Nursing Math & Dosage Foundations · 500-Question Practice Bank (worked answers)
Reconstitution — practice set (Q161–220)
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60 dosage-calculation problems (questions 161–220) with a full worked answer for each: dimensional-analysis setup, raw calculation, rounding rule, final labeled answer, rationale and clinical pearl. Work each one on paper first, then open the answer.
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60 review questions from the chapter. Try each one, then open the answer.
Question 161. Scenario: A nurse is preparing a dose of ceftriaxone for an adult admitted with community-acquired pneumonia. Order: ceftriaxone 1 g IV. Available: Ceftriaxone 1 g powder vial. Label: "Reconstitute with 9.6 mL Sterile Water for Injection." Question: Which diluent should the nurse use to reconstitute this medication? A) 0.9% sodium chloride B) Sterile Water for Injection C) Dextrose 5% in water (D5W) D) Lactated Ringer's
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Correct answer: B) Sterile Water for Injection Setup (dimensional analysis): Not applicable (diluent identification). Raw calculation: N/A Rounding: N/A Final answer: Sterile Water for Injection Rationale: The vial label specifies the exact diluent to use ("Reconstitute with 9.6 mL Sterile Water for Injection"). The nurse must use only the diluent named on the manufacturer's label; substituting another solution can change stability, cause precipitation, or alter the concentration. Clinical pearl: Always read the reconstitution directions on the label; the specified diluent and volume are product-specific.
Question 162. Scenario: A nurse is preparing an intramuscular antibiotic for a patient with a soft-tissue infection. Order: ampicillin 1 g IM. Available: Ampicillin 1 g powder vial. Label: "Add 3.5 mL Sterile Water for Injection to yield 250 mg/mL." Question: How many mL of diluent should the nurse add to the vial? Round to the nearest tenth.
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Correct answer: 3.5 mL Setup (dimensional analysis): Diluent volume is read directly from the label: add 3.5 mL Sterile Water for Injection. Raw calculation: 3.5 mL Rounding: Already to the nearest tenth. Final answer: 3.5 mL Rationale: The label directs exactly 3.5 mL of diluent to yield a 250 mg/mL solution. Adding a different volume would change the final concentration and lead to a dosing error. Clinical pearl: The amount of diluent stated on the label already accounts for the powder's displacement volume, so the stated final concentration is only correct if that exact diluent volume is added.
Question 163. Scenario: A nurse reconstitutes an antibiotic for a postoperative patient. Order: ampicillin 500 mg IM. Available: Ampicillin 500 mg powder vial. The nurse adds 1.8 mL Sterile Water for Injection; the resulting total volume is 2 mL. Question: What is the resulting concentration of the reconstituted solution (mg/mL)?
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Correct answer: 250 mg/mL Setup (dimensional analysis): concentration = amount of drug ÷ final volume = 500 mg ÷ 2 mL Raw calculation: 500 ÷ 2 = 250 Rounding: Exact value; no rounding needed. Final answer: 250 mg/mL Rationale: Concentration is the total drug mass divided by the total (final) volume after reconstitution. The 1.8 mL of diluent plus the powder's 0.2 mL displacement yields 2 mL; 500 mg in 2 mL is 250 mg/mL. Clinical pearl: After reconstitution, the total drug amount stays the same — only the volume (and therefore concentration) changes.
Question 164. Scenario: A nurse is drawing up an intramuscular dose of ampicillin for a child with otitis media. Order: ampicillin 500 mg IM. Available: Ampicillin 1 g vial, reconstituted to a concentration of 250 mg/mL. Question: How many mL should the nurse administer? Round to the nearest tenth.
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Correct answer: 2 mL Setup (dimensional analysis): 500 mg × (1 mL / 250 mg) = ? mL Raw calculation: 500 ÷ 250 = 2 Rounding: Exact value; no rounding needed. Final answer: 2 mL Rationale: Using dimensional analysis, mg units cancel, leaving mL. A 500 mg dose drawn from a 250 mg/mL solution requires 2 mL. Clinical pearl: Divide the ordered dose by the concentration (mg ÷ mg/mL) to find the volume to administer.
Question 165. Scenario: A nurse is reconstituting a cephalosporin for intravenous administration. Order: ceftriaxone 1 g IV. Available: Ceftriaxone 1 g powder vial. Label: "Add 9.6 mL Sterile Water for Injection; final volume 10 mL." Question: What volume (mL) does the ceftriaxone powder itself occupy in the vial (the displacement volume)?
