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Alligation Alternate is a vital method used in pharmacy math to calculate the proportions of different concentrations or strengths when preparing mixtures or solutions. Mastering the formulas involved can significantly simplify complex calculations, ensuring accuracy in pharmaceutical preparations.
Understanding Alligation Alternate
Alligation Alternate is a technique used to find the ratio in which two or more solutions of different strengths should be mixed to produce a solution of desired strength. It is especially useful when dealing with mixtures involving medicinal solutions, chemicals, or compounds of varying concentrations.
Essential Formulas
1. Calculation of Parts
To determine the parts of each solution to be mixed, use the following formulas:
- Parts of Solution A = Difference between the desired strength and the strength of Solution B
- Parts of Solution B = Difference between the strength of Solution A and the desired strength
2. Total Parts of Mixture
The total parts of the mixture are the sum of the parts of individual solutions:
Total Parts = Parts of Solution A + Parts of Solution B
3. Concentration of Mixture
The concentration of the final mixture is calculated as:
Concentration of Mixture = (Parts of Solution A × Concentration of A + Parts of Solution B × Concentration of B) / Total Parts
Example Calculation
Suppose you need to prepare 100 mL of a 20% solution by mixing a 30% solution and a 10% solution. How much of each solution should you use?
Step 1: Identify known values:
Desired concentration = 20%
Solution A (higher strength) = 30%
Solution B (lower strength) = 10%
Total volume = 100 mL
Step 2: Calculate parts:
Parts of Solution A = Difference between desired and B’s concentration = 20% – 10% = 10
Parts of Solution B = Difference between A’s and desired concentration = 30% – 20% = 10
Step 3: Total parts = 10 + 10 = 20
Step 4: Calculate volume of each solution:
Volume of Solution A = (Parts of A / Total Parts) × Total Volume = (10 / 20) × 100 mL = 50 mL
Volume of Solution B = (Parts of B / Total Parts) × Total Volume = (10 / 20) × 100 mL = 50 mL
Thus, mix 50 mL of 30% solution with 50 mL of 10% solution to obtain 100 mL of 20% solution.
Summary
The alligation alternate method simplifies the process of mixing solutions of different strengths. Remember these key formulas:
- Parts of Solution A = Difference between desired and B’s concentration
- Parts of Solution B = Difference between A’s and desired concentration
- Total Parts = Sum of individual parts
- Volume of each solution = (Part of solution / Total parts) × Total volume
Applying these formulas ensures precise and efficient preparation of pharmaceutical mixtures, essential for maintaining drug efficacy and safety.