Percentage Ratio Strength and Other Expressions of Concentration

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

Objectives � Define percent weight-in-volume, percent volume-involume, 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 m. L of liquid preparation.

Percentage Preparations � Percent Weight in Volume (w/v): number of grams in 100 m. L of solution. Expressed as: ______%w/v � Percent Volume in Volume (v/v): number of milliliters in 100 m. L 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% Sig. For the nose 30 m. L

Example 2 � How many milligrams of certified red color should be used in preparing 5 liters of a 0. 01% solution?

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 m. L of solution, what is the percentage strength (w/v) of clindamycin HCl in the prescription?

Example 4 � If 425 g of sucrose is dissolved in enough water to make 500 m. L, what is the percentage strength of the solution?

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?

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?

Example 7 � How many grams of a drug substance should be dissolved in 1800 m. L of water to make a 10% (w/w) solution?

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 m. L

Example 9 � 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?

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.

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 m. L of a 2% (w/w) solution of a drug substance in a solvent having a specific gravity of 1. 25?

Example 12 � If 1500 m. L 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?

Example 13 � If 5 g of boric acid is dissolved in 100 m. L of water, what is the percentage strength (w/w) of the solution?

Example 14 � If 1000 m. L of syrup with a specific gravity of 1. 313 contains 850 g of sucrose, what is its percentage strength (w/w)?

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

Ratio Strength � Solids in liquids = 1: 1000 = 1 g in 1000 m. L of solution � Liquids in liquids = 1: 1000 = 1 m. L in 1000 m. L 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.

Example 17 � How many mg of gentian violet should be used in preparing the following solution? Rx Gentian violet solution 500 m. L 1: 10, 000 Sig. Instill as directed

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.

Conversion to mg/m. L � Convert 4% (w/v) to mg/m. L

Example 19 � Convert 1: 10, 000 (w/v) to mg/m. L � Convert a product concentration of 1 g per 250 m. L to mg/m. L

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

Example 20 � Express 5 ppm of iron in water in percent strength and ratio strength.

Problem 21 Rx Gentamicin (40 mg/m. L) Inj. Gentamicin (0. 3%) Oph. Soln. 2 m. L 5 m. L Calculate the percent concentration of gentamicin in this fortified ophthalmic solution.

Problem 22 � Mellaril-S Suspension contains 25 mg of thioridazine per 5 m. L of suspension. What is the percentage strength (w/v) of thioridazine in the suspension?

� Rx � Ofloxacin Opthalmic Solution 0. 3% � Disp 10 m. L � Sig: 2 drops into eyes q 4 hours x 2 days; then 2 drops q 6 hours x 4 days � How many grams of Ofloxacin should be used in preparing the prescription