Dose Calculations: Concentration - Pharmacology

1. An order is written to prepare a dopamine infusion by adding 400 mg of dopamine to 250 mL of D5W. The pharmacy stocks dopamine in a 10 mL vial with a concentration of 80 mg/mL. What volume of the dopamine stock solution should be added to the D5W bag?
   Answer: 5.0 mL The question asks for the volume of the stock solution to add to the IV bag. The key is to use the desired dose (400 mg) and the concentration of the stock vial (80 mg/mL). The volume of the IV bag (250 mL) and the volume of the stock vial (10 mL) are distractors for this step. The calculation is: $400 \text{ mg} \div 80 \text{ mg/mL} = 5.0 \text{ mL}$.
2. A chemotherapy drug is prescribed at a dose of 100 mg/m². The patient has a Body Surface Area (BSA) of 1.7 m². The drug is supplied in a 50 mL vial with a concentration of 10 mg/mL. What volume of the drug solution should be administered?
   Answer: 17.0 mL First, calculate the total dose required for the patient based on their BSA: $100 \text{ mg/m}^2 \times 1.7 \text{ m}^2 = 170 \text{ mg}$. Next, calculate the volume needed to deliver this dose using the available concentration: $170 \text{ mg} \div 10 \text{ mg/mL} = 17.0 \text{ mL}$. The vial volume of 50 mL is extra information, only confirming there is enough drug available.
3. A patient is to receive a loading dose of 1 g of phenytoin. The available concentration is 50 mg/mL. To minimize adverse effects, the total volume must be split into three equal doses administered 2 hours apart. What is the volume of each individual dose?
   Answer: 6.7 mL First, convert the total dose from grams to milligrams: $1 \text{ g} = 1000 \text{ mg}$. Next, calculate the total volume required for the loading dose: $1000 \text{ mg} \div 50 \text{ mg/mL} = 20 \text{ mL}$. Finally, divide the total volume by three to find the volume of each individual dose: $20 \text{ mL} \div 3 = 6.66... \text{ mL}$, which rounds to 6.7 mL.
4. Give 0.1 mL/kg of 10 mg/mL solution. Patient weighs 25 kg. Dose (mg)?
   Answer: 25 mg First find the volume to give: 0.1 mL/kg times 25 kg equals 2.5 mL. Then multiply by the concentration: 2.5 mL times 10 mg/mL equals 25 mg. The tempting wrong answer is 250 mg, which skips the 0.1 mL/kg factor and just multiplies 10 mg by 25 kg.
5. A patient is ordered to receive 250 mcg of digoxin IV push. The available stock solution has a concentration of 0.5 mg/mL. What is the correct volume to administer?
   Answer: 0.5 mL This calculation requires a unit conversion. First, convert the ordered dose from micrograms (mcg) to milligrams (mg): $250 \text{ mcg} \div 1000 \text{ mcg/mg} = 0.25 \text{ mg}$. Then, calculate the volume to administer using the available concentration: $0.25 \text{ mg} \div 0.5 \text{ mg/mL} = 0.5 \text{ mL}$.
6. A 176-lb patient with a severe infection is prescribed an antibiotic at a dose of 7.5 mg/kg. The pharmacy supplies the medication in a multi-dose vial with a concentration of 100 mg/mL. What volume, in mL, of the antibiotic should be administered to the patient?
   Answer: 6.0 mL This is a multi-step calculation requiring weight conversion and dose volume calculation. First, convert the patient's weight from pounds (lbs) to kilograms (kg): $176 \text{ lbs} \div 2.2 \text{ lbs/kg} = 80 \text{ kg}$. Next, calculate the total required dose in mg: $80 \text{ kg} \times 7.5 \text{ mg/kg} = 600 \text{ mg}$. Finally, calculate the volume to administer using the provided concentration: $600 \text{ mg} \div 100 \text{ mg/mL} = 6.0 \text{ mL}$.
7. A pharmacist needs to prepare an oral suspension for a child prescribed 45 mg of amoxicillin. The stock bottle is a powder that, when reconstituted, has a final concentration of 125 mg per 5 mL. What volume, in mL, should the pharmacist instruct the parent to administer per dose?
   Answer: 1.8 mL First, determine the concentration in mg/mL. The concentration is 125 mg per 5 mL, so $125 \text{ mg} \div 5 \text{ mL} = 25 \text{ mg/mL}$. Next, calculate the volume needed for the 45 mg dose: $45 \text{ mg} \div 25 \text{ mg/mL} = 1.8 \text{ mL}$.
8. A 0.25 mg/mL solution is available. How many mL for 500 mcg?
   Answer: 2.0 mL Since 500 mcg equals 0.5 mg, divide the needed dose by the concentration: 0.5 mg / 0.25 mg/mL = 2 mL. The tempting wrong answer is 0.5 mL because it mistakes 0.5 mg for a volume instead of applying the 0.25 mg/mL strength.