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Correct answer: 0.4 mL Setup (dimensional analysis): displacement = final volume − diluent added = 10 mL − 9.6 mL Raw calculation: 10 − 9.6 = 0.4 Rounding: Exact value; no rounding needed. Final answer: 0.4 mL Rationale: The powder occupies some volume in the vial. When 9.6 mL of diluent is added and the final volume is 10 mL, the difference (0.4 mL) is the volume the powder displaces. Clinical pearl: Displacement volume explains why the final volume is greater than the volume of diluent added — it matters when you must prepare a specific final concentration.
Question 166. Scenario: A nurse is preparing an intramuscular antibiotic for an adult with a urinary tract infection. Order: ceftriaxone 250 mg IM. Available: Ceftriaxone 500 mg powder vial. Label: "Add 4.8 mL Sterile Water for Injection; final volume 5 mL (100 mg/mL)." Question: How many mL should the nurse administer? Round to the nearest tenth. A) 0.5 mL B) 1 mL C) 2.5 mL D) 5 mL
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Correct answer: C) 2.5 mL Setup (dimensional analysis): 250 mg × (5 mL / 500 mg) = ? mL Raw calculation: 250 × 5 ÷ 500 = 2.5 Rounding: Exact to the tenth (2.5 mL). Final answer: 2.5 mL Rationale: The reconstituted vial is 100 mg/mL (500 mg in 5 mL). A 250 mg dose is half the vial's contents, so 2.5 mL is required. Clinical pearl: When a dose is a clean fraction of the vial contents (half, quarter), the volume can be quickly sanity-checked against the vial's total volume.
Question 167. Scenario: A nurse is preparing vancomycin for an intravenous infusion for a patient with methicillin-resistant Staphylococcus aureus (MRSA) bacteremia. Order: vancomycin 1 g IV. Available: Vancomycin 1 g powder vial. Label: "Add 20 mL Sterile Water for Injection to yield 50 mg/mL." The supply room has Sterile Water for Injection, 0.9% sodium chloride, D5W, and bacteriostatic normal saline. Question: Which diluent, and in what amount, should the nurse use to reconstitute this vial?
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Correct answer: Sterile Water for Injection, 20 mL Setup (dimensional analysis): Not applicable (diluent identification); volume read directly from label. Raw calculation: 20 mL Rounding: N/A Final answer: Sterile Water for Injection, 20 mL Rationale: The label names Sterile Water for Injection as the diluent and 20 mL as the volume. The nurse must use the specified diluent, not a different solution available in the supply room. Clinical pearl: "Available" solutions are not interchangeable — the reconstitution diluent is chosen by the manufacturer for stability and compatibility.
Question 168. Scenario: A nurse is verifying the total dose contained in a reconstituted cephalosporin vial. Order: ceftriaxone 1 g IV. Available: Reconstituted ceftriaxone vial with a total volume of 10 mL and a labeled concentration of 100 mg/mL. Question: What is the total amount of drug (mg) in the vial?
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Correct answer: 1000 mg (1 g) Setup (dimensional analysis): total drug = concentration × total volume = 100 mg/mL × 10 mL Raw calculation: 100 × 10 = 1000 Rounding: Exact value. Final answer: 1000 mg (1 g) Rationale: The vial contains all of the drug that was packaged in it regardless of the volume used to reconstitute it. 100 mg/mL × 10 mL = 1000 mg, confirming the 1 g vial size. Clinical pearl: Reconstitution never changes the total amount of drug in the vial — only its concentration and volume.
Question 169. Scenario: A nurse is preparing an intramuscular dose of ampicillin for an adult with cellulitis. Order: ampicillin 750 mg IM. Available: Ampicillin 2 g powder vial, reconstituted to a total volume of 8 mL (250 mg/mL). Question: How many mL should the nurse administer? Round to the nearest tenth. A) 1 mL B) 2 mL C) 3 mL D) 4 mL
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Correct answer: C) 3 mL Setup (dimensional analysis): 750 mg × (1 mL / 250 mg) = ? mL Raw calculation: 750 ÷ 250 = 3 Rounding: Exact value. Final answer: 3 mL Rationale: The 2 g vial reconstituted to 8 mL gives 250 mg/mL. A 750 mg dose requires 750 ÷ 250 = 3 mL. Clinical pearl: Always confirm the concentration on the reconstituted vial before calculating the dose volume.
Question 170. Scenario: A nurse is reconstituting a corticosteroid for an adult with an acute asthma exacerbation. Order: methylprednisolone 62.5 mg IV. Available: Methylprednisolone 125 mg powder vial. Label: "Add 2 mL Sterile Water for Injection; final volume 2 mL." Question: What is the resulting concentration of the reconstituted solution (mg/mL)?
