Bachelor Pharmaceutical Calculations Ansel 13th Edition PDF

Reducing and Enlarging Formulas 16 Objectives Upon successful completion of this chapter, the student will be able to: Perform calculations to reduce or enlarge formulas for pharmaceutical preparations s...

Reducing and Enlarging Formulas 16 Objectives Upon successful completion of this chapter, the student will be able to: Perform calculations to reduce or enlarge formulas for pharmaceutical preparations stated in metric quantities. Perform calculations to reduce or enlarge formulas for pharmaceutical preparations stated in proportional parts. Pharmacists may have to reduce or enlarge formulas for pharmaceutical preparations in the course of their professional practice or manufacturing activities. Official (United States Pharmaco- peia—National Formulary) formulas generally are based on the preparation of 1000 mL or 1000 g. Other formulas, as those found in the literature, may be based on the preparation of a dosage unit (e.g., 5 mL, 1 capsule) or another quantity (e.g., 100 mL). Industrial formulas may be scaled up to quantities of ingredients sufficient to prepare hundreds of thousands of dosage units in a production batch. In each of these instances, a pharmacist may calculate the quantities of each ingredient required for a smaller or greater quantity by reducing or enlarging the specified formula, while maintaining the correct proportion of one ingredient to the other. Calculations to reduce or enlarge formulas may be performed by a two-step process: Step 1. Using the following equation, determine the factor that defines the multiple or the decimal fraction of the amount of formula to be prepared: Quantity of formula desired  Factor Quantity of formula given A factor greater than 1 represents the multiple of the formula, and a factor less than 1 indicates the fraction of the formula to be prepared. Step 2. Multiply the quantity of each ingredient in the formula by the factor to determine the amount of each ingredient required in the reduced or enlarged formula. Applying the equation and factor: If a formula for 1000 mL contains 6 g of a drug, how many grams of drug are needed to prepare 60 mL of the formula? 60 mL Step 1.  0.06 (factor) 1000 mL Step 2. 6 g  0.06  0.36 g, answer. 279 280 PHARMACEUTICAL CALCULATIONS Example Calculations of Reducing and Enlarging Formulas From the following formula, calculate the quantity of each ingredient required to make 240 mL of calamine lotion. Calamine 80 g Zinc Oxide 80 g Glycerin 20 g Bentonite Magma 250 mL Calcium Hydroxide Topical Solution, to make 1000 mL 240 mL  0.24 (factor) 1000 mL Using the factor 0.24, the quantity of each ingredient is calculated as follows: Calamine  80 g  0.24  19.2 g Zinc Oxide  80 g  0.24  19.2 g Glycerin  20 g  0.24  4.8 mL Bentonite Magma  250 g  0.24  60 mL Calcium Hydroxide Topical Solution, to make 240 mL, answers. Or, solving by dimensional analysis: 80 g 240 mL Calamine   19.2 g 1000 mL 1 80 g 240 mL Zinc Oxide   19.2 g 1000 mL 1 20 mL 240 mL Glycerin   4.8 mL 1000 mL 1 250 mL 240 mL Bentonite Magma   60 mL 1000 mL 1 Calcium Hydroxide Topical Solution, to make 240 mL, answers. From the following formula for artificial tears,1 calculate the quantity of each ingredient required to prepare a dozen 30-mL containers. Polyvinyl Alcohol 1.4 g Povidone 0.6 g Chlorobutanol 0.5 g Sterile Sodium Chloride Solution, 9% ad 100 mL 30 mL  12  360 mL 360 mL  3.6 (factor) 100 mL Using the factor 3.6, the quantity of each ingredient is calculated as follows: Polyvinyl Alcohol  1.4 g  3.6  5.04 g Povidone  0.6 g  3.6  2.16 g Chlorobutanol  0.5 g  3.6  1.8 g Sterile Sodium Chloride Solution, 9% ad 360 mL, answers. From the following formula for an estradiol vaginal gel,2 calculate the quantity of each ingredient required to prepare 1 lb. of gel.  