Pharmaceutical Calculations Percentage Ratio Strength and Other Expressions

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

Objectives • Define the expressions percent weight-involume, 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 m. L solution – % w/v • Percent volume-in-volume (v/v) – Number of m. L of a solute in 100 m. L solution – % w/v • Percent weight-in-weight (w/w) – Number of grams of a solute in 100 m. L solution – % w/w

Important notes • When to use which term – 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 m. L solution • For a 3% solution… – 3 g of solute in 100 m. L solution

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

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

Percentage Volume-in-Volume • Number of m. L of solute in 100 m. L solution • For a 5% solution… – 5 m. L of solute in 100 m. L solution

Problem 3 (v/v) • How many m. L of liquified phenol should be used in compounding of the following prescription? – Liquified phenol – Calamine lotion 2. 5 m. L = x m. L 100 m. L 240 m. L 2. 5% ad 240 m. L x = 6 m. L

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 m. L? 800 g water = 800 m. L water 1000 m. L = x m. L 4000 m. L 1000 m. L 800 m. L / 0. 800 = 1000 m. L 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 m. L of a 2% (w/w) solution of a drug substance in a solvent having a specific gravity of 1. 25? 100 m. L 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

Problem 6 (w/w) • If 5 g of boric acid is added to 100 m. L of water, what is the percentage strength (w/w) of the solution? 100 m. L water = 100 g water (solvent) + 5 g boric acid (solute) = 105 g solution 5 g = x 105 g 100 m. L x = 4. 76%

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 100 x parts x = 5000 Answer: 1: 5000 • Express 1: 4000 as a percentage strength 1 part = x 4000 parts 100 x = 0. 025%

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 = 1 g 1 m. L x = 500 m. L Answer: 1: 500

Problem 8 (ratio) • How many milligrams of hexachlorophene should be used in compounding the following prescription? – Hexochlorophane – Hydrophillic ointment 1 g 400 g = xg 10 g 1: 400 ad 10 g x = 0. 025 g = 25 mg

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 = xg 1000000 g 5200 g x = 0. 065 g = 65 mg

Questions

Reference • Ansel, H. C. (2009) Phamaceutical Calculations (13 th 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 m. L of topical solution, what would be the percentage strength (w/v) of clindamycin phosphate in the prescription?

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?

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?

Chapter 6 Problem 38 • If 500 g of dextrose are dissolved in 600 m. L 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?

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.

Chapter 6 Problem 65 • In acute hypersensitivity reactions, 0. 5 m. L of a 1: 1000 (w/v) solution of epinephrine may be administered subcutaneously or intramuscularly. Calculate the milligrams of epinephrine given.

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 -m. L vial of insulin?