20 wt% NaOH" are both precise; "20% caustic" floating in a balance is an invitation to a mistake. When you see a percent, ask by mass or by volume; when you see a concentration, ask whether the density that produced it was the right one for the temperature. The calculator below does the mass-basis arithmetic and keeps the units consistent; the sodium-hydroxide hub supplies the density that lets you cross to g/L without guessing.
Diagram
Now run it
- Concentration calculator →Calculator
Enter a solute mass and a solution volume to get the mass concentration, and use it to check a wt%-to-g/L conversion.
- Sodium hydroxide hub →Substance hub
Read the caustic density at your concentration and temperature to supply the density bridge the conversion needs.
Worked thread
Convert a 20 wt% caustic solution to g/L using the committed density node, the conversion the concentration calculator backs.
- 01Density node: NaOH 20 wt% at 25 °C = 1217.1 kg/m³ (sodium-hydroxide.json grid).
- 02g/L = wt% × density ÷ 100 = 20 × 1217.1 ÷ 100
- 03g/L = 243.42 g/L NaOH
20 wt% caustic at 25 °C is 243.4 g/L NaOH — the density node, not 200 g/L, sets the answer.
sodium-hydroxide.json committed density grid (20 wt%, 25 °C node).
Sources
- •Perry, R.H. & Green, D.W. (eds.), Perry’s Chemical Engineers’ Handbook, 8th ed., 2008.
- •Laliberté, M. & Cooper, W.E., Model for Calculating the Density of Aqueous Electrolyte Solutions, J. Chem. Eng. Data, 2004.
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