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Danielle DelVillano, Pharm.D.
Pharmaceutical Calculations: Density, Specific Gravity, and Specific Volume Danielle DelVillano, Pharm.D.
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Objectives Define density, specific gravity, and specific volume and determine each through appropriate calculations Apply specific gravity correctly in converting weight to volume and volume to weight
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Density Mass per unit volume of a substance
Most often expressed as g/mL Density = Mass Volume
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Density Example If 10 mL of sulfuric acid weighs 18 g, what is its density? Density = 18 g 10 mL = 1.8 g/mL
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Specific Gravity Ratio of a weight of substance to a weight of equal volume of standard Usually water Expressed without units Specific Gravity = Weight of substance Weight of equal vol. water <1 are lighter than water >1 are heavier than water
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Specific Gravity Example
If mL of an oil weighs g, what is the specific gravity of that oil? Specific Gravity = g oil 54.96 g water *why g of water? Because mL of water weighs g (specific gravity of 1)
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Displacement (Plummet) Method
A body immersed in a liquid displaces an amount of the liquid equal to its own volume and suffers an apparent weight loss in weight equal to the weight of the displaced liquid Weigh plummet in air Weigh plummet in water Weight plummet in oil Weight of displaced oil = weight of plummet in air – weight of plummet in oil Weight of displaced water = weight of plummet in air - weight of plummet in water
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Plummet Method Example
A glass plummet weighs g in air, 8.57 g when immersed in water, and 9.12 g when immersed in an oil. Calculate the specific gravity of the oil. Specific gravity = Weight of displaced oil Weight of displaced water = g – 9.12 g g – 8.57 g = 0.865
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Specific Volume Ratio of the volume of a substance to an equal weight of another substance taken as a standard Water
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Specific Volume Example
If 25 g of glycerin measures 20 mL and the standard for comparison is (25 g) water, what is the specific volume of glycerin? Specific Volume = 20 mL glycerin 25 mL water = 0.8
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Practice Problems
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Chapter 5 Page 73 What is the weight, in grams, of 3620 mL of alcohol with a specific gravity of 0.820? 2968 g
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Chapter 5 Page 74 What is the volume, in pints, of 50 lbs of glycerin having a specific gravity of 1.25? 38.4 pints (1 pint = 473 mL)
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Chapter 5 Problem 2 A piece of copper metal weighs 53.6 g and has a volume of 6 mL. Calculate its density. 0.812 g/mL
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Chapter 5 Problem 6 If 380 g of cottonseed oil measures 415 mL, what is its specific gravity? 0.916
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Chapter 5 Problem 15 If chloroform has a specific gravity of 1.476, what is its specific volume? 0.678
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Chapter 5 Problem 18 What is the weight, in pounds, of 5 pints of nitric acid? (1 pint = 473 mL) (1 lb = 2.2 kg) 7.4 lbs
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Chapter 5 Problem 27 If fifty glycerin suppositories are made from the following formula, how many milliliters of glycerin, having a specific gravity of 1.25, would be used in the preparation of 96 suppositories? Glycerin g Sodium stearate 9 g Purified water 5 g mL
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Chapter 5 Problem 29 How many grams of dextrose are contained in a 250 mL intravenous infusion of a dextrose injection containing 60 g of dextrose per 100 mL if its specific gravity is 1.20? 150 g
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Chapter 5 Problem 24 Glycerin,USP (specific gravity 1.25) costs $54.25 per pound. If students in a dispensing laboratory use 1 pint of glycerin in preparing compounded prescriptions, what is the cost of the glycerin used? (1 pint = 473 mL) $70.65
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Questions
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Reference Ansel, H. C. (2009) Phamaceutical Calculations (13th Ed.). Philadelphia:Lippincott Williams & Wilkins, and Wolters Kluwer Publishers
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