How to Calculate Dilution (C1V1 = C2V2)
Learn how to use the dilution equation C1V1 = C2V2 to calculate new concentrations or volumes when diluting solutions. Includes worked examples and practical lab tips.
What Is Dilution?
Dilution is the process of reducing the concentration of a solute in a solution by adding more solvent, usually water. The amount of solute (moles) remains constant during dilution — only the volume and therefore the concentration change. Dilution is one of the most common operations in a chemistry laboratory, used to prepare working solutions from concentrated stock solutions.
The Dilution Equation: C1V1 = C2V2
The dilution equation states that the product of the initial concentration (C1) and initial volume (V1) equals the product of the final concentration (C2) and final volume (V2): C1V1 = C2V2. This works because both sides represent the number of moles of solute: moles = concentration x volume. The equation can be rearranged to solve for any one of the four variables as long as the other three are known.
Step-by-Step Example
You have a 6.0 M HCl stock solution and need to prepare 250 mL of 0.50 M HCl. Rearrange for V1: V1 = C2V2 / C1 = (0.50 M x 250 mL) / 6.0 M = 20.8 mL. Measure 20.8 mL of the 6.0 M HCl stock, add it to a 250 mL volumetric flask containing some water, then add water to the 250 mL mark. The result is 250 mL of 0.50 M HCl.
Units Must Be Consistent
The volumes V1 and V2 must be in the same units (both mL or both L), and the concentrations C1 and C2 must be in the same units (both M, both mM, etc.). If they are consistent, you do not need to convert to liters — the units cancel in the ratio. However, if you need to calculate moles separately for stoichiometry, always convert to liters using 1 L = 1000 mL.
Serial Dilutions
A serial dilution involves performing multiple sequential dilutions, each using the result of the previous step. If a 1:10 dilution is performed three times, the overall dilution factor is 10 x 10 x 10 = 1000, and the final concentration is C1 / 1000. Serial dilutions are used in microbiology to count bacterial colonies and in analytical chemistry to create calibration curves spanning several orders of magnitude.
Lab Safety Tip: Acid Dilution
When diluting concentrated acids — especially sulfuric acid (H2SO4) — always add acid to water, never water to acid. Adding water to concentrated acid can cause a violent exothermic reaction and spattering. The mnemonic "Do as you oughter, add acid to water" is a useful reminder. Use a large beaker, add ice if necessary, and stir constantly to dissipate heat during the dilution.
Applications Beyond the Lab
The C1V1 = C2V2 equation applies anywhere a concentration is changed by adding diluent: diluting bleach for cleaning solutions, adjusting fertilizer concentrations for agriculture, and preparing intravenous drug solutions in medicine. Pharmacists use this equation when diluting stock medications to the prescribed dosage strength. The simplicity of the formula makes it universally applicable across many scientific and practical fields.
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