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Joh Ch06.qxd8/29/0712:55 PMPage 25CHAPTER6Concentrationsand DilutionsL earning ObjectivesAfter completing this chapter, youshould be able to: Calculate weight/weightpercent concentrations.INTRODUCTIONConcentrations of many pharmaceutical preparations areexpressed as a percent strength. This is an important conceptto understand. Percent strength represents how many gramsof active ingredient are in 100 mL. In the case of solids suchas ointment, percent strength would represent the number ofgrams contained in 100 g. Percent strength can be reduced toa fraction or to a decimal, which may be useful in solvingthese calculations. It is best to convert any ratio strengths to apercent. We assume that 1 g of solute displaces exactly 1 mLof liquid. Therefore, you will notice that grams and millilitersare used interchangeably depending on whether you areworking with solids in grams or liquids in milliliters. Calculate weight/volumepercent concentrations. Calculate volume/volumepercent concentrations. Calculate dilutions of stocksolutions.25

Joh Ch06.qxd8/29/0712:55 PMPage 26ConcentrationsWEIGHT/WEIGHTPercent concentrations for solids such as ointments or creams are expressedas % w/w. You can determine these by establishing a proportion and thenconverting it into a percentage, as discussed in Chapter 4.Calculating weight/weight concentrations can be easily and accuratelyperformed by following these steps:1. Set up a proportion with the amount of active ingredient listed over thetotal quantity, as grams over grams.2. Convert the proportion to a decimal (by dividing the numerator by thedenominator).3. Multiply the converted number by 100 to express the finalconcentration as a percentage.EXAMPLE 6.11 g of active ingredient powder is mixed with 99 g of whitepetrolatum. What is the final concentration [w/w]?Let’s look at the information that has been provided and iscritical to solving the calculation:1 g active ingredientamount of active99 g white petrolatumamount of base100 g*total quantity (1 g of active 99 g of the base)*It is important to be careful in determining the amount for thetotal quantity. If you do not add both the active and base quantitiesfor the total quantity, if not listed, the calculation will be set upincorrectly from the very start!The first step is to set up a proportion with the amount of active ingredientlisted over the total quantity.1 g (active)100 g (total)Next, convert the proportion to a decimal by dividing the numerator bythe denominator.1 g , 100 g 0.01Now, multiply the converted number by 100 to express the final concentration as a percentage.0.01 * 100 1%So, the final weight/weight concentration is 1%.26Chapter SixConcentrations and Dilutions

Joh Ch06.qxd8/29/07EXAMPLE 6.212:55 PMPage 2712 g of active ingredient powder is in a 120 g compounded cream.What is the concentration [w/w]?Let’s look at the information that has been provided and iscritical to solving the calculation:12 g active ingredientamount of activenot providedamount of base120 g*total quantity*In this example, we are not provided with the amount of base,but only the amount of active ingredient and the total quantity.First set up a proportion with the amount of active ingredient listed overthe total quantity.12 g (active)120 g (total)Now, convert the proportion to a decimal by dividing the numerator bythe denominator.12 g , 120 g 0.1Finally, multiply the converted number by 100 to express the final concentration as a percentage.0.1 * 100 10%Therefore, the final weight/weight concentration of the compoundedcream is 10%.EXAMPLE 6.330 g of a compounded ointment contains 105 mg of neomycinsulfate. What is the final concentration [w/w]?Let’s look at the information that has been provided and iscritical to solving the calculation:0.105 g* active ingredientamount of activenot providedamount of base30 gtotal quantity*To accurately perform concentration calculations, the proportionmust be set up as grams over grams. In this example, the problemprovides the amount of active ingredient in milligrams, which mustbe converted to grams.Set up a proportion with the amount of active ingredient listed over thetotal quantity.0.105 g (active)30 g (total)Then, convert the proportion to a decimal by dividing the numerator bythe denominator.0.105 g , 30 g 0.0035Chapter SixConcentrations and Dilutions27

