Unit Conversions for Dosing - Pharmacology

1. A compounding pharmacy has 1.2 grams of a bulk chemical powder. A technician is tasked with preparing capsules, each containing 20 mg of the chemical. If a 5% loss of the powder is anticipated during the encapsulation process, what is the maximum number of complete capsules that can be prepared?
   Answer: 57 First, convert the starting mass of the powder to milligrams: 1.2 g 1000 mg/g = 1200 mg. Next, calculate the amount of powder that will be available after the 5% loss. This can be done by calculating the loss (1200 mg 0.05 = 60 mg) and subtracting it (1200 mg - 60 mg = 1140 mg), or by calculating the remaining percentage (1200 mg * 0.95 = 1140 mg). Finally, divide the available powder by the amount per capsule to find the number of capsules: 1140 mg / 20 mg/capsule = 57 capsules. Since the result is a whole number, 57 complete capsules can be prepared.
2. A patient experiencing an anaphylactic reaction requires an intramuscular injection of epinephrine. The order is for 0.01 mg/kg. The patient weighs 165 lbs. The epinephrine is available in an ampule with a concentration of 1:1,000. How many milliliters should be administered? (Round to the nearest tenth).
   Answer: 0.8 mL First, convert the patient's weight from pounds to kilograms: 165 lbs / 2.2 lbs/kg = 75 kg. Next, calculate the required dose in mg: 0.01 mg/kg 75 kg = 0.75 mg. Then, interpret the concentration. A 1:1,000 solution means 1 g of drug in 1,000 mL of solution. Convert this to mg/mL: (1 g / 1,000 mL) (1000 mg / 1 g) = 1 mg/mL. Finally, calculate the volume to administer: 0.75 mg / 1 mg/mL = 0.75 mL. Rounding to the nearest tenth gives 0.8 mL.
3. A patient is prescribed 0.05 mg of levothyroxine daily. The pharmacy only has 25 mcg tablets in stock. If the prescription is written for a 3-month supply (90 days), how many tablets should be dispensed?
   Answer: 180 tablets First, convert the prescribed daily dose from milligrams (mg) to micrograms (mcg) to match the tablet strength: 0.05 mg 1000 mcg/mg = 50 mcg. Next, determine the number of tablets needed per day: 50 mcg/day / 25 mcg/tablet = 2 tablets/day. Finally, calculate the total number of tablets for a 90-day supply: 2 tablets/day 90 days = 180 tablets.
4. A pharmacist needs to prepare 500 mL of a 0.04% (w/v) antiseptic solution. The pharmacy stocks a concentrated solution of the antiseptic at a strength of 1:20 (w/v). How many milliliters of the concentrated stock solution are required to prepare the final product?
   Answer: 4.0 mL First, calculate the total mass of antiseptic needed for the final solution. A 0.04% w/v solution is 0.04 g per 100 mL. For 500 mL, the mass needed is (0.04 g / 100 mL) 500 mL = 0.2 g. Next, determine the concentration of the stock solution. A 1:20 w/v solution means 1 g per 20 mL. To find the volume of the stock solution that contains 0.2 g of antiseptic, use a proportion: (1 g / 20 mL) = (0.2 g / x mL). Solving for x gives x = 0.2 20 = 4.0 mL.
5. An order is written for 2.5 million units of Penicillin G to be administered intravenously. The pharmacy supplies a vial with a concentration of 500,000 units/mL. This dose is to be infused over 45 minutes. At what rate in mL/hour should the infusion pump be set?
