C1V1 = C2V2: Complete Reference

C1V1 = C2V2 is the standard equation for ordinary dilution. It says the solute amount before dilution equals the solute amount after dilution.

Pick the rearrangement that isolates your unknown. Substitute values only after units are consistent.

Find V1: 2.0 M stock to make 250 mL of 0.10 M gives V1 = 12.5 mL.

Find C2: 5.0 mL of 1.0 M diluted to 100 mL gives C2 = 0.050 M.

Find V2: 20 mL of 0.50 M diluted to 0.10 M gives V2 = 100 mL.

Find C1: 25 mL stock makes 500 mL of 0.20 M, so C1 = 4.0 M.

Find solvent: if V1 = 12.5 mL and V2 = 250 mL, solvent to add = 237.5 mL.

Find factor: 1.0 M to 0.020 M gives DF = 50, written as 1:50.

Molar units convert by powers of 1000. Mass concentration requires molar mass when converting to molarity.

• 1 M = 1000 mM
• 1 mM = 1000 µM
• 1 µM = 1000 nM
• 1 mg/mL = 1 g/L
• 1 ppm is approximately 1 mg/L in dilute water solutions

Dilution factor connects concentration and volume. For normal dilution, DF = C1/C2 = V2/V1.

A larger dilution factor means a weaker final solution. DF = 50 means the final concentration is 1/50 of the original.

After solving, substitute your answer back into C1V1 = C2V2. Both sides should match after unit conversion.

Also check whether the result makes physical sense. A dilution should have lower concentration and larger final volume.