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Correct answer: 62.5 mg/mL Setup (dimensional analysis): concentration = 125 mg ÷ 2 mL Raw calculation: 125 ÷ 2 = 62.5 Rounding: Exact value. Final answer: 62.5 mg/mL Rationale: After reconstitution, 125 mg is present in 2 mL, so the concentration is 62.5 mg/mL. This is used for subsequent dose calculations. Clinical pearl: Some medications yield non-whole-number concentrations (e.g., 62.5 mg/mL) — keep the decimal carefully when dividing.
Question 171. Scenario: A nurse is preparing an intravenous antibiotic for a patient with syphilis. Order: penicillin G potassium 5,000,000 units IV. Available: Penicillin G potassium 5,000,000 unit powder vial. Label: "Add 8 mL Sterile Water for Injection; final volume 10 mL (500,000 units/mL)." Question: How many mL of diluent should the nurse add to the vial?
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Correct answer: 8 mL Setup (dimensional analysis): Diluent volume read directly from the label. Raw calculation: 8 mL Rounding: N/A Final answer: 8 mL Rationale: The label directs adding 8 mL of Sterile Water for Injection; the powder displaces 2 mL, giving a final volume of 10 mL and a concentration of 500,000 units/mL. Clinical pearl: The final volume (10 mL) equals diluent (8 mL) plus powder displacement (2 mL); know which number the label is telling you to add.
Question 172. Scenario: A nurse is documenting an intramuscular antibiotic dose after administration. Order: ceftriaxone 500 mg IM. Available: Ceftriaxone vial reconstituted to 250 mg/mL. Question: The nurse withdrew and administered 2 mL. What dose (mg) did the patient receive?
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Correct answer: 500 mg Setup (dimensional analysis): dose = concentration × volume = 250 mg/mL × 2 mL Raw calculation: 250 × 2 = 500 Rounding: Exact value. Final answer: 500 mg Rationale: Each mL of the reconstituted solution contains 250 mg, so 2 mL delivers 500 mg, matching the order. Clinical pearl: To reverse-check a dose, multiply the volume drawn by the concentration (mL × mg/mL = mg).
Question 173. Scenario: A nurse reconstitutes an antibiotic and needs to confirm the concentration before drawing a dose. Order: ampicillin 500 mg IM. Available: Ampicillin 1 g powder vial. The nurse adds 3.5 mL Sterile Water for Injection; the final volume is 4 mL. Question: What is the resulting concentration (mg/mL)? A) 200 mg/mL B) 250 mg/mL C) 300 mg/mL D) 500 mg/mL
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Correct answer: B) 250 mg/mL Setup (dimensional analysis): concentration = 1000 mg ÷ 4 mL Raw calculation: 1000 ÷ 4 = 250 Rounding: Exact value. Final answer: 250 mg/mL Rationale: A 1 g (1000 mg) vial reconstituted to a final volume of 4 mL yields 250 mg/mL. Clinical pearl: Convert grams to milligrams (1 g = 1000 mg) before calculating concentration.
Question 174. Scenario: A nurse is preparing an intravenous corticosteroid for a patient with an acute flare of multiple sclerosis. Order: methylprednisolone 62.5 mg IV. Available: Methylprednisolone 125 mg powder vial, reconstituted to 62.5 mg/mL. Question: How many mL should the nurse administer? Round to the nearest tenth.
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Correct answer: 1 mL Setup (dimensional analysis): 62.5 mg × (1 mL / 62.5 mg) = ? mL Raw calculation: 62.5 ÷ 62.5 = 1 Rounding: Exact value. Final answer: 1 mL Rationale: The ordered dose equals the concentration per mL, so exactly 1 mL delivers 62.5 mg. Clinical pearl: When the ordered dose equals the mg/mL concentration, the volume is 1 mL — a quick check.
Question 175. Scenario: A nurse is reconstituting an oral antibiotic suspension for a pediatric patient. Order: amoxicillin 250 mg PO. Available: Amoxicillin 250 mg/5 mL powder for oral suspension, 100 mL bottle. Label: "Add 68 mL water to make 100 mL total." Question: After the nurse adds exactly 68 mL of water as directed, what total volume (mL) of suspension should result?
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Correct answer: 100 mL Setup (dimensional analysis): Final volume is stated on the label ("add 68 mL water to make 100 mL"). Raw calculation: 68 mL added → 100 mL total Rounding: N/A Final answer: 100 mL Rationale: For oral suspensions, the label directs a specific volume of water to produce a specific total volume; the powder occupies the difference (32 mL here). The finished suspension should be 100 mL. Clinical pearl: Oral suspensions are dosed from the final total volume; do not confuse the water added with the total volume.
