Free tool
Fill in any three of stock concentration, stock volume, final concentration and final volume. Leave the fourth blank and the calculator solves for it, shows the working and tells you how much solvent to add.
Built for General Chemistry IUnits can differ between boxes; the calculator converts everything to M and L first.
Fill in three values and leave one blank.
Dilution problems are quick once the setup is automatic. Encodr keeps formulas like C1V1 = C2V2 on a spaced-repetition schedule so they stick.
Get started freeAdding solvent changes the volume but not the number of moles of solute. Moles = concentration × volume,
so the moles before equal the moles after: C1 × V1 = C2 × V2. C1 and V1 describe the
stock you measure out; C2 and V2 describe the solution you end up with. Any concentration and volume units work
as long as both sides use the same ones.
Worked example: how much 12.0 M HCl do you need to make 500. mL of 0.500 M HCl? V1 = C2V2 ÷ C1 = (0.500 M × 500. mL) ÷ 12.0 M = 20.8 mL of stock, diluted to a final volume of 500. mL (about 479 mL of water). Safety note from the lab: add acid to water, not water to acid.
The "solvent to add" figure is V2 − V1, the usual intro-course approximation. In practice you add solvent up to the V2 mark on a volumetric flask. C1V1 = C2V2 only works for dilution, not for reactions like a titration, where the mole ratio from the balanced equation matters. Full walkthrough: C1V1 = C2V2 explained. Practice set: the free General Chemistry I flashcards.
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