9. A patient in anaphylactic shock requires an intramuscular injection of 0.3 mg of epinephrine. The available stock is a vial labeled "Epinephrine 1:1000". What volume should be drawn into the syringe for administration?
   Answer: 0.3 mL First, interpret the ratio concentration. A 1:1000 ratio means 1 gram of solute per 1000 mL of solvent. Convert grams to milligrams: $1 \text{ g} = 1000 \text{ mg}$. Therefore, the concentration is 1000 mg/1000 mL, which simplifies to 1 mg/mL. Next, calculate the volume required for the 0.3 mg dose: $0.3 \text{ mg} \div 1 \text{ mg/mL} = 0.3 \text{ mL}$.
10. A patient needs 50 units of regular insulin. The pharmacy only has U-500 insulin vials available, which contain 500 units/mL. What volume, in mL, must be drawn using a tuberculin syringe to administer the correct dose?
    Answer: 0.1 mL The dose is 50 units and the concentration of the available insulin is U-500, which is 500 units per mL. To find the required volume, divide the dose by the concentration: $50 \text{ units} \div 500 \text{ units/mL} = 0.1 \text{ mL}$. It is critical to use a tuberculin syringe for such a small and precise volume of a high-concentration insulin.
11. A 500 mL IV bag is prepared with heparin, resulting in a final concentration of 50 units/mL. The infusion pump has administered 150 mL of the solution. How many units of heparin has the patient received?
    Answer: 7,500 units The question asks for the amount of drug delivered, not the amount remaining. The concentration is 50 units/mL and the volume administered is 150 mL. To find the total units received, multiply the volume administered by the concentration: $150 \text{ mL} \times 50 \text{ units/mL} = 7,500 \text{ units}$. The total initial volume of the bag (500 mL) is used to calculate distractor answers.
12. An order is written for 0.75 g of an antibiotic. The medication is available in a solution with a concentration of 250 mg/mL. What volume of this solution should be administered?
    Answer: 3.0 mL When you encounter dosage calculation problems, you're working with unit conversions and basic proportional reasoning - fundamental skills for safe medication administration. To solve this problem, you need to convert the ordered dose to the same units as the concentration, then use the formula: Volume = Dose ÷ Concentration. First, convert 0.75 g to milligrams: $0.75 \text{ g} \times 1000 \text{ mg/g} = 750 \text{ mg}$ Now calculate the volume needed: $\text{Volume} = \frac{750 \text{ mg}}{250 \text{ mg/mL}} = 3.0 \text{ mL}$ Looking at the wrong answers: Choice A (0.3 mL) represents a decimal placement error - you might get this if you incorrectly converted grams to milligrams or made an arithmetic mistake. Choice B (30.0 mL) is ten times too large, likely from forgetting to convert grams to milligrams and working with 0.75 instead of 750. Choice C (7.5 mL) could result from dividing 750 by 100 instead of 250, or other calculation errors. The correct answer is D (3.0 mL). Study tip: Always write out your unit conversions explicitly and double-check that your final answer makes practical sense. In this case, since you need 750 mg and each mL contains 250 mg, you'd expect to need several milliliters - not a fraction of one (A) or an unusually large volume (B). Practice dosage calculations regularly, as they're critical for patient safety.
13. A patient weighing 80 kg is prescribed vancomycin 15 mg/kg IV. Based on the information in the passage, what volume of the reconstituted solution is needed before further dilution?
    Answer: 12 mL When you encounter dosage calculations in pharmacology, you need to work systematically through three key values: the patient's dose requirement, the concentration of your prepared solution, and the volume needed from that solution. First, calculate the total dose needed for this 80 kg patient: $80 \text{ kg} \times 15 \text{ mg/kg} = 1200 \text{ mg}$ Next, determine how much reconstituted solution contains this dose. The passage tells you that after reconstitution, the concentration is 100 mg/mL. Using the formula: Volume = Dose ÷ Concentration, you get: $\frac{1200 \text{ mg}}{100 \text{ mg/mL}} = 12 \text{ mL}$ Therefore, D) 12 mL is correct. Here's why the other options are wrong: A) 10 mL would only provide 1000 mg of vancomycin (10 mL × 100 mg/mL), which is 200 mg short of the required dose. B) 20 mL represents the total volume of diluent used for reconstitution, not the volume needed for the patient's dose—this would deliver 2000 mg, significantly overdosing the patient. C) 15 mL might seem tempting since it matches the mg/kg dose, but this would provide 1500 mg of vancomycin, which is 300 mg more than needed. The key strategy here is to never skip the dose calculation step, even when the numbers seem to align coincidentally. Always calculate the patient's total dose first, then determine the volume needed based on the final concentration after reconstitution.
14. A patient receives a daily 750 mg dose of an antibiotic. The medication is supplied in a 20 mL multi-dose vial with a concentration of 300 mg/mL. How many full daily doses can be obtained from one vial?