   Answer: 6.7 mL/hr When you encounter IV infusion rate calculations, you need to work through three key steps: determine the volume needed, convert time units appropriately, and calculate the hourly rate. First, find the total volume required. You have 2.5 million units ordered and a concentration of 500,000 units/mL. Using dimensional analysis: $\frac{2,500,000 \text{ units}}{500,000 \text{ units/mL}} = 5 \text{ mL}$ Next, convert the infusion time to hours since pump rates are expressed in mL/hr. The 45-minute infusion equals $\frac{45}{60} = 0.75 \text{ hours}$ Finally, calculate the infusion rate: $\frac{5 \text{ mL}}{0.75 \text{ hr}} = 6.67 \text{ mL/hr}$, which rounds to 6.7 mL/hr. Looking at the incorrect options: Choice A (5.0 mL/hr) represents the total volume needed but ignores the time calculation entirely. Choice B (8.3 mL/hr) likely results from incorrectly converting minutes to hours, perhaps using 36 minutes instead of 45. Choice C (3.8 mL/hr) suggests an error in the initial dose calculation, possibly using the wrong concentration conversion. For infusion rate problems, always set up your dimensional analysis carefully and double-check your time conversions. Remember that pump rates are universally expressed in mL/hr, so any time given in minutes must be converted to hours by dividing by 60. Keep your calculator handy and verify that your final answer makes logical sense given the volume and timeframe.
6. A patient is prescribed an ophthalmic solution with instructions to instill 1 drop into the left eye every 6 hours. The solution concentration is 0.5% (w/v), and the dropper is calibrated to deliver 25 drops/mL. What is the total mass of drug in micrograms (mcg) delivered to the patient over a 24-hour period?
   Answer: 800 mcg First, calculate the number of doses in 24 hours: 24 hours / 6 hours/dose = 4 doses. Total drops per day: 1 drop/dose 4 doses = 4 drops. Next, convert drops to volume: 4 drops / 25 drops/mL = 0.16 mL. Now, determine the concentration in mg/mL. A 0.5% w/v solution is 0.5 g/100 mL, which is 500 mg/100 mL, or 5 mg/mL. Calculate the total daily dose in mg: 0.16 mL 5 mg/mL = 0.8 mg. Finally, convert mg to mcg: 0.8 mg * 1000 mcg/mg = 800 mcg.
7. A patient is prescribed a topical cream containing 0.025% (w/w) of an active pharmaceutical ingredient. The patient is instructed to apply approximately 1.5 grams of the cream to the affected area twice daily. How many milligrams of the active ingredient does the patient apply over a 5-day period?
   Answer: 3.750 mg First, interpret the concentration: 0.025% w/w means 0.025 g of drug per 100 g of cream. Calculate the amount of drug in mg per gram of cream: (0.025 g / 100 g) 1000 mg/g = 0.25 mg of drug per gram of cream. Next, calculate the mg of drug per application: 1.5 g cream/application 0.25 mg/g = 0.375 mg/application. Then, calculate the total daily dose: 0.375 mg/application 2 applications/day = 0.75 mg/day. Finally, calculate the total amount over 5 days: 0.75 mg/day 5 days = 3.75 mg.
8. A patient requires a continuous IV infusion of a drug at a rate of 3 mg/min. The pharmacy supplies a solution of this drug with a concentration of 0.2% (w/v). At what rate in mL/hr should the infusion pump be set?
   Answer: 90 mL/hr First, convert the percentage strength to mg/mL. A 0.2% w/v solution means 0.2 g of drug per 100 mL of solution. Convert grams to milligrams: 0.2 g 1000 mg/g = 200 mg. So, the concentration is 200 mg/100 mL, which simplifies to 2 mg/mL. Next, calculate the required flow rate in mL/min: (3 mg/min) / (2 mg/mL) = 1.5 mL/min. Finally, convert the flow rate from mL/min to mL/hr: 1.5 mL/min 60 min/hr = 90 mL/hr.
9. A patient is prescribed a fentanyl transdermal patch that delivers 50 mcg/hr. The patch is to be worn continuously and changed every 72 hours. How many milligrams of fentanyl will the patient absorb from one patch over the entire 72-hour period?
