Calculations Involving Allegation, Proof Spirit, and Isotonic Solutions
Calculations Involving Allegation:
Allegation is used to calculate the proportions when mixing two solutions of different strengths to achieve a desired intermediate strength.
Formula for allegation:
- Parts of higher % strength = Desired strength – Lower strength
- Parts of lower % strength = Higher strength – Desired strength
- Total parts = Sum of parts from higher and lower strengths
Example 1: Mix 200 ml of 12%, 150 ml of 10%, and 100 ml of 5% alcohol. Find the resultant % strength.
- 200 ml × 12% = 2400
- 150 ml × 10% = 1500
- 100 ml × 5% = 500
- Total volume = 450 ml, total alcohol = 4400
- Resultant % strength = 4400 / 450 = 9.78%
Example 2: Prepare 450 ml of 70% alcohol using 95% and 50% alcohol.
- Parts of 95% = 70 – 50 = 20
- Parts of 50% = 95 – 70 = 25
- Total parts = 20 + 25 = 45
- Volume of 95% = (20/45) × 450 = 200 ml
- Volume of 50% = (25/45) × 450 = 250 ml
Calculations Involving Proof Spirit:
A proof spirit contains 57.1% v/v ethyl alcohol, equal to 100 proof. Strengths above this are ‘over proof’ (O.P.), below are ‘under proof’ (U.P.).
Calculation formulas:
- 1% alcohol = 1.753 volume proof spirit
- Over proof = (Percentage strength × 1.753) – 100 (if positive)
- Under proof = 100 – (Percentage strength × 1.753) (if negative)
Convert percentage strength to proof strength and vice versa using these formulas.
Calculations Involving Isotonic Solutions
1. Freezing Point Method:
The lachrymal secretion and blood plasma freeze at -0.52°C. Solutions freezing at this point are isotonic.
Equation:
Freezing point of tear secretion = Freezing point of drug + Freezing point of adjusting substance
Calculation:
- W = Weight in g of added substance per 100 ml
- a = Depression of freezing point by medicament (value × strength % w/v)
- b = Depression of freezing point caused by 1% of adjusting substance
2. Molecular Weight Method:
Isotonicity depends on the number of effective ions (n), molecular weight (m), and weight of substance (g):
Quantity of additive = (g / m) × n
Values of n:
- 1 for non-ionizable substances (e.g., dextrose)
- 1.5 for partially ionizable substances with 2 ions (e.g., silver nitrate)
- 2 for highly ionizable substances with 2 ions (e.g., sodium chloride)
- 2 for partially ionizable substances with 3 ions (e.g., sodium sulfate)
Normal saline (0.9% sodium chloride) is isotonic, with a tonicity factor of 0.03.
Alcohol Dilutions:
Diluted alcohols are made from 95% alcohol mixed with water. Dilution causes a temperature rise and volume contraction. Turbidity appears due to solubility differences.
Formula:
Quantity of stronger solution × concentration of alcohol = Quantity required × concentration required
Example 1:
What is the strength when 500 ml of 15% solution is diluted to 1500 ml?
Solution:
500 ml × 15% = 1500 ml × X%
X = (500 × 15) / 1500 = 5%
Example 2:
Calculate % strength of an ointment with 75 gm hydrocortisone in 2000 gm ointment.
X = (75/2000) × 100 = 3.75%
Detailed Notes:
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