CHAPTER 2 Pharmaceutical Calculations
SYSTEMS OF MEASURE
Summary of conversion between metric, apothecaries’ and avoirdupois systems:
Per the United States Pharmacopeia, 1 grain = 64.8 mg.
METRIC SYSTEM
Prefixes
| kilo- | 103 | 1 thousand (1000) times the basic unit |
| hecto- | 102 | 1 hundred (100) times the basic unit |
| deka- | 10 | 1 ten (10) times the basic unit |
| deci- | 10−1 | 1 tenth (0.1) times the basic unit |
| centi- | 10−2 | 1 hundredth (0.01) times the basic unit |
| milli- | 10−3 | 1 thousandth (0.001) times the basic unit |
| micro- | 10−6 | 1 millionth times the basic unit |
| nano- | 10−9 | 1 billionth times the basic unit |
| pico- | 10−12 | 1 trillionth times the basic unit |
INTERPRETATION OF MEDICATION ORDERS
Example 1:
A prescription for prednisone 5 mg should be taken as follows:
Example 1:
How many grams of drug should be used to prepare 120 grams of a 2% w/w solution in water?
Example 2
What is the percentage strength (w/v) of a solution of drug if 40 mL contain 5 grams?
Example
Solution
The coal tar (active ingredient) is added to a diluent (petroleum) currently containing no coal tar.
Example
First, determine how many kcal the patient needs from each component:
Next, convert these kcals into grams:
Then, calculate how many milliliters are needed from each stock solution:
For females
If the individual is obese or not within 30% of their ideal body weight, other methods of calculating creatinine clearance should be used. Ideal body weight (IBW) or adjusted body weight (ideal body weight plus 40% of obese weight) instead of actual body weight in the Cockcroft-Gault equation will provide a better estimate of creatinine clearance.
CALCULATIONS FOR PEDIATRIC DOSES
Various pediatric formulas have been used historically to calculate APPROXIMATE pediatric dosages.
Ansel H., Stoklosa M. Pharmaceutical Calculations, ed 12. Baltimore, MD: Lippincott Williams & Wilkins, 2005.
Bhatt S.H.L. Aminoglycoside Pharmacokinetics and Therapeutics. MCPHS Boston Campus, MA: White Hall, 2006.
Institute of the Certification of Pharmacy Technicians (ICPT). ExCPT Exam for the Certification of Pharmacy Technicians. Available at http://www.nationaltechexam.org/pdf/math_questions-answers070618.pdf Accessed December 24, 2008
London, Eastern and South East Specialist Pharmacy Services, Available at http://www.londonpharmacy.nhs.uk/educationandtraining/prereg/supportMaterial/calculations/download/Calculations%20WorkBook%202005.pdf Accessed December 24, 2008
Pearson J., Powers M. Systematically Initiating Insulin. The Staged Diabetes Management Approach. Diabetes Educ. 2006;32(Suppl 1):23s.
Shargel L. Applied Biopharmaceutics & Pharmacokinetics. New York: McGraw-Hill Medical Publishing Division, 2005;43-46.
Zatz J. Pharmaceutical Calculations, ed 4, Hoboken, NJ: John Wiley & Sons, Inc; 2005:30-33.
Mosteller R.D. Simplified Calculation of Body Surface Area. N Engl J Med. 1987;317:1098. (letter)
REVIEW QUESTIONS
(Answers and Rationales on page 313.)
1. A patient is prescribed 10 mEq of potassium daily. The source of potassium chloride in the pharmacy is 5 mEq/mL in 1 mL vials. How many vials per day is needed for the patient?
2. How much elemental iron is present in every 150 mg of ferrous sulfate (FeSO4 • 7H2O)? (Atomic weights are iron = 55.9; sulfur = 32.1; oxygen = 16.0; and hydrogen = 1.0. Iron has valences of +2 and +3)
3. A 130-lb patient has a creatinine clearance rate of 40 mL/min. Assuming Drug X is eliminated exclusively by renal mechanisms, what maintenance dose should be administered if the normal maintenance dose is 3 mg/lb of body weight?
4. An IV medication is available as 3.5 g/ 500 mL with a strength calculation of 0.25 mg/kg/min is prescribed to a 130-lb patient. What is the infusion rate in mL/hour?
