C₁V₁ = C₂V₂
C₁
Initial concentration
V₁
Initial volume
C₂
Final concentration
V₂
Final volume
C₂ = (C₁ × V₁) / V₂
C₁ = (C₂ × V₂) / V₁
V₂ = (C₁ × V₁) / C₂
V₁ = (C₂ × V₂) / C₁
Lab Safety Disclaimer
Results assume ideal mixing and accurate laboratory measurements. Always verify calculations and follow proper laboratory safety protocols when handling chemicals.
Dilution is the process of decreasing the concentration of a solute in a solution, usually by adding more solvent. In chemistry and biology laboratories, dilution is a fundamental technique used to prepare solutions of desired concentrations from stock solutions. The process involves adding a measured amount of solvent (typically water) to a known volume of a more concentrated solution.
The key principle behind dilution is that the total amount of solute remains constant before and after dilution. This is expressed mathematically by the dilution equation: C₁V₁ = C₂V₂, where C represents concentration and V represents volume. The subscripts 1 and 2 refer to the initial (concentrated) and final (diluted) states, respectively.
The dilution equation C₁V₁ = C₂V₂ is derived from the conservation of mass principle. The product of concentration and volume gives the total amount of solute (in moles if concentration is in molarity). Since no solute is added or removed during dilution, this quantity must remain constant.
Key Variables
- C₁ (Initial Concentration): The concentration of the stock or starting solution
- V₁ (Initial Volume): The volume of stock solution used
- C₂ (Final Concentration): The desired concentration after dilution
- V₂ (Final Volume): The total volume of the diluted solution
Important Note
The amount of solvent to add equals V₂ - V₁, not V₂. A common mistake is to add V₂ amount of solvent instead of adding enough solvent to bring the total volume to V₂.
Dilution calculations are essential in numerous scientific and everyday applications:
Laboratory Research
Preparing reagents, buffer solutions, and media at specific concentrations for experiments.
Medical & Clinical
Preparing medications, IV solutions, and diagnostic reagents at precise concentrations.
Industrial Applications
Manufacturing cleaning products, food processing, and water treatment facilities.
Environmental Testing
Preparing standard solutions for calibration and quality control in environmental analysis.
1. Use Appropriate Glassware
Use volumetric flasks for final volume measurements and graduated pipettes or micropipettes for transferring precise volumes of stock solution.
2. Add Solvent to Solute
When diluting concentrated acids, always add acid to water, never water to acid. This prevents dangerous exothermic reactions.
3. Mix Thoroughly
Ensure complete mixing after adding solvent to achieve a uniform concentration throughout the solution.
4. Account for Temperature
Volume measurements should be made at a consistent temperature, as liquids expand and contract with temperature changes.