   Answer: 3.6 mg Transdermal patch calculations require careful attention to units and time periods. When you see dosing rates given per hour, you need to multiply by the total time to find the cumulative dose. The patch delivers 50 mcg/hr and is worn for 72 hours. To find the total dose: $50 \text{ mcg/hr} \times 72 \text{ hr} = 3,600 \text{ mcg}$ Since the answer choices are in milligrams, convert by dividing by 1,000: $3,600 \text{ mcg} \div 1,000 = 3.6 \text{ mg}$ Looking at the wrong answers: Choice A (1.2 mg) represents a calculation error where someone might have used 24 hours instead of 72 hours (50 × 24 ÷ 1,000 = 1.2). Choice B (36.0 mg) occurs when you forget to convert from micrograms to milligrams—this is the answer in the wrong units (3,600 mcg written as 36.0 mg). Choice C (12.0 mg) could result from miscalculating the time period or making an arithmetic error in the conversion. The key strategy for transdermal patch problems is to work systematically: identify the rate, multiply by the total time period, then convert units carefully. Always double-check your unit conversions—micrograms to milligrams is a common source of errors on pharmacology exams. Remember that 1 mg = 1,000 mcg, and pay close attention to whether answers are requested in mg or mcg.
10. A patient is tapering off a liquid medication. The starting regimen is 2 teaspoons BID. The instructions are to decrease the total daily dose by 1 mL every other day. The medication concentration is 25 mg/5 mL. What is the patient's total daily intake in milligrams on Day 5 of the taper?
    Answer: 90 mg When you encounter medication tapering calculations, you need to track three key variables: initial dose, tapering schedule, and concentration. Work systematically through each day to avoid calculation errors. Start by converting the initial dose to milliliters. The patient takes 2 teaspoons BID (twice daily). Since 1 teaspoon = 5 mL, the initial daily dose is $2 \times 5 \text{ mL} \times 2 = 20 \text{ mL}$. The instructions specify decreasing by 1 mL every other day, so reductions occur on Days 2, 4, 6, etc. Now track the daily volumes: Day 1 = 20 mL, Day 2 = 19 mL, Day 3 = 19 mL, Day 4 = 18 mL, Day 5 = 18 mL. On Day 5, the patient takes 18 mL total. Convert to milligrams using the concentration. With 25 mg/5 mL, you have $\frac{25 \text{ mg}}{5 \text{ mL}} = 5 \text{ mg/mL}$. Therefore, 18 mL contains $18 \times 5 = 90 \text{ mg}$. Choice A (85 mg) represents the dose after one additional taper step that hasn't occurred yet. Choice B (100 mg) corresponds to the Day 1 dose, suggesting confusion about when tapering begins. Choice C (95 mg) reflects the Day 3 dose, indicating an error in tracking which days have reductions. Study tip: For tapering calculations, always create a day-by-day chart showing the volume changes first, then convert to milligrams at the end. This prevents mixing up units and helps you track the "every other day" pattern accurately.
11. A patient uses U-100 insulin, which has a concentration of 100 units/mL. The prescribed dose is 35 units subcutaneously each morning. The insulin is supplied in 10 mL vials. After starting a new vial, on which day will the patient need to open a new vial?
    Answer: Day 29 First, calculate the total number of insulin units in one vial: 100 units/mL * 10 mL/vial = 1000 units/vial. Next, calculate how many full days the vial will last by dividing the total units by the daily dose: 1000 units / 35 units/day = 28.57 days. This means the vial contains enough insulin for 28 full days. The patient will exhaust the supply during Day 29, so they will need to open a new vial on Day 29.
12. A patient is receiving a dobutamine infusion at a rate of 15 mL/hr. The IV bag was prepared by adding 500 mg of dobutamine to 250 mL of normal saline. The patient weighs 198 lbs. Calculate the dose the patient is receiving in mcg/kg/min.