9. A patient is prescribed 20 mEq of potassium chloride daily. The source of potassium chloride in the pharmacy is 2 mEq/ mL in 20 mL vials. How many mL per day are needed for this patient?
10. A patient is prescribed 10 mEq of potassium chloride daily. The source of potassium chloride in the pharmacy is 2 mEq/ mL in 20 mL vials. How many mL per day are needed for this patient?
12. What volume of diluent (assume sterile water) is needed to make an isotonic solution from 0.45 g of sodium chloride?
13. The ratio strength of a solution is 1:900 (w/v). What is the percent weight by volume [(w/v)%] of the solution?
14. The ratio strength of a solution is 1:5000 (w/v). What is the percent weight by volume [(w/v)%] of the solution?
15. A vial of tobramycin sulfate contains 40 mg of drug per mL of injection. A patient was given 0.5 mL. How much tobramycin sulfate was administered?
19. JK is a 42 year-old woman who has a prescription for 32 mEq of oral potassium chloride. However, your pharmacy only has 600 mg controlled-release potassium chloride tablets in stock. How many tablets are required each day to provide this dose? (MW = 75)
20. If a patient has a temperature of 102.2° F, what is the patient’s temperature in degrees Celsius?
21. If 500 mL of a 15% (v/v) solution of methyl salicylate in alcohol is diluted to 1500 mL, what will be the percentage strength (v/v)?
24. What is the percent weight by volume [%(w/v)] if 250 grams of dextrose is dissolved in 300 mL of water to make a final volume of 500 mL?
34. A pharmacist has 25 mL of 0.5% gentian violet solution. What will be the final ratio strength if he or she dilutes this solution to 600 mL with purified water?
35. An order is written for 1 g of lidocaine in 250 mL of D5W to infuse at 60 mg/hr. What is the correct infusion in (mL/hr)?
36. An order is written for 25,000 units of heparin in 250 mL of D5W to infuse at 17 mL/hr. How many units of heparin will the patient receive in 6 hours?
37. An order calls for 2.5 million units of aqueous penicillin. How many milliliters are needed if the vial concentration is 500,000 units/mL?
38. How many milliliters are needed for 5 million units of penicillin if the vial concentration is 1 million units per mL?
39. Valproic acid syrup comes in a 250 mg/5 mL concentration. How many mg are present in 7.5 mL of solution?
43. How many milliliters contain 2.5 g of cephalothin if the concentration of the solution is 1 g/4.5 mL?
47. The unit of weight measurement that is the same in both the apothecaries’ and avoirdupois systems is the?
49. Calculate the drip rate for 120 mL of IV fluids to be given over a half hour via an IV set that delivers 15 gtt/mL.
50. If a patient is given IV fluids at a rate of 25 gtt/min over 1 hour, how much fluid will be administered? The drop factor is 15 gtt/ml.
51. In order to achieve better pain control, codeine phosphate 0.7 mL SC × 1 is ordered for a patient. The injectable form of codeine phosphate is available in a concentration of 50 mg/mL. How much codeine will this patient receive in this dose?
52. Morphine is ordered for a patient, and the nurse gives him 1.9 mL from a vial with a concentration of 40 mg/2.5 mL. How much morphine was the patient given?
53. The vial of hydromorphone that you have in stock has a concentration of 1.5 mg/0.5 mL. If the patient is given 0.7 mL, how much hydromorphone did she receive?
54. What is the concentration (in percent) of a solution containing 20 mEq of potassium chloride per 15 mL of liquid? (MW = 75)
55. Diazepam is to be administered by the IV route to an adult patient. It is given at a rate of 5 mg/min over 90 seconds. How much diazepam is given to this patient?
56. How many milligrams of morphine were given to a patient who received 6.2 mL of a 5 mg/mL solution?
57. A nurse wants to give 300 mcg of levothyroxine IV to a patient, from a vial containing 0.4 mg/mL. How many milliliters should be given to the patient?
58. A patient is to take 2.6 mL of oral furosemide, and each teaspoon contains 40 mg. How much furosemide will the patient be taking in their 2.6 mL dose?
59. What is the percent weight=weight (%[w/w]) if 250 grams of dextrose is dissolved in 300 mL of water to make a final volume of 500 mL?