Joh Ch06.qxd8/29/0712:55 PMPage 28Now, multiply the converted number by 100 to express the final concentration as a percentage.0.0035 * 100 0.35%The final weight/weight concentration is 0.35%.EXAMPLE 6.4If you add 3 g of salicylic acid to 97 g of an ointment base, what isthe final concentration [w/w] of the product?Let’s look at the information that has been provided and iscritical to solving the calculation:3 g active ingredientamount of active97 gamount of base100 gtotal quantity (3 g 97 g)Set up a proportion with the amount of active ingredient listed over thetotal quantity.3 g (active)100 g (total)Now, convert the proportion to a decimal by dividing the numerator bythe denominator.3 g , 100 g 0.03Multiply the converted number by 100 to express the final concentrationas a percentage.0.03 * 100 3%The final weight/weight concentration of the ointment is 3%.EXAMPLE 6.5How much oxiconazole nitrate powder is required to prepare thisorder?Rx—1% Oxiconazole Nitrate OintmentDisp. 45 gLet’s look at the information that has been provided . . . andwhat is missing.28Chapter SixConcentrations and Dilutionsnot providedamount of activenot providedamount of base45 gtotal quantity1%final

Joh Ch06.qxd8/29/0712:55 PMPage 29Now this problem has given us the final concentration, and we arebeing asked to determine the amount of active ingredient needed. Noticethat, in essence, the previous examples could be solved by using theformula below.g Active* 100 Final % Strengthg Total QtyUp until this point, we have been able to solve for the final % strength byfilling in the other amounts and solving. This is the same approach thatwe will take to solving this problem; the only difference is that we will besolving for the number of grams of active ingredient.Using the information we know and the formula above, let’s fill in everything we can.x g (active)* 100 1%45 g (total)To solve for x, the unknown quantity of active ingredient, we can divideboth sides of the equation by 100 . . . which will cancel it out on the left sideand create a fraction on the right side.x g (active)1001* 45 g (total)100100Now, we have a ratio and proportion, which can be solved by cross multiplication and solving for x.x g (active)1 45 g (total)100Cross-multiply.x * 100 100x1 * 45 45So . . .100x 45Now, we can divide both sides by 100 to solve for x (the quantity of active ingredient needed).100x45 100100x 0.45So, 0.45 g or 450 mg of oxiconazole nitrate powder is needed for thisorder.Chapter SixConcentrations and Dilutions29

Joh Ch06.qxd8/29/0712:55 PMPage 30EXAMPLE 6.6How much fluorouracil powder is in 5% Efudex cream 25 g?Let’s look at the information that has been provided.not providednot provided25 g5%amount of activeamount of basetotal quantityfinalAgain, this problem has given us the final concentration, and we arebeing asked to determine the amount of active ingredient needed.Using the information known and the formula, fill in everything you can.x g (active)* 100 5%25 g (total)Divide both sides of the equation by 100 to set up a ratio and proportionwhich can be solved.x g (active)5* 100 25 g (total)100Now, we have a ratio and proportion, which can be solved by cross multiplication and solving for x.x g (active)5 25 g (total)100Cross-multiply.x * 100 100x5 * 25 125So . . .100x 125Now, divide both sides by 100 to solve for x (the quantity of active ingredient needed).100 x125 100100x 1.25So, 1.25 g of fluorouracil powder is contained in 25 g of 5% Efudex cream.PRACTICE PROBLEMS 6.11. 3 g of Zovirax ointment contains 150 mg of acyclovir. What isconcentration of this product?2. 15 g of Tinactin contains 0.15 g of tolnaftate powder. What is the %strength of this cream?3. Bactroban ointment contains 0.6 g of mupirocin per 30 g tube. What isthe % strength?30Chapter SixConcentrations and Dilutions

Joh Ch06.qxd8/29/0712:55 PMPage 314. Zonalon cream contains 1.5 g of dosepin HCl with 28.5 g of a creambase. What is the concentration of Zonalon ?5. To prepare a topical cream, you add 150 mg of metronidazole with14.85 g of a cream base. What is the final percent strength of thecream?6. 6 g of azelaic acid is added to 24 g of cream base to produce Azelex cream. What is the concentration of this product?7. Hytone contains 500 mg of hydrocortisone powder with 19.5 gof emollient base. What is the percentage strength of Hytone ?8. How much boric acid is contained in 30 g of a 10% boric acidointment?9. How much sulfur is contained in 120 g of 5% Plexion SCT cream?10. Vaniqa cream contains 13.9% eflornithine HCl. How many grams ofactive ingredient is contained in 30 grams?WEIGHT/VOLUMEPercent concentrations for liquids in which an active ingredient starting out asa powder is dissolved in a liquid, such as distilled water or normal saline, areexpressed as % w/v. Again, you can determine these by establishing a proportion and then converting it into a percentage. Calculating weight/volume concentrations can be easily and accurately performed by following these steps:1. Set up a proportion with the amount of active ingredient listed over thetotal quantity, as grams over milliliters.2. Convert the proportion to a decimal (by dividing the numerator by thedenominator).3. Multiply the converted number by 100 to express the finalconcentration as a percentage.EXAMPLE 6.7100 g of active ingredient powder is mixed with 500 mL normalsaline. What is the final concentration [w/v]?Let’s look at the information that has been provided and iscritical to solving the calculation:100 g active ingredient500 mL normal saline500 mL*amount of activeamount of basetotal quantity*When mixing powders with liquids, the liquid (base) quantity isconsidered the total quantity, since the powder will either dissolveor suspend within the base liquid.The first step is to set up a proportion with the amount of active ingredient listed over the total quantity.100 g (active)500 mL (total)Chapter SixConcentrations and Dilutions31