Question 176. Scenario: A nurse is preparing a vancomycin infusion for a patient with sepsis. Order: vancomycin 500 mg IV. Available: Vancomycin 1 g powder vial. Label: "Add 20 mL Sterile Water for Injection to yield 50 mg/mL." Question: After reconstitution, how many mL should the nurse withdraw from the vial to add to the IV bag for a 500 mg dose? Round to the nearest tenth.
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Correct answer: 10 mL Setup (dimensional analysis): 500 mg × (1 mL / 50 mg) = ? mL Raw calculation: 500 ÷ 50 = 10 Rounding: Exact value. Final answer: 10 mL Rationale: The 1 g vial reconstituted with 20 mL yields 50 mg/mL. A 500 mg dose requires 10 mL, which is then added to the IV bag and further diluted before infusion. Clinical pearl: Vancomycin is reconstituted to a concentrated solution first, then diluted to a final infusion concentration — these are two separate steps.
Question 177. Scenario: A nurse reconstitutes a multi-dose vial of ampicillin for a patient who will need several doses over the shift. Order: ampicillin 500 mg IM q6h. Available: Ampicillin 1 g powder vial, reconstituted to 250 mg/mL. Question: Before storing the reconstituted multi-dose vial, what must the nurse write on the label? A) The patient's room number B) The date and time of reconstitution and the nurse's initials C) The vial's lot number only D) Nothing — the original label is sufficient
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Correct answer: B) The date and time of reconstitution and the nurse's initials Setup (dimensional analysis): N/A Raw calculation: N/A Rounding: N/A Final answer: Date and time of reconstitution plus the nurse's initials Rationale: A multi-dose vial must be labeled with the date and time it was reconstituted and the initials of the person who prepared it, so the beyond-use period can be tracked. Room numbers and lot numbers do not substitute for this. Clinical pearl: Without a reconstitution date/time, the beyond-use time cannot be determined — never use an unlabeled reconstituted vial.
Question 178. Scenario: A nurse is mixing a vancomycin dose into a piggyback bag. Order: vancomycin 250 mg IV. Available: Vancomycin 500 mg powder vial. Label: "Add 10 mL Sterile Water for Injection to yield 50 mg/mL." The nurse adds the 10 mL of diluent, then withdraws 5 mL and injects it into a 100 mL bag of normal saline. Question: What vancomycin dose (mg) is now in the IV bag?
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Correct answer: 250 mg Setup (dimensional analysis): dose = concentration × volume withdrawn = 50 mg/mL × 5 mL Raw calculation: 50 × 5 = 250 Rounding: Exact value. Final answer: 250 mg Rationale: After reconstitution the vial is 50 mg/mL. Withdrawing 5 mL removes 250 mg, which is the dose now in the 100 mL bag. The 100 mL of saline is the diluent, not additional drug. Clinical pearl: When a portion of a reconstituted vial is used, the dose equals the concentration times the volume withdrawn.
Question 179. Scenario: A nurse is selecting a syringe to give an intramuscular antibiotic. Order: ampicillin 350 mg IM. Available: Ampicillin 1 g vial, reconstituted to 250 mg/mL. Question: The nurse calculates the volume to be 1.4 mL. Which syringe size is most appropriate to measure this dose accurately? A) 1 mL syringe B) 3 mL syringe C) 5 mL syringe D) 10 mL syringe
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Correct answer: B) 3 mL syringe Setup (dimensional analysis): volume = 350 mg ÷ 250 mg/mL = 1.4 mL (already given). Raw calculation: 1.4 mL to be measured Rounding: N/A Final answer: 3 mL syringe Rationale: A 1 mL syringe cannot hold 1.4 mL. A 3 mL syringe is the smallest syringe that holds the full 1.4 mL dose and offers fine graduation for accuracy; a 5 or 10 mL syringe is unnecessarily large and harder to read precisely for small volumes. Clinical pearl: Select the smallest syringe that accommodates the full volume to maximize measurement accuracy.
Question 180. Scenario: A nurse is preparing a large intravenous ampicillin dose for a patient with endocarditis. Order: ampicillin 1.5 g IV. Available: Ampicillin 1 g powder vials, each reconstituted to 250 mg/mL (4 mL total per vial). Question: How many vials are needed, and how many total mL should the nurse withdraw for the 1.5 g dose? Round mL to the nearest tenth.