61. If the adult dose of a drug is 200 mg, what is the estimated dose for a child with a BSA of 0.8 m2, using the BSA estimation method?
62. If Lanoxin Pediatric Elixir contains 0.1 mg of digoxin per mL, how many mcg of digoxin are in 6 mL elixir?
63. What is the percentage of alcohol in a mixture of 200 mL of 95% v/v alcohol, 1000 mL of 70% v/v alcohol, and 200 mL of 80% v/v alcohol?
64. A TPN order requires 500 mL of D5W. How many mL of D50W should be used if the D5W is not available?
65. How much sodium chloride is needed to make the following prescription isotonic given E value for zinc sulfate is 0.15?
66. How much elemental iron is present in 500 mg of ferrous sulfate (FeSO4 • 7H2O) with atomic weights are Fe = 55.9; sulfur = 32.1; oxygen = 16.0; and hydrogen = 1.0. Iron has valences of +2 and +3)?
67. What will be the final ratio strength of a solution if one wishes to dilute 100 mL of 0.5% gentian violet solution to 1250 mL with purified water?
68. How many beclomethasone (Qvar) inhalers should be dispensed to provide a 90-day supply? The recommended dose is 168 mcg BID. The commercial inhaler delivers 42 mcg per metered dose and contains 200 inhalations
69. If 6.25 g of boric acid are dissolved in sufficient alcohol to make a total volume of 100 mL, what is the strength of boric acid in the solution in mg/mL?
70. If 50 mL of 4% (w/v) Xylocaine solution are added to 100 mL bag of D5W injection, what is the percentage strength (w/v) of Xylocaine in the final product?
83. If the reorder point for simvastatin 40 mg is 2 and the maximum is 5, how many bottles should be ordered if there is 1 bottle of simvastatin 40 mg?
84. You have a bottle of 1 g amoxicillin powder for oral suspension. How many mL of purified water are needed to prepare a 125 mg/5 mL suspension?
85. How much dilutant needs to be added to a 500 mg vial of Merrem to obtain a concentration of 50 mg/mL?
86. A patient is to receive 1000 mL of solution over 8 hours. If the administration set delivers 20 gtt/mL, at how many gtt/min should the solution be infused?
87. A solution is to be administered by IV infusion at a rate of 100 mL/hr. How many gtt/min should be infused if the administration set delivers 20 drops/mL?
88. A patient is to receive 1 L of a normal saline by IV infusion over 12 hours. What is the rate of infusion expressed as gtt/min if the infusion set delivers 20 gtt/mL?
89. An IV infusion for a 22-lb child calls for 4 mcg/kg/min at a rate of 1.2 mL/hr. How many milligrams of a drug are required in a 100-mL infusion solution to supply the required dose?
90. If 100 g dextrose is dissolved in 100-mL water to make a final volume of 150 mL, what is the %w/v of this solution?
91. What is the %w/v concentration of a 100 mL of amoxicillin oral suspension containing 150 mg/5 mL?
94. The required dose for a 110-lb patient is 0.5 mg/kg/min. If the concentration of the medication is 1 g/100 mL, what is the infusion rate in mL/hr?
95. If 2.54 g of a drug is used to make 1000 tablets, roughly how many milligrams will 60 tablets contain?
98. If the required dose is 1 tsp bid, how long will an 180-mL bottle of clemastine fumerate syrup 0.5 mg/5 mL last?
100. The recommended daily adult dose of a medication is 2 mg/kg body weight in 4 divided doses. What is the daily dose for a person weighing 110 lb?
101. Kefzol is ordered at a dose of 30 mg/kg/day divided three times daily for an elderly female patient who weighs 88 lbs. How much Kefzol will be given to her daily?
102. How much Kefzol would have to be drawn up from the vial and injected into an IV bag to make one dose of Kefzol for the patient in question 101? The vial you have on hand was compounded to a concentration of 325 mg/mL.
103. A bag with 250 mL of NS will be infused over 2 hours using a microdrip set (60 gtt/mL). What is the flow rate in drops per minute?
104. An IV bag with 1250 mL of IV fluids is to be infused over 3 hours with a 15 gtt/mL set. How many milliliters will be infused over each hour?
105. A 240 lb male patient is prescribed zidovudine at a dose of 2 mg/kg three times daily. How much zidovudine will this patient receive daily?
