Biology Dilution Calculator

The dilution formula C₁V₁ = C₂V₂ is based on the conservation of solute — when you dilute a solution, you're adding solvent (usually water) but the total amount of solute stays the same. **The Formula**: C₁V₁ = C₂V₂ Where: - C₁ = Initial (stock) concentration - V₁ = Initial volume needed - C₂ = Target (diluted) concentration - V₂ = Final (diluted) volume **Solving for Common Variables**: **Find V₁ (how much stock to use)**: V₁ = (C₂ × V₂) / C₁ **Find C₂ (resulting concentration)**: C₂ = (C₁ × V₁) / V₂ **Find V₂ (final volume)**: V₂ = (C₁ × V₁) / C₂ **Units Consistency**: The formula works with any consistent units: - Both concentrations in M (molarity) - Both concentrations in mg/mL - Both concentrations in g/L - Both volumes in mL - Both volumes in L The UNITS must match on both sides! **Example 1: Basic Dilution** Dilute 100 mM stock to 10 mM, need 50 mL final: C₁V₁ = C₂V₂ 100 × V₁ = 10 × 50 V₁ = 500/100 = 5 mL Take 5 mL of stock, add 45 mL of diluent, final 50 mL at 10 mM. **Example 2: Making Working Solution** You have 1 mg/mL stock. Need 200 μL at 50 μg/mL: 50 μg/mL × 200 μL = 1000 μg/mL × V₁ V₁ = 10,000 / 1000 = 10 μL Take 10 μL stock, add 190 μL diluent. **Serial Dilutions**: Multiple consecutive dilutions, each diluting by the same factor: **1:10 Serial Dilution**: - Tube 1: 100 μL sample + 900 μL diluent (10x dilution) - Tube 2: 100 μL from Tube 1 + 900 μL diluent (100x dilution) - Tube 3: 100 μL from Tube 2 + 900 μL diluent (1,000x dilution) - etc. Used for: - Standard curves (ELISA, PCR, flow cytometry) - Cell counting (viable cell counts) - Microbiology (bacterial concentrations) - Drug response curves **Final concentration** after n serial dilutions: C_final = C_initial × (dilution_factor)^(-n) **Example**: Stock 10 mM, do 1:5 dilution three times - 1st: 10/5 = 2 mM - 2nd: 2/5 = 0.4 mM - 3rd: 0.4/5 = 0.08 mM Or: 10 × (1/5)³ = 10/125 = 0.08 mM **Common Dilution Applications**: **PCR Primers**: - Stock: 100 μM - Working: 10 μM - Dilution: 1:10 (10 μL stock + 90 μL water) **Antibodies for ELISA/Western**: - Stock: 1 mg/mL - Working: 1-10 μg/mL - Often 1:1000 to 1:10,000 dilutions **Cell Culture Media**: - Serum: 10% typical dilution - Antibiotics: 100x to 1000x dilutions - Growth factors: Variable **DNA for Sequencing**: - Stock: Often 100 ng/μL - Working: 5-25 ng/μL typical - Dilution depends on protocol **Dilution Factor**: Dilution Factor = V_final / V_initial Or equivalently: C_initial / C_final Examples: - 1:10 dilution = 10x dilution (10 times less concentrated) - 1:100 dilution = 100x dilution - 1:2 dilution = 2x dilution **'1:X' Notation**: Common lab convention: '1:10' can mean two things: 1. **1 part sample + 9 parts diluent** (10 total parts) = 1/10 final 2. **1 part sample + 10 parts diluent** (11 total parts) = 1/11 final Most labs use the FIRST interpretation. Always clarify if unclear! **Preparing Diluted Solutions Correctly**: 1. **Calculate V₁** using formula 2. **Measure carefully** (pipet vs graduated cylinder) 3. **Add stock to partial volume** of diluent 4. **Mix thoroughly** (vortex or inversion) 5. **Bring to final volume** (volumetric flask for precision) 6. **Label clearly**: concentration, date, initials **Pipetting Considerations**: - **P10**: 1-10 μL (most accurate for small volumes) - **P20**: 2-20 μL - **P200**: 20-200 μL - **P1000**: 200-1000 μL - **Serological pipette**: For larger volumes - **Volumetric flask**: Most accurate for final volumes **Accuracy vs Precision**: - **Accurate**: Close to true value - **Precise**: Reproducible - Ideal: Both accurate and precise Good labs calibrate pipettes regularly and use appropriate tools for each volume range. **Common Lab Concentrations**: | Component | Stock | Working | |-----------|-------|---------| | PBS | 10x | 1x | | Tris buffer | 1 M | 50-100 mM | | EDTA | 500 mM | 5-25 mM | | SDS | 20% | 0.1-1% | | Glycerol | 100% | 10-50% | | DMSO | 100% | 0.1-10% | **Dilutions in Cell Culture**: For seeding cells at specific density: Example: Need 2 × 10⁵ cells/mL in 10 mL 1. Count cells (get current concentration, e.g., 5 × 10⁶/mL) 2. Calculate: 2 × 10⁵ × 10 = 2 × 10⁶ cells needed 3. Volume of cell suspension: 2 × 10⁶ / 5 × 10⁶ = 0.4 mL 4. Add 0.4 mL cells + 9.6 mL media **Common Mistakes**: 1. **Wrong order of operations**: Calculate V₁ first, then add diluent 2. **Unit mismatches**: Convert to same units 3. **Forgetting to mix**: Always mix thoroughly after dilution 4. **Expiration**: Diluted solutions may have shorter shelf life 5. **Contamination**: Use sterile technique 6. **Pipetting errors**: Use appropriate pipette range 7. **Stock concentration drift**: Verify stock concentration periodically **Dilution Errors Propagate**: Small errors in each step of a serial dilution multiply: - 1% error per step × 5 steps = ~5% error - 5% error per step × 5 steps = ~27% error For standard curves, accuracy matters more than for routine buffer prep.