    Answer: 5.6 mcg/kg/min Dosage calculations for IV infusions require a systematic approach to convert between different units while accounting for patient weight. You'll need to find the concentration of the solution, determine the actual drug delivery rate, and normalize it per kilogram of body weight. First, calculate the drug concentration: 500 mg dobutamine in 250 mL gives you 2 mg/mL. At an infusion rate of 15 mL/hr, the patient receives $15 \text{ mL/hr} \times 2 \text{ mg/mL} = 30 \text{ mg/hr}$. Next, convert the patient's weight: $198 \text{ lbs} ÷ 2.2 = 90 \text{ kg}$. Now convert the hourly dose to per-minute and per-kilogram: $30 \text{ mg/hr} ÷ 60 \text{ min} = 0.5 \text{ mg/min}$. Convert to micrograms: $0.5 \text{ mg/min} \times 1000 = 500 \text{ mcg/min}$. Finally, normalize per kilogram: $500 \text{ mcg/min} ÷ 90 \text{ kg} = 5.6 \text{ mcg/kg/min}$, confirming answer A. Answer B (2.8 mcg/kg/min) represents half the correct value, likely from incorrectly doubling the weight or halving the concentration. Answer C (9.3 mcg/kg/min) suggests using pounds instead of kilograms in the final calculation. Answer D (12.4 mcg/kg/min) indicates an error in unit conversion, possibly forgetting to convert mg to mcg or minutes to hours. Always work through dosage calculations step-by-step: concentration → delivery rate → weight conversion → final normalization. Double-check your unit conversions, especially lb to kg and mg to mcg.
13. A patient is instructed to prepare a foot soak using potassium permanganate tablets to create a 1:10,000 solution. The patient will prepare the soak in a basin containing 2 liters of water. If the pharmacy supplies 100 mg tablets, how many tablets are needed to prepare this solution?
    Answer: 2 tablets When you encounter dilution problems involving ratio concentrations like 1:10,000, you're working with parts per unit calculations where the first number represents the solute (drug) and the second represents the total solution volume. A 1:10,000 potassium permanganate solution means 1 gram of drug per 10,000 mL of total solution. To find how much drug you need for 2 liters (2,000 mL), set up a proportion: $\frac{1 \text{ gram}}{10,000 \text{ mL}} = \frac{x \text{ grams}}{2,000 \text{ mL}}$ Cross-multiplying: $x = \frac{1 \times 2,000}{10,000} = 0.2 \text{ grams} = 200 \text{ mg}$ Since each tablet contains 100 mg, you need: $\frac{200 \text{ mg}}{100 \text{ mg/tablet}} = 2 \text{ tablets}$ Answer A (2 tablets) is correct. Answer B (1 tablet) would only provide 100 mg, creating a 1:20,000 solution that's too weak. Answer C (4 tablets) gives 400 mg, making a 1:5,000 solution that's twice as strong as intended. Answer D (5 tablets) provides 500 mg, resulting in a 1:4,000 solution that's 2.5 times too concentrated. Study tip: For ratio dilutions, always convert the ratio to a fraction (1:10,000 = 1/10,000), then multiply by your desired volume to find the amount of drug needed. Remember that stronger solutions have smaller denominators in their ratios.
14. A patient is prescribed 1.5 grams of an antibiotic IV over 6 hours. The pharmacy dispenses a 500 mL IV bag containing 3 grams of the antibiotic in 0.9% sodium chloride. To deliver the prescribed dose over the specified time, at what rate in mL/min should the pump be set? (Round to one decimal place).
    Answer: 0.7 mL/min First, determine the volume of the solution that contains the prescribed dose. The bag contains 3 g in 500 mL. The prescribed dose is 1.5 g, which is half the total amount. Therefore, the volume to be infused is half the total volume: 500 mL / 2 = 250 mL. Next, convert the infusion time to minutes: 6 hours * 60 min/hour = 360 minutes. Finally, calculate the rate in mL/min: Rate = Volume / Time = 250 mL / 360 min ≈ 0.694 mL/min. Rounding to one decimal place gives 0.7 mL/min.
15. Based on the information in the passage, if a physician orders a dose of 300 mg, how many milliliters of the reconstituted solution should be administered?