106. A patient weighing 155 lbs is ordered dobutamine at a rate of 5 mcg/kg/min. When the drug is admixed, 200 mg of dobutamine was put into a 500 mL bag of normal saline (NS). What is the final concentration of the solution in mcg/mL?
107. The required dose of Drug X for a 150-lb patient is 1 mg/kg/min. If the concentration of the medication is 5 g/100 mL, what is the infusion rate in mL/hr?
109. If a solution contains 1 g of sodium chloride dissolved in 100 mL of D5W, how many milliosmoles are present? (Na = 23; Cl = 35.5; hydrous dextrose = 198)
110. An order is received in the pharmacy for an irrigation solution of 0.25% w/v acetic acid. The acetic acid in stock is 99.9% w/w, and must be added to 128 oz of purified water. How many grams of 99.9% w/w acetic acid must be added to the purified water in order to prepare the final irrigation solution?
111. One gram of a given chemical is soluble in 10 mL of alcohol. What is the specific gravity of alcohol if a saturated solution is made with this chemical into an 11.1% w/w solution?
113. A technician is preparing a potassium chloride infusion for a hypokalemic patient. The IV bag contains 250 mL of normal saline and 5.86 g of KCl (KCl molecular weight = 74.6). In the final infusion preparation, how many milliequivalents of potassium chloride are present?
114. What is the volume of distribution of a drug with a clearance of 9 L/hr, F = 50, and an elimination half life of 7.8 hours?
115. How many mL of tetracycline suspension 250 mg/5 mL must be given in order for the patient to receive 150 mg?
116. An acidic drug has a pKa of 5.4. What percentage of the drug is ionized in urine with a pH of 6.0?
118. A patient is to receive 2 mg/min of labetalol hydrochloride that has been prepared by adding 200 mg of labetalol hydrochloride injection to 250 mL of D5W to attain a final concentration of 2 mg/3 mL. How many milliliters per hour should the nurse infuse?
119. A patient is to receive 4 L of D5NS over 24 hours. If the IV tubing has a drip factor of 15 gtt/mL, what is the drip rate?
122. The hydrogen ion concentration of a topical solution is 1 × 10−8. What is the pH of this solution?
124. A patient is prescribed 10 mEq KCl once daily to compensate for the potassium wasting effects of furosemide. How many mg of KCl is in each dose? (MW of KCl = 74.5)
125. CH is a 72-year-old woman who requires empiric vancomycin treatment for pneumonia. She is 5′ 2″ and weighs 125 lbs. Her SCr is 1.2 mg/dL. What is her calculated creatinine clearance?
126. JW is a 64-year-old man with a prior medical history positive for hypertension and poorly controlled diabetes. He presents to the ED today complaining of fever and chills that have progressively worsened over the last 24 hours. His physical exam is unremarkable with the exception of an oozing foot ulcer. The medical team wants to begin empiric antibiotic treatment including an aminoglycoside. What is his calculated creatinine clearance? (height = 5′ 8″, weight = 247 lbs, SCr = 1.1 mg/dL)
127. A patient’s labs show serum calcium of 8.7 mg/dL and serum albumin of 3.2 g/dL. What is her corrected calcium concentration?
128. How many milliliters of water should be added to 100 mL of a 1:125 (w/v) solution to obtain a solution such that 25 mL diluted to 100 mL will yield a 1:4000 strength solution?
129. Using the following WBC and differential, calculate this patient’s absolute neutrophil count (ANC). WBC: 2.0 × 103/mm3
130. What is the pH of a buffer solution containing 0.25 M of acetic acid and 0.75 M of sodium acetate? (Ka = 1.75 × 10-5)
131. A drug is available as both a 150-mg tablet and 100 mg capsule. The AUC for the tablet was calculated to be 76.3 mg.hr/L and for the capsule 84.2 mg.hr/L. What is the relative bioavailability of the tablet with respect to the capsule?
133. TJ is a 23-year-old woman who has a long history of poorly controlled asthma. She is admitted to the hospital with a severe asthma attack is is started on aminophylline. She is currently receiving a continuous infusion of aminophylline at 40 mg/hour. The patient has not experienced any adverse effects and is responding well to therapy. Her steady-state theophylline concentration is 12.6 mg/mL. What dose of oral theophylline sustained-release formulation may she be converted to?
