Pharmaceutical Calculations: Reducing and Enlarging Formulas Danielle DelVillano, Pharm.D.

Objectives 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

Determining the “Factor” To go from a larger to smaller quantity, or vice versa, determine the “factor” by which to reduce or enlarge the formula Ex. USP recipe is for 1000 mL but you only wish to make 100 mL of solution Quantity of the formula desired = Factor Quantity of the formula given Then multiply the quantity of each ingredient in the formula given by the factor to determine the amount of each ingredient needed to prepare the desired compund

Example 1 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 (quantity desired) = 0.06 (factor) 1000 mL (quantity given) 6 g x 0.06 = 0.36 g of drug needed

Problem 1: Solve by using factor 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 solutionn, to make 1000 mL

Problem 1: Solve by using factor 240 mL (quantity desired) = 0.24 (factor) 1000 mL (quantity required) Calamine: 80 g x 0.24 = 19.2 g Zinc Oxide: 80 g x 0.24 = 19.2 g Glycerin: 20 g x 0.24 = 4.8 g Bentonite: 250 mL x 0.24 = 60 mL Calcium hydroxide: to make 240 mL

Problem 1: Solve by Using Dimensional Analysis Calamine 80 g x 240 mL = 19.2 g 1000 mL Zinc Oxide 80 g x 240 mL = 19.2 g Glycerin 20 mL x 240 mL = 4.8 mL Bentonite 250 mL x 240 mL = 60 mL Calcium hydroxide to make 240 mL

Problem 2 From the following formula for an estradiol vaginal gel, calculate the quantity of each ingredient required to prepare 1 lb of gel. Estradiol 200 g Polysorbate 80 1 g Methylcellulose Gel, 2% 95 g

Problem 2: Solve Using a Factor Estradiol - 306.8 g Polysorbate 80 – 1 g Methylcellulose Gel, 2% - 95 g

Problem 2: Solve Using Dimensional Analysis Estradiol - 306.8 g Polysorbate 80 – 1 g Methylcellulose Gel, 2% - 95 g

Problem 3: Proportional 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 Hydrophillic Ointment 50 parts

Problem 3: Proportional Parts Total number of parts: 5 + 10 + 50 = 65 parts So 1000g will contain 65 parts Coal Tar 5 parts = x g 65 parts 1000 g x = 76.92 g Zinc Oxide 10 parts = x g y = 153.85 g Hydrophillic Ointment 50 parts = x g z = 769.23 g

Additional Problems

Chapter 16 Problem 5 Calculate the quantity of each ingredient needed to prepare 15 mL of the following ophthalmic solution: Eryromycin lactobionate 500 mg Dexamethasone sodium phosphate 100 mg Glycerin 2.5 mL Sterile Water for Injection, a.d. 100 mL Erythromycin – 75 mg Dexamethasone – 15 mg Glycerin – 0.375 mL Sterile water qs ad 15 mL

Chapter 16 Problem 5

Chapter 16 Problem 10 According to the literature, when the product Amevive (alefacept) is reconstituted with sterile water for injection it contains the following in each 0.5 mL Alefacept 7.5 mg Sucrose 12.5 mg Glycine 5 mg Sodium citrate, dihydrate 3.6 mg Citric acid, monohydrate 0.06 mg

Chapter 16 Problem 10 continuted How much alefacept would be needed to manufacture a 5000 batch of vials for reconstitution? A) 12.5 mg B) 31.25 g C) 37.5 g D) 45 g D) 45 g

Chapter 16 Problem 10

Chapter 16 Problem 11 The formula for a ciprofloxacin otic drop is given in the literature as follows: Ciprofloxacin 1 g Propylene glycol 50 mL Glycerin qs ad 100 mL How many grams of ciprofloxacin would be required to prepare 200 15 mL bottles of the ear drop? 30 g

Chapter 16 Problem 11

Questions

Reference Ansel, H. C. (2009) Phamaceutical Calculations (13th Ed.). Philadelphia:Lippincott Williams & Wilkins, and Wolters Kluwer Publishers