Percentage, Ratio Strength, and Other Expressions of Concentration Yewande Dayo Student Pharmacist

Objectives Define percent weight-in-volume, percent volume-in-volume, and percent weight-in-weight. Define ratio strength. Convert percent strength to ratio strength and ratio strength to percent strength. Calculate the percent strength and ratio strength of a pharmaceutical preparation. Apply percent strength and ratio strength to calculate the quantity of an ingredient present in a pharmaceutical preparation. Apply percent strength and ratio strength to calculate the quantity of an ingredient to use in compounding a pharmaceutical preparation.

Percentage Strength Percentage strength and its corresponding sign (%) means rate per hundred 50% = 50 parts in 100 = 0.50 The pharmacist usually encounters liquid preparations where the parts represent grams of ingredient in 100 mL of liquid preparation.

Percentage Preparations Percent Weight in Volume (w/v): number of grams in 100mL of solution. Expressed as: ______%w/v Percent Volume in Volume (v/v): number of milliliters in 100 mL of solution. Expressed as: ______%v/v Percent weight in weight (w/w): number of grams in 100 grams of solution. Expressed as: ______%w/w

Assumptions If the term % is used without qualification the following are assumed: mixtures of solids and semisolids (%w/w) solutions or suspensions of solid in liquid (%w/v) solutions of liquid in liquid (%v/v)

Example 1 How many milligrams of ephedrine sulfate should be used in preparing the following prescription? Rx Sol. Ephedrine Sulfate ½% 30 mL Sig. For the nose Ans:0.15 g or 150 mg

Example 2 How many milligrams of certified red color should be used in preparing 5 liters of a 0.01% solution? Ans: 500 mg

Example 3 If a pharmacist dissolves the contents of eight capsules containing 250 mg clindamycin HCl per capsule into sufficient amount of astringent liquid to prepare 120 mL of solution, what is the percentage strength (w/v) of clindamycin HCl in the prescription? Ans: 1.67% (w/v)

Example 4 If 425 g of sucrose is dissolved in enough water to make 500 mL, what is the percentage strength of the solution? Ans: 85% (w/v)

Example 5 A sunscreen lotion contains 5% (v/v) of methyl salicylate. How many milliliters of methyl salicylate should be used in preparing 5 pints of the lotion? Ans: 118.25 mL

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

Example 7 How many grams of a drug substance should be dissolved in 1800 mL of water to make a 10% (w/w) solution? Ans: 18 g

Example 8 How many grams of potassium permanganate should be used in compounding the following prescription Rx Potassium Permanganate 0.02% Purified water ad 250 mL Ans: 0.05 g

Example 9 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? Ans: 45.45%

Example 10 One pound of fungicidal ointment contains 9.08 g of undecylenic acid. Calculate the percentage w/w of undecylenic acid in the ointment. Ans: 1.99% (w/w)

Final volume in w/w It is usually impossible to prepare a final specific volume of % w/w solution because the volume displaced by the active drug cannot be known in advance.

Example 11 How would you prepare 100 mL of a 2% (w/w) solution of a drug substance in a solvent having a specific gravity of 1.25? Ans: 2.55 g

Example 12 If 1500 mL of a solvent with a specific gravity 0.85 are used to dissolve 75 g of a drug substance, what is the percentage strength (w/w) of the solution? Ans: 5.55%

Example 13 If 5 g of boric acid is dissolved in 100 mL of water, what is the percentage strength (w/w) of the solution? Ans: 4.76%

Example 14 If 1000 mL of syrup with a specific gravity of 1.313 contains 850 g of sucrose, what is its percentage strength (w/w)? Ans: 64.7%

Example 15 What weight of a 5% (w/w) solution can be prepared from 2 g of active ingredient? Ans: 40 g

Ratio Strength Solids in liquids = 1:1000 = 1 g in 1000 mL of solution Liquids in liquids = 1:1000 = 1 mL in 1000 mL of solution. Solids in solids = 1:1000 = 1 g in 1000 g of mixture.

Example 16 Express 0.02% as a ratio strength and 1:4000 as percentage strength. Ans: 1:5000, 0.025%

Example 17 How many mg of gentian violet should be used in preparing the following solution? Rx Gentian violet solution 500 mL 1:10,000 Sig. Instill as directed Ans: 0.050 g or 50 mg

Example 18 How many mg of hexachlorophene should be used in compounding the following prescription? Rx Hexachlorophene 1:400 Hydrophilic Oint. ad 10 g Sig. Apply. Ans: 0.025 g or 25 mg

Conversion to mg/mL Convert 4% (w/v) to mg/mL Ans: 40 mg/mL

Example 19 Convert 1:10,000 (w/v) to mg/mL Convert a product concentration of 1g per 250 mL to mg/mL Ans: 1 mg/10 mL and 4 mg/mL

Parts per Million (PPM) 1 part of solute per 1 million part of the solution, e.g., 1:1,000,000

Example 20 Express 5 ppm of iron in water in percent strength and ratio strength. Ans: 1:200,000 and 0.0005%

Problem 21 Rx Gentamicin (40 mg/mL) Inj. 2 mL Gentamicin (0.3%) Oph. Soln. 5 mL Calculate the percent concentration of gentamicin in this fortified ophthalmic solution. Ans: 1.36% (w/v)

Problem 22 Mellaril-S Suspension contains 25 mg of thioridazine per 5 mL of suspension. What is the percentage strength (w/v) of thioridazine in the suspension? Ans: 0.5% (w/v)

Ofloxacin Opthalmic Solution 0.3% Disp 10 mL Rx Ofloxacin Opthalmic Solution 0.3% Disp 10 mL Sig: 2 drops into eyes q 4 hours x 2days; then 2 drops q 6 hours x 4 days How many grams of Ofloxacin should be used in preparing the prescription Ans:0.03 g