Alligation: Pharmacy, Mixing
Alligation medial: C_final = Σ(C_i×V_i)/ΣV_i. Alligation alternate: parts of each = |target − C_other|. Used in pharmacy compounding, IV prep, and concentration blending.
Why This Chemistry Calculation Matters
Why: Alligation determines mixing proportions for target concentration. Essential for pharmacy, IV preparation, and formulation.
How: Medial: enter concentrations and volumes. Alternate: enter two concentrations and target. Parts = |target − C_other|.
- ●Medial: weighted average of concentrations.
- ●Alternate: proportion for two-component mix.
- ●Pharmacy and IV standard method.
Sample Examples
💊 Pharmacy Compounding
Mix 10% and 50% solutions to make 25% solution
🩺 IV Solution Preparation
Prepare 0.9% saline from 5% and 0.45% solutions
🍷 Alcohol Dilution
Mix 40% and 10% alcohol to achieve 25%
⚗️ Three Solution Mix
Calculate final concentration from three solutions
🏭 Industrial Chemical Mixing
Blend acids of different concentrations
💉 Pharmaceutical Formulation
Prepare drug solution at specific concentration
⚖️ Weight-Based Mixing
Mix solutions by weight instead of volume
🧪 Lab Buffer Preparation
Prepare buffer from stock solutions
Alligation Calculator
Solutions
Solution 1
Solution 2
For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
Alligation medial: C_final = Σ(C_i×V_i)/ΣV_i.
— Pharmacy
Alternate: parts A = |target − C_B|; parts B = |target − C_A|.
— Mixing
Used for IV solutions, dilutions, compounding.
— Clinical
Ratio of parts gives mixing proportion.
— Formulation
What is Alligation?
Alligation is a mathematical method used to calculate the proportions in which solutions of different concentrations must be mixed to obtain a desired concentration, or to determine the final concentration when mixing known quantities of solutions. It's widely used in pharmacy, chemistry, and industrial applications.
Two Main Methods
Alligation Medial
Calculates the final concentration when mixing known quantities of solutions with different concentrations.
Alligation Alternate
Determines the proportions needed to achieve a target concentration from two or more stock solutions.
How Does Alligation Work?
Alligation methods use simple arithmetic to solve mixing problems. The key principle is conservation of mass - the total amount of solute before mixing equals the total amount after mixing.
🔬 Alligation Medial Derivation
Principle
Total solute = C₁V₁ + C₂V₂ + ... + CₙVₙ
Total volume = V₁ + V₂ + ... + Vₙ
Cfinal = Total solute / Total volume
Example
Mix 100 mL of 10% solution + 200 mL of 30% solution
Total solute = (10 × 100) + (30 × 200) = 1000 + 6000 = 7000
Total volume = 100 + 200 = 300 mL
Final concentration = 7000 / 300 = 23.33%
📊 Alligation Alternate Method
The Alligation Cross
Ratio = |Ctarget - C₂| : |Ctarget - C₁|
Example
Target: 25% from 10% and 50% solutions
Difference 1: |25 - 50| = 25 parts of 10%
Difference 2: |25 - 10| = 15 parts of 50%
Ratio: 25:15 = 5:3 (10%:50%)
For 100 mL total: 62.5 mL of 10% + 37.5 mL of 50%
When to Use Alligation
Alligation is essential for anyone working with solution preparation, especially in pharmacy, clinical settings, and chemical laboratories.
Pharmacy Compounding
Prepare custom medication concentrations from stock solutions.
- Dilute concentrated drugs
- Mix different strengths
- Prepare patient-specific doses
IV Solutions
Prepare intravenous solutions at specific concentrations for patient care.
- Saline solutions
- Medication infusions
- Electrolyte solutions
Industrial Mixing
Blend chemicals, acids, or solutions for manufacturing processes.
- Chemical production
- Quality control
- Batch preparation
Formulas and Key Points
Alligation Medial Formula
Where Cᵢ is concentration and Vᵢ is volume (or weight) of solution i.
Alligation Alternate Rule
Parts of C₂ = |Ctarget - C₁|
The target concentration must lie between the two stock concentrations.
⚠️ Important Considerations
- • Volume vs. Weight: Use consistent units (volume or weight) throughout calculations
- • Concentration Units: Ensure all concentrations use the same units (% w/v, % w/w, M, mg/mL, etc.)
- • Temperature Effects: Volume mixing may not be perfectly additive due to density changes
- • Accuracy: For critical applications (pharmacy, medical), verify calculations and use precise measurements
- • Multiple Solutions: For 3+ solutions, alligation alternate becomes more complex and may require iterative methods
Practical Examples
Example 1: Pharmacy Compounding
Problem:
- Need 25% solution
- Have 10% and 50% stock solutions
- Want 100 mL total
Solution:
Difference 1: |25 - 50| = 25 parts
Difference 2: |25 - 10| = 15 parts
Total parts: 40
10%: (25/40) × 100 = 62.5 mL
50%: (15/40) × 100 = 37.5 mL
Example 2: IV Saline Preparation
Problem:
- Need 0.9% NaCl
- Have 5% and 0.45% solutions
- Want 500 mL
Solution:
Difference 1: |0.9 - 5| = 4.1 parts
Difference 2: |0.9 - 0.45| = 0.45 parts
Total parts: 4.55
5%: (0.45/4.55) × 500 = 49.5 mL
0.45%: (4.1/4.55) × 500 = 450.5 mL
Example 3: Alligation Medial
Problem:
- Mix 200 mL of 15% solution
- Mix 300 mL of 30% solution
- Mix 500 mL of 45% solution
Solution:
Total solute = (15×200) + (30×300) + (45×500)
= 3000 + 9000 + 22500 = 34500
Total volume = 200 + 300 + 500 = 1000 mL
Final = 34500 / 1000 = 34.5%
📚 Official Data Sources
⚠️ Disclaimer: Alligation results are for educational and compounding reference. For clinical or pharmaceutical use follow USP and institutional guidelines.
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