Alligation is a rapid arithmetic method used to solve problems related to mixtures of ingredients with different concentrations or strengths to form the desired concentrations or strengths.
Application of Alligation Method in Pharmaceutics
- The amount of diluent that must be added to a given amount of higher strength formula to make a desired lower strength.
- The amounts of active ingredient that must be added to a given amount of lower strength formula to make a higher strength.
- The amount of higher and lower strength active ingredient that must be combined to make a desired strength.
There are two types of alligation method:
Alligation medial: Alligation medial is used to find the quantity of a mixture given the quantities of its ingredients. For example, if you have 200 mL of a 5% solution and 400 mL of a 10% solution, what is the concentration of the final mixture?
Alligation alternate: Alligation alternate is used to find the amount of each ingredient needed to make a mixture of a given quantity and concentration or strength. For example, if you want to prepare 1000 mL of a 10% solution using a 5% solution and a 20% solution, how much of each solution do you need?
Alligation Formula for Pharmaceutical Calculation
Q1 / Q2 = (Cm - C2) / (C1 – Cm)
Where Q is quantity, C is concentration or strength, 1 and 2 are the ingredients, and m is the mixture.
For example, if you want to prepare 100 mL of a 15% solution using a 10% solution and a 20% solution, you can use this formula to find Q1 and Q2:
Q1 / Q2 = (15 - 10) / (20 - 15);
Q1 / Q2 =5/5
Q1 / Q2 =1
This means that Q1 and Q2 are equal.
We also know that,
Qm = Q1 + Q2
So, Q1 = Qm/2
Q1 =100/2
Q1=50
and,
Q2 = Qm/2
Q2 = 100/2
Q2 = 50
Therefore, you need 50 mL of each solution to make 100 mL of a 15% solution.
Example-1:
Example-2:
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