The Dilution Formula: C1V1 = C2V2

For a solution, amount of solute equals concentration multiplied by volume. In symbols, n = CV.

During dilution, no solute is created or destroyed. The amount before dilution equals the amount after dilution, so C1V1 = C2V2.

C1 is the initial or stock concentration. V1 is the volume of that stock solution used in the preparation.

C2 is the target final concentration. V2 is the final total volume after stock and solvent are mixed.

• C1: stock concentration
• V1: stock volume to measure
• C2: final concentration
• V2: final total volume

You can solve for any one unknown as long as the other three variables are known. Rearranging is just algebra: isolate the variable you want on one side.

To find V1, suppose C1 = 2.0 M, C2 = 0.10 M, and V2 = 250 mL. V1 = (0.10 × 250) / 2.0 = 12.5 mL.

To find C2, suppose C1 = 1.0 M, V1 = 5.0 mL, and V2 = 100 mL. C2 = (1.0 × 5.0) / 100 = 0.050 M.

To find V2, suppose C1 = 0.50 M, V1 = 20 mL, and C2 = 0.10 M. V2 = (0.50 × 20) / 0.10 = 100 mL.

To find C1, suppose C2 = 0.20 M, V2 = 500 mL, and V1 = 25 mL. C1 = (0.20 × 500) / 25 = 4.0 M.

C1 and C2 must use compatible concentration units, and V1 and V2 must use compatible volume units. You can use mL instead of L as long as both volume values use the same unit.

Mixing M with mg/mL requires molar mass. Mixing mL with µL requires conversion before substitution.

C1V1 = C2V2 assumes the solute amount is conserved and that volume is the relevant change. It may not describe reactive mixtures, evaporating solvents, or non-ideal highly concentrated solutions.

For concentrated acids or mixtures with heat generation and volume contraction, follow the lab protocol and safety data, not only the ideal dilution equation.