Danielle DelVillano, Pharm.D. Pharmaceutical Calculations: Percentage, Ratio Strength, and Other Expressions of Concentration Danielle DelVillano, Pharm.D.

Objectives Define the expressions percent weight-in-volume, percent volume-in-volume, percent weight-in-weight, ratio strength Convert percent strength to ratio strength and vice versa Apply percent strength and ratio strength to pharmaceutical calculations

Percentage Definition: rate per hundred Expressed as: 50/100 50% 0.50 Example: express 12.5% as an equivalent decimal fraction 12.5/100, or 0.125

Percentage Preparations Percent weight-in-volume (w/v) Number of grams of solute in 100 mL solution % w/v Percent volume-in-volume (v/v) Number of mL of a solute in 100 mL solution Percent weight-in-weight (w/w) Number of grams of a solute in 100 mL solution % w/w

Important notes When to use which term *Overall idea of this section* w/v – solutions, suspensions of solids in liquids v/v – liquids in liquids w/w – mixtures of solids (creams) *Overall idea of this section* Solution = Solute + Solvent

Percentage Weight-in-Volume Number of grams of solute in 100 mL solution For a 3% solution… 3 g of solute in 100 mL solution

Problem 1 (w/v) How many grams of dextrose are required to prepare 4000 mL of a 5% solution? (5% solution = 5 g of dextrose in 100 mL) 5 g = x g 100 mL 4000 mL x = 200 g

Problem 2 (w/v) What is the percentage strength of a solution of urea, if 80 mL contains 12 g? (% strength = x g in 100 mL) 12 g = x g 80 mL 100 mL x = 15%

Percentage Volume-in-Volume Number of mL of solute in 100 mL solution For a 5% solution… 5 mL of solute in 100 mL solution

Problem 3 (v/v) How many mL of liquified phenol should be used in compounding of the following prescription? Liquified phenol 2.5% Calamine lotion ad 240 mL 2.5 mL = x mL x = 6 mL 100 mL 240 mL

Problem 4 (v/v) What is the percentage strength (v/v) of a solution of 800 g of a liquid with a specific gravity of 0.800 in enough water to make 4000 mL? 800 g water = 800 mL water 1000 mL = x mL 4000 mL 1000 mL 800 mL / 0.800 = 1000 mL solute x = 25 %

Percentage Weight-in-Weight Number of g of solute in 100 g solution For a 8% solution… 8 g of solute in 100 g solution *Important to note* Unlike w/v, the weight of the solute is INCLUDED in the weight of the solution for these problems

Problem 5 (w/w) How should you prepare 100 mL of a 2% (w/w) solution of a drug substance in a solvent having a specific gravity of 1.25? 100 mL solvent * 1.25 = 125 g solvent 100% solution – 2% solute = 98% solvent 2% = x g 98% 125 g Mix 2.25 g drug with 125 g x = 2.25 g of solvent Note how the proportion is set up differently in this problem

Problem 6 (w/w) If 5 g of boric acid is added to 100 mL of water, what is the percentage strength (w/w) of the solution? 100 mL water = 100 g water 100 g water (solvent) + 5 g boric acid (solute) = 105 g solution 5 g = x x = 4.76% 105 g 100 mL

Ratio Strength Another way of expressing the percentage strength of a solution Example: Express 5% as a ratio strength 5 parts per 100, or 5:100 Commonly we express ratio strength as 1:x So 5:100 would be expressed 1:20 General form: 1 part of solute per x parts of solution

Converting between the Strength Expressions Express 0.02% as a ratio strength 0.02 = 1 part x = 5000 100 x parts Answer: 1:5000 Express 1:4000 as a percentage strength 1 part = x x = 0.025% 4000 parts 100

Problem 7 (ratio) A certain injectable contains 2 mg of drug per milliliter of solution. What is the ratio strength (w/v) of the solution? 2 mg = 0.002 g 0.002 g = 1 g x = 500 mL 1 mL x mL Answer: 1:500

Problem 8 (ratio) How many milligrams of hexachlorophene should be used in compounding the following prescription? Hexochlorophane 1:400 Hydrophillic ointment ad 10 g 1 g = x g x = 0.025 g = 25 mg 400 g 10 g

Parts Per Million (PPM) and Parts Per Billion (PPB) Strengths of very dilute solutions Example: 1-4 PPM flouride in drinking water 1 PPM – 4 PPM 1:1000000 – 4:1000000

Problem 9 (PPM) The concentration of a drug additive in an animal feed is 12.5 ppm. How many milligrams of the drug should be used in preparing 5.2 kg of feed? 12.5 PPM = 12.5:1000000 12.5 g = x g x = 0.065 g = 65 mg 1000000 g 5200 g

Questions

Reference Ansel, H. C. (2009) Phamaceutical Calculations (13th Ed.). Philadelphia:Lippincott Williams & Wilkins, and Wolters Kluwer Publishers

Additional Problems

Chapter 6 Problem 7 If a pharmacist dissolved the contents of eight capsules, each containing 300 mg of clindamycin phosphate, into a sufficient amount of an astringent liquid base to prepare 60 mL of topical solution, what would be the percentage strength (w/v) of clindamycin phosphate in the prescription? 4%

Chapter 6 Problem 29 A topical solution contains 3% w/v hydroquinone. How many liters of the solution can be prepared from 30 g of hydroquinone? 10 L

Chapter 6 Problem 30 What is the percentage strength (v/v) if 225 g of a liquid having a specific gravity of 0.8 is added to enough water to make 1.5 liters of the solution? 18.75%

Chapter 6 Problem 38 If 500 g of dextrose are dissolved in 600 mL of water with a resultant final volume of 1 liter, what is the percentage strength of dextrose in the solution on a w/w basis? 45.45%

Chapter 6 Problem 57 A sample of white petrolatum contains 10 mg of tocopherol per kilogram as a preservative. Express the amount of tocopherol as a ratio strength. 1:100000

Chapter 6 Problem 65 In acute hypersensitivity reactions, 0.5 mL of a 1:1000 (w/v) solution of epinephrine may be administered subcutaneously or intramuscularly. Calculate the milligrams of epinephrine given. 0.5 mg

Chapter 6 Problem 70 If a commercially available insulin preparation contains 1 ppm of proinsulin, how many micrograms of proinsulin would be contained in a 10-mL vial of insulin? 10 mcg