    Answer: 1.50 mL The key is to first determine the final concentration of the reconstituted solution. The vial contains 2 grams (2000 mg) of drug, and the final volume after reconstitution is 10 mL. Therefore, the concentration is 2000 mg / 10 mL = 200 mg/mL. The dose ordered is 300 mg. To find the volume, divide the dose by the concentration: 300 mg / 200 mg/mL = 1.5 mL. The volume of diluent added (9.6 mL) is extra information not needed for this final calculation.
16. A child weighing 55 lbs is prescribed an antibiotic at a dose of 30 mg/kg/day, to be given in three divided doses. The available oral suspension has a concentration of 125 mg/5 mL. How many milliliters should be administered for each dose?
    Answer: 10.0 mL First, convert the child's weight to kilograms: 55 lbs / 2.2 lbs/kg = 25 kg. Second, calculate the total daily dose in mg: 30 mg/kg/day * 25 kg = 750 mg/day. Third, calculate the amount per single dose, as the daily dose is divided into three: 750 mg/day / 3 doses = 250 mg/dose. Finally, calculate the volume of the suspension needed for one dose. The concentration is 125 mg/5 mL, which is 25 mg/mL. Volume = 250 mg / (25 mg/mL) = 10 mL.
17. A patient is prescribed a liquid medication with instructions to take 1/2 tablespoonful three times daily. The medication is supplied in a bottle containing 8 fluid ounces. The drug concentration is 50 mg per teaspoon. How many milligrams of the drug will the patient have consumed when exactly one-quarter of the bottle has been used?
    Answer: 600 mg First, determine the volume consumed. The bottle contains 8 fl oz. One-quarter of the bottle is 8 fl oz / 4 = 2 fl oz. Next, convert fluid ounces to milliliters (1 fl oz ≈ 30 mL): 2 fl oz 30 mL/fl oz = 60 mL. The concentration is given as 50 mg per teaspoon (tsp). Convert teaspoons to milliliters (1 tsp = 5 mL). So the concentration is 50 mg / 5 mL = 10 mg/mL. Finally, calculate the total mg consumed: 60 mL 10 mg/mL = 600 mg. The dosing instruction (1/2 tablespoonful TID) is extraneous information.
18. An intensive care patient weighing 70 kg is ordered to receive a norepinephrine infusion at 0.1 mcg/kg/min. The standard IV admixture available is 4 mg of norepinephrine in 250 mL of D5W. What is the correct infusion rate in mL/hr?
    Answer: 26.3 mL/hr First, calculate the required dose in mcg/min: 0.1 mcg/kg/min 70 kg = 7 mcg/min. Next, determine the concentration of the IV solution in mcg/mL. Convert the drug amount from mg to mcg: 4 mg 1000 mcg/mg = 4000 mcg. The concentration is 4000 mcg / 250 mL = 16 mcg/mL. Now, calculate the required rate in mL/min: (7 mcg/min) / (16 mcg/mL) = 0.4375 mL/min. Finally, convert this rate to mL/hr: 0.4375 mL/min * 60 min/hr = 26.25 mL/hr, which rounds to 26.3 mL/hr.
19. A pediatric patient weighing 33 lbs is prescribed a medication at a dose of 40 mcg/kg. The medication is available as an oral solution with a concentration of 0.2 mg/mL. How many milliliters should be administered to the patient?
    Answer: 3.0 mL This is a multi-step calculation requiring several unit conversions. First, convert the patient's weight from pounds (lbs) to kilograms (kg): 33 lbs / 2.2 lbs/kg = 15 kg. Second, calculate the total required dose in micrograms (mcg): 15 kg * 40 mcg/kg = 600 mcg. Third, convert the required dose from mcg to milligrams (mg) to match the concentration unit: 600 mcg / 1000 mcg/mg = 0.6 mg. Finally, calculate the volume to administer using the available concentration: 0.6 mg / 0.2 mg/mL = 3.0 mL.

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