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DrX Whiz Niraj
Pharmaceutical Calculations: Alligation & Isotonicity
Master the math of Pharmacy! Detailed notes on Weights & Measures, Alligation method, Proof spirit, and Isotonic solutions (Freezing point method).
Pharmaceutical calculations require strict adherence to specific systems of measurement. Historically, the Imperial System was used, but today, the Metric System is universally accepted in pharmacy.
Imperial System
An older system of weights and measures, mostly obsolete but sometimes seen in old prescriptions. It has two subsystems:
- Avoirdupois System: Used for bulk goods. The standard unit is the Pound (lb).
(1 lb = 16 ounces = 7000 grains). - Apothecaries System: Used strictly for compounding medicines. The standard unit of weight is the Grain (gr).
(1 scruple = 20 grains).
Metric System
The modern, decimal-based system used universally in science and pharmacy.
- Weight: Kilogram (kg), Gram (g), Milligram (mg).
- Volume: Liter (L), Milliliter (ml).
- Key Conversions: 1 kg = 1000 g | 1 g = 1000 mg | 1 L = 1000 ml.
Essential Inter-conversions (Learn these!):
- 1 fluid ounce (fl oz) ≈ 30 ml (Exactly 29.57 ml)
- 1 grain (gr) ≈ 65 mg (Exactly 64.8 mg)
- 1 Pound (lb) ≈ 454 grams
- 1 Teaspoonful ≈ 5 ml | 1 Tablespoonful ≈ 15 ml
- 1 Drop ≈ 0.06 ml
Percentage Solutions: There are three common ways to express percentage concentrations in pharmacy:
- Weight in Volume (% w/v): Grams of solute dissolved in 100 ml of solution (Most common for solid drugs in liquid).
- Volume in Volume (% v/v): Milliliters of liquid solute in 100 ml of solution.
- Weight in Weight (% w/w): Grams of solute in 100 g of mixture (Used for ointments and creams).
The Alligation Method
Alligation is an arithmetic method used to solve problems involving the mixing of solutions or solids of different strengths (concentrations) to obtain a mixture of a desired intermediate strength. It is divided into Alligation Medial (finding the average strength of a mix) and Alligation Alternate (finding the ratio of ingredients).
Proof spirit is a legal standard used historically to express the strength of alcohol. In India, Proof Spirit is defined as a mixture of alcohol and water that contains exactly 57.1% v/v of ethyl alcohol at 15.6°C.
- Over Proof (OP): Alcohol strength greater than 57.1% v/v.
- Under Proof (UP): Alcohol strength less than 57.1% v/v.
Note: If the answer is above 100, subtract 100 to get "Over Proof (OP)". If it is below 100, subtract it from 100 to get "Under Proof (UP)".
When a formulation (like eye drops or IV injections) is instilled into the body, it should ideally have the same osmotic pressure as blood plasma and tear fluid. Such a solution is called Isotonic.
Methods for Adjusting Isotonicity
Blood plasma and tear fluid freeze at -0.52°C. Any solution that freezes at -0.52°C is isotonic with blood plasma (e.g., 0.9% w/v NaCl).
1. Freezing Point Method
Used to calculate the amount of adjusting substance (like NaCl) needed to make a solution isotonic.
W = Weight (g) of NaCl per 100ml.
a = Freezing point depression of unadjusted drug sol (1%).
b = Freezing point depression of 1% NaCl (0.576°C).
2. Molecular Weight Method
Based on the principle that equimolar quantities of substances produce the same osmotic pressure.
W = Conc. required (g/100ml).
M = Gram Molecular Weight.
N = Number of ions yielded by the substance.
Clinical Danger: Hypotonic Injections
If a Hypotonic solution (like pure sterile water) is mistakenly injected intravenously, water rapidly rushes into the Red Blood Cells via osmosis. The RBCs swell and eventually burst (Hemolysis), which can be fatal for the patient. Always ensure IV fluids are Isotonic!