    Answer: 8 doses First, calculate the total amount of medication in the vial: $20 \text{ mL} \times 300 \text{ mg/mL} = 6000 \text{ mg}$. Next, divide the total amount of medication by the amount per dose to find the number of doses: $6000 \text{ mg} \div 750 \text{ mg/dose} = 8 \text{ doses}$. Since the result is a whole number, 8 full doses can be obtained.
15. A patient is prescribed 40 mg of furosemide IV. The medication is available in a solution of 10 mg/mL. The medication is to be diluted in 50 mL of normal saline and infused over 15 minutes. What volume of the furosemide solution should be drawn from the vial to be added to the normal saline?
    Answer: 4.0 mL The question asks for the volume of furosemide solution to be drawn from the vial. The information about dilution volume (50 mL) and infusion time (15 minutes) is not needed for this calculation. The required dose is 40 mg, and the available concentration is 10 mg/mL. The calculation is: $40 \text{ mg} \div 10 \text{ mg/mL} = 4.0 \text{ mL}$.
16. How many mL of a 2% w/v solution provides 40 mg?
    Answer: 2 mL A 2% w/v solution contains 2 g per 100 mL, which equals 2000 mg per 100 mL or 20 mg per mL. To get 40 mg, divide 40 by 20, giving 2 mL. The tempting error is 20 mL, which incorrectly treats 2% as 2 mg per mL instead of 20 mg per mL.
17. A patient on a tapering schedule for liquid prednisone was taking 30 mg yesterday. Today's dose is to be reduced by 20%. The prednisone oral solution has a concentration of 5 mg/mL. What volume should be administered today?
    Answer: 4.8 mL This question tests your ability to perform dosage calculations involving percentage reductions and concentration conversions - a fundamental skill in pharmaceutical dosing that requires careful step-by-step calculation. Start by calculating today's reduced dose. The patient was taking 30 mg yesterday, and today's dose should be reduced by 20%. A 20% reduction means the patient receives 80% of yesterday's dose: $30 \text{ mg} \times 0.80 = 24 \text{ mg}$ Next, convert this dose to volume using the concentration. The oral solution contains 5 mg/mL, so you need: $\frac{24 \text{ mg}}{5 \text{ mg/mL}} = 4.8 \text{ mL}$ This confirms answer D is correct. Now examine why the other options are wrong. Answer A (1.2 mL) represents a calculation error - possibly dividing 24 mg by 20 instead of using the correct concentration. Answer B (6.0 mL) corresponds to the original 30 mg dose (30 ÷ 5 = 6 mL), meaning the student forgot to apply the 20% reduction entirely. Answer C (5.0 mL) might result from incorrectly calculating 20% of 30 mg as 5 mg instead of the proper reduction, then converting that wrong amount. Study tip: For dosage reduction problems, always work in sequence: calculate the new dose amount first, then convert to the required units. Double-check percentage calculations - a 20% reduction means you give 80% of the original dose, not 20%.
18. A pediatric patient is prescribed a 15 mg dose of a medication. The medication is supplied in a 5 mL single-use vial with a concentration of 10 mg/mL. After administering the correct dose, how much medication must be discarded?
    Answer: 3.5 mL This is a multi-step problem. First, calculate the volume to be administered: $15 \text{ mg} \div 10 \text{ mg/mL} = 1.5 \text{ mL}$. Next, calculate the volume to be discarded. The vial contains 5 mL total. The volume to be discarded is the total volume minus the administered volume: $5 \text{ mL} - 1.5 \text{ mL} = 3.5 \text{ mL}$.
19. An order is written to add 80 mEq of potassium chloride (KCl) to a 1 L bag of 0.9% sodium chloride. The pharmacy stocks KCl in vials with a concentration of 2 mEq/mL. What volume of the KCl solution must be added to the IV bag?
    Answer: 40 mL This is a direct calculation of volume from a required dose and a given concentration. The volume of the IV bag (1 L) is extraneous information for this specific question. The required dose is 80 mEq and the concentration of the stock solution is 2 mEq/mL. Calculate the volume to add: $80 \text{ mEq} \div 2 \text{ mEq/mL} = 40 \text{ mL}$.
20. A patient requires a local anesthetic block and is prescribed 75 mg of bupivacaine. The medication is available as a 0.5% solution. How many milliliters of the solution are required to deliver the correct dose?
    Answer: 15 mL First, convert the percentage concentration to mg/mL. A 0.5% solution means 0.5 g per 100 mL. Convert grams to milligrams: $0.5 \text{ g} = 500 \text{ mg}$. So, the concentration is 500 mg/100 mL, which simplifies to 5 mg/mL. Then, calculate the volume needed for the 75 mg dose: $75 \text{ mg} \div 5 \text{ mg/mL} = 15 \text{ mL}$.

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