Pharmaceutical Calculations Reducing and Enlarging Formulas Danielle Del

Pharmaceutical Calculations: Reducing and Enlarging Formulas Danielle Del. Villano, Pharm. D. 1

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 2

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 m. L but you only wish to make 100 m. L of solution Quantity of the formula desired Quantity of the formula given = Factor • 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 3

Example 1 • If a formula for 1000 m. L contains 6 g of a drug, how many grams of drug are needed to prepare 60 m. L of the formula? 60 m. L (quantity desired) = 0. 06 (factor) 1000 m. L (quantity given) 6 g x 0. 06 = 0. 36 g of drug needed 4

Problem 1: Solve by using factor • From the following formula, calculate the quantity of each ingredient required to make 240 m. L of calamine lotion – Calamine – Zinc Oxide – Glycerin – Bentonite magma – Calcium hydroxide solutionn, to make 80 g 20 g 250 m. L 1000 m. L 5

Problem 1: Solve by using factor 240 m. L (quantity desired) 1000 m. L (quantity required) Calamine: 80 g x Zinc Oxide: 80 g x Glycerin: 20 g x Bentonite: 250 m. L Calcium hydroxide: = 0. 24 (factor) 0. 24 = 19. 2 g 0. 24 = 4. 8 g x 0. 24 = 60 m. L to make 240 m. L 6

Problem 1: Solve by Using Dimensional Analysis Calamine 80 g x 240 m. L 1000 m. L Zinc Oxide 80 g x 240 m. L 1000 m. L Glycerin 20 m. L x 240 m. L 1000 m. L Bentonite 250 m. L x 240 m. L 1000 m. L Calcium hydroxide to make 240 m. L = 19. 2 g = 4. 8 m. L = 60 m. L 7

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 – Polysorbate 80 – Methylcellulose Gel, 2% 200 g 1 g 95 g 8

Problem 2: Solve Using a Factor 9

Problem 2: Solve Using Dimensional Analysis 10

Problem 3: Proportional Parts • From the following formula, calculate the quantity of each ingredient required to make 1000 g of the ointment – Coal Tar – Zinc Oxide – Hydrophillic Ointment 5 parts 10 parts 50 parts 11

Problem 3: Proportional Parts Total number of parts: 5 + 10 + 50 = 65 parts So 1000 g will contain 65 parts Coal Tar 5 parts = xg 65 parts 1000 g x = 76. 92 g Zinc Oxide 10 parts 65 parts y = Hydrophillic Ointment 50 parts 65 parts z = xg 1000 g = 153. 85 g xg 1000 g = 769. 23 g 12

Additional Problems 13

Chapter 16 Problem 5 • Calculate the quantity of each ingredient needed to prepare 15 m. L of the following ophthalmic solution: – Eryromycin lactobionate – Dexamethasone sodium phosphate – Glycerin – Sterile Water for Injection, a. d. 500 mg 100 mg 2. 5 m. L 100 m. L 14

Chapter 16 Problem 5 15

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 m. L – Alefacept – Sucrose – Glycine – Sodium citrate, dihydrate – Citric acid, monohydrate 7. 5 mg 12. 5 mg 3. 6 mg 0. 06 mg 16

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 17

Chapter 16 Problem 10 18

Chapter 16 Problem 11 • The formula for a ciprofloxacin otic drop is given in the literature as follows: – Ciprofloxacin – Propylene glycol – Glycerin qs ad 1 g 50 m. L 100 m. L • How many grams of ciprofloxacin would be required to prepare 200 15 m. L bottles of the ear drop? 19

Chapter 16 Problem 11 20

Questions 21

Reference • Ansel, H. C. (2009) Phamaceutical Calculations (13 th Ed. ). Philadelphia: Lippincott Williams & Wilkins, and Wolters Kluwer Publishers 22