Dilution Calculator

Dilution: C₁·V₁ = C₂·V₂

Add solvent to a solution and the amount of solute stays the same; what shifts is the volume and the concentration. That fact is the whole basis for the dilution equation: C₁·V₁ = C₂·V₂, with (C₁, V₁) being the starting concentration and volume and (C₂, V₂) the ones you end up with. Say you take 50 mL of 1 M HCl and bring it up to 250 mL. Then C₂ = 1·50/250 = 0.2 M. Two things to watch: the unit of C has to be the same on both sides (mol/L, g/L, %, ppm), and V is the total final volume, not just the solvent you poured in. The usual concentration units are molar (mol/L), molal (mol/kg), %m/m, %m/V, %V/V, and ppm (mg/kg or mg/L for dilute aqueous solutions). Safety: diluting an acid, you add the acid to the water and never the other way around, since the reaction releases heat and a top layer of water can boil and spit acid back at you.

Applications

It turns up all over the place: analytical chemistry, clinical labs preparing reagents and calibration standards, water treatment (in chlorination, ANVISA Ordinance 888/2021 caps residual chlorine at 5 mg/L), agriculture when you mix fertilizers and pesticides to the recommended dose, brewing and winemaking, and the food industry's acid solutions for cleaning-in-place.

FAQ

Does the formula work for any unit? Yes, provided you keep the same unit on both sides. C in mol/L is fine, and V can be mL or L as long as it's the same in both spots. Convert first, then plug in.

What about successive dilutions? The factors multiply, so a 1:10 followed by a 1:100 lands you at 1:1000. You see this a lot in microbiology and analytical chemistry.

Why never pour water into concentrated acid? Hydration gives off a lot of heat. When the water sits on top, it can boil at that spot and spatter acid out of the container. Add the acid slowly into the water instead, stirring as you go.