CHAPTER 16 REDUCING AND ENLARGING FORMULAS 281 Estradiol 200 g Polysorbate 80 1g Methylcellulose Gel, 2% 95 g 1 lb.  454 g Formula weight  200 g  1 g  95 g  296 g 454 g  1.534 (factor) 296 g Using the factor 1.534, the quantity of each ingredient is calculated as follows: Estradiol  200 g  1.534  306.8 g Polysorbate 80  1 g  1.534  1.534 g Methylcellulose Gel, 2%  95 g  1.534  145.73 g, answers. From the following formula for a dexamethasone ophthalmic ointment,3 calculate the quantity of each ingredient needed to prepare 7.5 g of ointment. Dexamethasone Sodium Phosphate 55 mg Lanolin, Anhydrous 5 g Mineral Oil 10 g White Petrolatum ad 100 g 7.5 g  0.075 (factor) 100 g Using the factor 0.075, the quantity of each ingredient is calculated as follows: Dexamethasone Sodium Phosphate  55 mg  0.075  4.125 mg Lanolin, Anhydrous  5 g  0.075  0.375 g Mineral Oil  10 g  0.075  0.75 g White Petrolatum ad  100 g ad 7.5 g, answers. Formulas That Specify Proportional Parts On a rare occasion, a pharmacist may encounter an old formula that indicates the ingredients in ‘‘parts’’ rather than in measures of weight or volume. The parts indicate the relative proportion of each of the ingredients in the formula by either weight or volume, but not both. A formula for solid or semisolid ingredients, therefore, may be considered in terms of grams, whereas a formula of liquids may be considered in terms of milliliters. Example Calculation of a Formula Expressed in Parts From the following formula, calculate the quantity of each ingredient required to make 1000 g of the ointment. Coal Tar 5 parts Zinc Oxide 10 parts Hydrophilic Ointment 50 parts Total number of parts (by weight)  65 1000 g will contain 65 parts 65 (parts) 1000 (g)  5 (parts) x (g) x  76.92 g of Coal Tar, 282 PHARMACEUTICAL CALCULATIONS and 65 (parts) 1000 (g)  10 (parts) y (g) y  153.85 g of Zinc Oxide, and 65 (parts) 1000 (g)  50 (parts) z (g) z  769.23 g of hydrophilic ointment, answers. (Check total: 1000 g) CALCULATIONS CAPSULE Reducing and Enlarging Formulas Pharmaceutical formulas are combinations of ingredients, each present in a specified amount. The quantitative relationship between ingredients is fixed; that is, irrespective of the total quantity of formula prepared, the relative amount of one ingredient to another remains the same. Formulas may be reduced or enlarged through the use of a factor generated by the following equation and applied consistently to each ingredient. Quantity of formula desired  Factor Quantity of formula given The quantity of each ingredient in a formula is multiplied by the factor to determine the quantity needed in a reduced or enlarged formula. PRACTICE PROBLEMS 1. From the following formula for 40 sertra- 3. From the following formula, calculate the line capsules,4 calculate the factor that quantities required to make 5 lb. of hy- would be used if a pharmacist wished to drophilic ointment. prepare 250 capsules. Methylparaben 0.25 g Sertraline Hydrochloride 300 mg Propylparaben 0.15 g Silica Gel 6g Sodium Lauryl Sulfate 10 g Calcium Citrate 4g Propylene Glycol 120 g Stearyl Alcohol 250 g 2. From the following formula for a proges- White Petrolatum 250 g terone nasal spray,5 calculate the factor Purified Water, to make 1000 g that would be used