Understanding Dilutions

A dilution is the process of reducing the concentration of a solution by adding more solvent. The dilution equation C₁V₁ = C₂V₂ expresses the relationship between the initial and final concentrations and volumes.

Variables:

• C₁: Initial concentration (before dilution)
• V₁: Initial volume (volume of stock solution)
• C₂: Final concentration (after dilution)
• V₂: Final volume (total volume after dilution)

Common Applications

• Laboratory preparations: Making working solutions from stock solutions
• Serial dilutions: Creating a series of solutions with decreasing concentrations
• Analytical chemistry: Preparing standards for calibration curves
• Biological assays: Diluting samples to optimal concentration ranges
• Quality control: Adjusting solution concentrations in manufacturing

Example Calculations

Example 1: You have 10 mL of 1.0 M HCl and want to dilute it to 0.1 M. What is the final volume?
Given: C₁ = 1.0 M, V₁ = 10 mL, C₂ = 0.1 M
Solution: V₂ = (C₁ × V₁) / C₂ = (1.0 M × 10 mL) / 0.1 M = 100 mL

Example 2: You need 250 mL of 0.5 M NaCl from a 2.0 M stock. How much stock solution do you need?
Given: C₁ = 2.0 M, C₂ = 0.5 M, V₂ = 250 mL
Solution: V₁ = (C₂ × V₂) / C₁ = (0.5 M × 250 mL) / 2.0 M = 62.5 mL

Important Notes

• Always add stock solution to solvent, never the reverse
• The dilution equation assumes ideal mixing (no volume changes upon mixing)
• For accurate work, use volumetric flasks and pipettes
• Consider temperature effects on volume measurements
• The final concentration is always lower than the initial concentration in a dilution