Dilution Calculator

C₁V₁ = C₂V₂ because the solute is conserved — and always add acid to water, never the reverse.

Stock to take62.5 mL0.25 × 500 ÷ 2

Diluent to add437.5 mLto reach 500 mL total. ADD THE STOCK TO THE DILUENT, not the other way round — especially with concentrated acid, where the heat of mixing can boil the first drops

Final volume500 mL

Dilution factor8×1 in 8 — one part stock to 7 parts diluent

The solute does not changethat IS the equationC₁V₁ and C₂V₂ are both the amount of solute, which is the same before and after. Adding solvent changes the volume and nothing else

Units cancelany concentration, any volumethe equation works in molarity and millilitres, or percent and litres, so long as each side is consistent

The formula

C₁V₁ = C₂V₂ — the moles of solute do not change

The solute is conserved

C₁V₁ is the amount of solute before and C₂V₂ is the amount after. Adding solvent does not create or destroy any, so the two are equal.

That is the entire derivation, and it is why the equation works with any units at all provided each side uses the same ones.

Acid into water, never water into acid

Diluting concentrated acid releases a great deal of heat.

Poured into water, the heat spreads through the bulk. Water poured into acid heats the first few drops enough to boil and spit concentrated acid out of the vessel. The order is not a convention.

Two steps beat one big one

A hundredfold dilution in a single step needs an accurately measured fraction of a millilitre.

Two tenfold steps use comfortable volumes at both stages, and the errors compound far less than the single measurement error would.

Standard atomic weights are averages

The masses used here are weighted means over the isotopes found naturally on Earth, which is why chlorine is 35.45 rather than a whole number.

For work with a specific isotope, or with material from an unusual source, the isotopic mass is the right figure and it is not this one.