1. What is the C₁V₁ = C₂V₂ Formula?
In chemistry, biochemistry, and biology laboratories, the C₁V₁ = C₂V₂ formula (also written as M₁V₁ = M₂V₂ when working in molar units) represents the mathematical statement of the Law of Conservation of Mass.
When a concentrated stock solution is diluted by adding pure solvent (such as deionized water or buffer), the total quantity of solute molecules remains strictly constant:
Solute Amount = C₁ × V₁ = C₂ × V₂
Because no additional solute is introduced, increasing the volume from V₁ to V₂ inevitably reduces the concentration from C₁ down to C₂ in direct linear proportion.
2. How to Perform a Serial Dilution?
A serial dilution is a stepwise sequence of geometric dilutions where the diluted solution from one tube serves as the stock for the subsequent tube. Serial dilutions are indispensable when preparing standard calibration curves for spectrophotometry, qPCR, or ELISA assays.
Common serial dilution formats:
- 1:10 Dilution Series: Mix 1 part sample with 9 parts diluent (10×, 100×, 1000×, 10,000×).
- 1:2 (Two-fold) Series: Mix 1 part sample with 1 part diluent (2×, 4×, 8×, 16×, 32×).
- 1:5 Series: Mix 1 part sample with 4 parts diluent (5×, 25×, 125×, 625×).
3. Real-World Laboratory Dilution Examples
Consider common bench applications encountered daily in molecular biology:
- Diluting 1M NaCl Stock to 50mM (in 500 mL):
V₁ = (C₂ × V₂) / C₁ = (0.05 M × 500 mL) / 1 M = 25 mL of stock NaCl + 475 mL of water. - Preparing 1× PBS from 10× Concentrated Stock (1 Liter):
V₁ = (1× × 1000 mL) / 10× = 100 mL of 10× PBS + 900 mL of water (1:10 dilution). - Diluting 20% SDS Detergent to 0.1% (in 100 mL):
V₁ = (0.1% × 100 mL) / 20% = 0.5 mL (500 µL) of SDS stock + 99.5 mL of water.
4. Pipetting Accuracy & Minimizing Solvent Errors
When preparing dilutions at the laboratory bench, pipetting volume accuracy is the single largest source of experimental variability.
Essential laboratory best practices:
- Avoid Pipetting < 2 µL: Pipetting volumes below 2 µL drastically increases coefficient of variation (CV%). If V₁ is calculated under 2 µL, perform a two-step intermediate dilution.
- Pre-wet Pipette Tips: Aspirate and dispense solvent once before measuring to equilibrate tip vapor pressure.
- Solvent Displacement (q.s.): For high solute volumes or viscous liquids, add stock to ~80% volume and bring up to final volume mark.