if a pharmacist wished to prepare 24 15-mL containers of the 4. The formula for an ophthalmic ointment product. is as follows: Progesterone 20 mg Sulfacetamide Sodium 10% w/w Dimethyl-␤-cyclodextrin 62 mg Prednisolone Acetate 0.2% w/w Purified Water ad 1 mL  CHAPTER 16 REDUCING AND ENLARGING FORMULAS 283 Phenylmercuric 9. The following is a formula for 100 triple Acetate 0.0008% w/w estrogen capsules.8 Calculate the quan- Mineral Oil 1% w/w tities of the first three ingredients, in White Petrolatum, qs ad 3.5 g grams, and the last two ingredients, in kilograms, required to prepare 5000 such How much of each ingredient would be capsules. needed to manufacture 2000 such tubes of ointment? Estriol 200 mg Estrone 25 mg 5. Calculate the quantity of each ingredient Estradiol 25 mg needed to prepare 15-mL of the following Polyethylene Glycol 1450 20 g ophthalmic solution.6 Polyethylene Glycol 3350 20 g Erythromycin Lactobionate 500 mg 10. According to the literature, when the Dexamethasone Sodium product AMEVIVE (alefacept) is reconsti- Phosphate 100 mg tuted with sterile water for injection to Glycerin 2.5 mL prepare 0.6 mL of injection, it contains Sterile Water for Injection the following in each 0.5 mL.9 ad 100 mL Alefacept 7.5 mg 6. According to the literature, the biotech- Sucrose 12.5 mg nology product NEULASTA (pegfilgras- Glycine 5 mg tim) contains the following in 0.6 mL pre- Sodium Citrate, Dihydrate 3.6 mg filled syringes7: Citric Acid, Monohydrate 0.06 mg Pegfilgrastim 6 mg How much alefacept would be needed Sorbitol 30 mg to manufacture a 5000 batch of vials for Polysorbate 20 0.02 mg reconstitution? Water for Injection, ad 0.6 mL (a) 12.5 mg How much of the first three ingredients (b) 31.25 g would be needed to manufacture 100,000 (c) 37.5 g such syringes? (d) 45 g 7. From the following formula, calculate the 11. The formula for a ciprofloxacin otic drop quantity of each ingredient required to is given in the literature as follows10: make 1500 g of the powder. Ciprofloxacin 1g Calcium Carbonate 5 parts Propylene Glycol 50 mL Magnesium Oxide 1 part Glycerin qs ad 100 mL Sodium Bicarbonate 4 parts How many grams of ciprofloxacin Bismuth Subcarbonate 3 parts would be required to prepare 200 15-mL 8. Calculate the quantity of benzocaine bottles of the ear drop? needed to prepare 240 g of the following 12. From the following formula for a proges- formula for a topical anesthetic. terone vaginal suppository, calculate the Benzocaine 14% w/w amount of each ingredient needed to pre- Butylaminobenzoate 2% w/w pare 36 suppositories. Tetracaine Hydrochloride 2% w/w Progesterone 75 mg Benzalkonium Chloride 1.5% w/w Polyethylene Glycol 3350 1g Cetyl Dimethyl Ethyl Polyethylene Glycol 1000 3g Ammonium Bromide 0.005% w/w Aquagel q.s. ad 30 g 284 PHARMACEUTICAL CALCULATIONS 13. The formula for a sports rub cream is Polyethylene Glycol 3350 60 mL given in the literature as follows11: Sodium Chloride 1.46 g Potassium Chloride 0.745 g Methyl Salicylate 15 mL Sodium Bicarbonate 1.68 g Menthol 10 g Sodium Sulfate 5.68 g Eucalyptus Oil 1g Water q.s. ad 4 L Hydrophilic Ointment, qs ad 100 g 17. The following is a formula for the prepara- tion of a suppository for the treatment If the specific gravity of methyl salicylate of migraine headaches.12 Calculate the is 1.18, how many grams of each ingredi- quantities of each ingredient needed to ent would be needed to prepare a dozen prepare 250 suppositories. 