Calculations Involving Percentage Solutions
The concentration of a solution is often expressed as the percentage of solute in the total amount of solution. Extremely dilute solutions may use parts per million (ppm). Concentration can be based on weight or volume.
A percentage solution means weight or volume of solute per 100 ml or 100 g of solution. Percentage means rate per hundred; for example, 50% means 50 parts in 100 parts or 0.5.
Types of Percentage Solutions
- Percentage weight by volume (w/v): grams of solute per 100 ml of solution.
- Percentage volume by volume (v/v): milliliters of solute per 100 ml of solution.
- Percentage weight by weight (w/w): grams of solute per 100 grams of solution.
1. Percentage Weight by Volume (w/v)
Calculation formula:
Concentration (%) = (Quantity or volume of solute / Quantity or volume of solution) × 100
Examples:
- How many grams of dextrose are required to prepare 4000 ml of 5% solution?
Solution: X = (5 × 4000) / 100 = 200 g - What is the % (w/v) of urea if 80 ml contains 12 g?
Solution: X = (12 × 100) / 80 = 15% - How many ml of 3% solution can be made from 27 g ephedrine sulfate?
Solution: X = (27 × 100) / 3 = 900 ml
2. Percentage Volume by Volume (v/v)
Calculation formula:
Concentration (%) = (Volume of solute / Volume of solution) × 100
Examples:
- How many ml of liquefied phenol should be used for 2.5% in 240 ml calamine lotion?
Solution: X = (2.5 × 240) / 100 = 60 ml - 4 ml liquid phenol used in 250 ml lotion; find % (v/v)
Solution: X = (4 × 100) / 250 = 1.6% - % strength (v/v) of 800 g liquid (specific gravity 0.8) in 4000 ml water?
Volume of solute = 800 / 0.8 = 1000 ml
Concentration = (1000 × 100) / 4000 = 25% v/v
3. Percentage Weight by Weight (w/w)
Calculation formula:
Concentration (%) = (Weight of solute / Weight of preparation) × 100
Examples:
- How many grams of phenol for 240 g of 5% (w/w) solution?
Solution: X = (5 × 240) / 100 = 12 g - Weight of drug required for 120 ml 20% (w/w) solution with specific gravity 1.15?
Weight of solution = 120 × 1.15 = 138 g
X = (20 × 138) / 100 = 27.6 g - Grams of drug to dissolve in 240 ml water to prepare 4% (w/w) solution?
Water weight = 240 g (assuming 1 ml = 1 g)
Using formula: X = (4 × 240) / 96 = 10 g - Preparation of 100 ml of 2% (w/w) solution in solvent with specific gravity 1.25?
Weight of solvent = 1.25 × 100 = 125 g
X = (2 × 125) / 98 = 2.55 g of drug
Detailed Notes:
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