Joh Ch06.qxd8/29/0712:55 PMPage 32Next, convert the proportion to a decimal by dividing the numerator bythe denominator.100 g , 500 mL 0.2Now, multiply the converted number by 100 to express the final concentration as a percentage.0.2 * 100 20%So, the final weight/volume concentration is 20%.EXAMPLE 6.825 g of active ingredient powder is mixed with 250 mL of distilledwater. What is the final percent strength [w/v]?Let’s look at the information that has been provided and iscritical to solving the calculation:25 g active ingredientamount of active250 mLtotal quantityFirst, set up a proportion with the amount of active ingredient listed overthe total quantity.25 g (active)250 mL (total)Next, convert the proportion to a decimal by dividing the numerator bythe denominator.25 g , 250 mL 0.1Now, multiply the converted number by 100 to express the final concentration as a percentage.0.1 * 100 10%So, the final weight/volume percent strength is 10%.EXAMPLE 6.99 g of sodium chloride is diluted in 1 L of SWFI (sterile water forinjection). What is the final percent strength [w/v]?Let’s look at the information that has been provided and iscritical to solving the calculation:9 g active ingredientamount of active1000 mL*total quantity*Remember that the total quantity must be expressed as milliliters,so the 1 L is converted to 1000 mL.Set up a proportion with the amount of active ingredient listed over thetotal quantity.9 g (active)1000 mL (total)32Chapter SixConcentrations and Dilutions

Joh Ch06.qxd8/29/0712:55 PMPage 33Next, convert the proportion to a decimal by dividing the numerator bythe denominator.9 g , 1000 mL 0.009Now, multiply the converted number by 100 to express the final concentration as a percentage.0.009 * 100 0.9%So, the final weight/volume percent strength is 0.9%.(This is the formula for normal saline)EXAMPLE 6.1030 mL of Xylocaine liquid contains 1.5 g of lidocaine HCl. What isthe final concentration [w/v]?Let’s look at the information that has been provided and iscritical to solving the calculation:1.5 g active ingredientamount of active30 mLtotal quantitySet up a proportion with the amount of active ingredient listed over thetotal quantity.1.5 g (active)30 mL (total)Now, convert the proportion to a decimal by dividing the numerator bythe denominator.1.5 g , 30 mL 0.05Finally, multiply the converted number by 100 to express the final concentration as a percentage.0.05 * 100 5%So, the final weight/volume concentration is 5%.EXAMPLE 6.11Melanex solution contains 0.9 g of hydroquinone in every 1 oz.bottle. What is the final percent strength [w/v]?Let’s look at the information that has been provided and iscritical to solving the calculation:0.9 g active ingredient30 mL*amount of activetotal quantity*Remember that the total quantity must be expressed as milliliters,so the 1 oz. is converted to 30 mL.Set up a proportion with the amount of active ingredient listed over thetotal quantity.0.9 g (active)30 mL (total)Chapter SixConcentrations and Dilutions33

Joh Ch06.qxd8/29/0712:55 PMPage 34Next, convert the proportion to a decimal by dividing the numerator bythe denominator.0.9 g , 30 mL 0.03Now, multiply the converted number by 100 to express the final concentration as a percentage.0.03 * 100 3%So, the final weight/volume percent strength is 3%.EXAMPLE 6.12Rogaine Extra Strength is a 5% solution of minoxidil in alcohol.How much active ingredient is in a 60 mL bottle?Let’s look at the information that has been provided . . . andwhat is missing.not providedamount of active60 mLtotal quantity5%final strengthNow this problem has given us the f