30-g tubes of ointment? Ergotamine Tartrate 2 mg 14. From the following formula for one rectal Caffeine 100 mg suppository, calculate the quantity of Hyoscyamine Sulfate 0.25 mg each ingredient required to prepare 24 Pentobarbital Sodium 60 mg such suppositories. FATTIBASE ad 2 g Promethazine Hydrochloride 25 mg 18. Each milliliter of an otic solution contains Ascorbyl Palmitate 1% the following ingredients. Calculate the White Wax 5% amount of each ingredient needed to man- Cocoa Butter ad 2g ufacture 1000 10-mL containers of the 15. From the following formula for a syn- product. thetic elastoviscous fluid for injection into Antipyrine 54 mg the knee to treat osteoarthritis, calculate Benzocaine 14 mg the quantities, in grams, of each of the Dehydrated Glycerin, first four ingredients needed to prepare to make 1 mL 5000 2-mL prefilled syringes. 19. From the following formula for an oral Hylan Polymers 16 mg electrolyte solution, calculate the amount Sodium Chloride 17 mg of each ingredient required to prepare 240 Disodium Hydrogen mL of the solution. Phosphate 0.32 mg Sodium Dihydrogen Sodium 45 mEq Phosphate 0.08 mg Potassium 20 mEq Water for Injection ad 2 mL Chloride 35 mEq Citrate 30 mEq 16. From the following formula for gas- Dextrose 25 g tric lavage prior to colonoscopy, calcu- Water ad 1000 mL late the quantity of sodium bicarbonate needed to prepare 100 liters of the for- mula.  CHAPTER 16 REDUCING AND ENLARGING FORMULAS 285 ANSWERS TO PRACTICE PROBLEMS 1. 6.25 11. 30 g ciprofloxacin 2. 360 12. 2.7 g progesterone 36 g polyethylene glycol 3350 3. 0.568 g methylparaben 108 g polyethylene glycol 1000 0.341 g propylparaben 22.7 g sodium lauryl sulfate 13. 63.72 g methyl salicylate 272.4 g propylene glycol 36 g menthol 567.5 g stearyl alcohol 3.6 g Eucalyptus oil 567.5 g white petrolatum 256.68 g hydrophilic ointment ad 2270 g or 5 lb. purified water 14. 0.6 g promethazine hydrochloride 4. 700 g sulfacetamide sodium 0.48 g ascorbyl palmitate 14 g prednisolone acetate 2.4 g white wax 56 mg phenyl mercuric acetate 44.52 g cocoa butter 70 g mineral oil 15. 80 g hylan polymers 6215.944 g white petrolatum 85 g sodium chloride 5. 75 mg erythromycin lactobionate 1.6 g disodium hydrogen phosphate 15 mg dexamethasone sodium phosphate 0.4 g sodium dihydrogen phosphate 0.375 mL glycerin q.s. ad 10,000 mL water for injection q.s. ad 15 mL sterile water for injection 16. 42 g sodium bicarbonate 6. 600 g pegfilgrastim 17. 500 mg ergotamine tartrate 3000 g sorbitol 25 g caffeine 2 g polysorbate 20 62.5 mg hyoscyamine sulfate 7. 576.923 g calcium carbonate 15 g pentobarbital sodium 115.385 g magnesium oxide 459.44 g FATTIBASE 461.539 g sodium bicarbonate 18. 540 g antipyrine 346.154 g bismuth subcarbonate 140 g benzocaine 8. 33.6 g benzocaine ad 10 L dehydrated glycerin 9. 10 g estriol 19. 10.8 mEq sodium 1.25 g estrone 4.8 mEq potassium 1.25 g estradiol 8.4 mEq chloride 1 kg polyethylene glycol 1450 7.2 mEq citrate 1 kg polyethylene glycol 3350 6 g dextrose ad 240 mL water 10. (d) 45 g alefacept REFERENCES 1. International Journal of Pharmaceutical Compounding 2000;4:376. 2. International Journal of Pharmaceutical Compounding 1998;2:51. 3. International Journal of Pharmaceutical Compounding 2003;7:215. 4. International Journal of Pharmaceutical Compounding 1998;2:443. 5. International Journal of Pharmaceutical Compounding 1998;2:56. 6. International Journal of Pharmaceutical Compounding 2002;6:452. 7. NEULASTA, Product Literature. Thousand Oaks, CA: Amgen, Inc., 2008. 8. International Journal of Pharmaceutical Compounding 1997;1:187. 9. AMEVIVE, Product Literature. Deerfield, IL: Astellas Pharma US Inc., 2008.