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Correct answer: 2 vials; 6 mL Setup (dimensional analysis): 1.5 g = 1500 mg; 1500 mg × (1 mL / 250 mg) = ? mL Raw calculation: 1500 ÷ 250 = 6 mL; vials needed = ceil(1500 mg ÷ 1000 mg/vial) = 2 Rounding: Exact value. Final answer: 2 vials; withdraw 6 mL total Rationale: The dose (1500 mg) exceeds a single 1 g vial, so two vials are needed. At 250 mg/mL, 1500 mg requires 6 mL, which can be withdrawn across the two reconstituted vials. Clinical pearl: When a dose exceeds the size of a single vial, count vials first, then calculate the total volume from the concentration.
Question 181. Scenario: A nurse further dilutes a reconstituted antibiotic before infusion. Order: ceftriaxone 1 g IV. Available: Ceftriaxone 1 g vial, reconstituted to 10 mL (100 mg/mL). The nurse adds the entire 10 mL to a 40 mL bag of normal saline. Question: What is the concentration (mg/mL) of the diluted ceftriaxone solution in the bag?
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Correct answer: 20 mg/mL Setup (dimensional analysis): concentration = total drug ÷ total volume = 1000 mg ÷ (10 mL + 40 mL) Raw calculation: 1000 ÷ 50 = 20 Rounding: Exact value. Final answer: 20 mg/mL Rationale: The full 1 g (1000 mg) is now in a 50 mL total volume (10 mL drug + 40 mL diluent), giving 20 mg/mL. Clinical pearl: After further dilution, recalculate concentration using the total combined volume, not just the bag volume.
Question 182. Scenario: A nurse is planning doses of vancomycin from a single multi-dose vial. Order: vancomycin 500 mg IV q12h. Available: Vancomycin 1 g powder vial, reconstituted to 50 mg/mL (20 mL total). Question: How many mL should the nurse give per dose, and how many complete 500 mg doses can be obtained from one vial? Round mL to the nearest tenth.
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Correct answer: 10 mL per dose; 2 doses Setup (dimensional analysis): 500 mg × (1 mL / 50 mg) = 10 mL; doses = 1000 mg ÷ 500 mg = 2 Raw calculation: 500 ÷ 50 = 10; 1000 ÷ 500 = 2 Rounding: Exact values. Final answer: 10 mL per dose; 2 complete doses per vial Rationale: At 50 mg/mL, 500 mg = 10 mL. A 1 g (1000 mg) vial yields exactly two 500 mg doses. Clinical pearl: For a multi-dose vial, divide the total drug in the vial by the per-dose amount to find the number of complete doses.
Question 183. Scenario: A nurse is preparing ampicillin for intravenous use and must choose the correct reconstitution from a dual-purpose label. Order: ampicillin 1 g IV. Available: Ampicillin 1 g powder vial. Label: "For IM: add 3.5 mL Sterile Water for Injection to yield 250 mg/mL. For IV: add 7.2 mL Sterile Water for Injection to yield 125 mg/mL." Question: Which concentration should the nurse use for the IV route, and how many mL should be administered for the 1 g dose?
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Correct answer: 125 mg/mL (IV concentration); 8 mL Setup (dimensional analysis): 1 g = 1000 mg; 1000 mg × (1 mL / 125 mg) = ? mL Raw calculation: 1000 ÷ 125 = 8 Rounding: Exact value. Final answer: Use the IV concentration (125 mg/mL); administer 8 mL Rationale: The label gives different concentrations for IM and IV use. Because the order is IV, the nurse uses the IV reconstitution (7.2 mL → 125 mg/mL). A 1 g dose at 125 mg/mL is 8 mL. Clinical pearl: Read dual-purpose labels carefully and match the reconstitution to the ordered route.
Question 184. Scenario: A nurse is reconstituting cefazolin for an intramuscular injection. Order: cefazolin 500 mg IM. Available: Cefazolin 1 g powder vial. Label: "Add 2.5 mL Sterile Water for Injection; final volume 3 mL (≈330 mg/mL)." Question: After adding the 2.5 mL of diluent, what is the final volume in the vial, and how many mL should the nurse administer for a 500 mg dose? Round mL to the nearest tenth.
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Correct answer: final volume 3 mL; 1.5 mL administered Setup (dimensional analysis): 500 mg × (1 mL / 330 mg) = ? mL Raw calculation: 500 ÷ 330 = 1.515…; final volume = 3 mL Rounding: 1.515 → 1.5 mL (nearest tenth). Final answer: Final volume 3 mL; administer 1.5 mL Rationale: The label states the final volume is 3 mL (2.5 mL diluent + 0.5 mL powder displacement) at ≈330 mg/mL. A 500 mg dose is 500 ÷ 330 = 1.5 mL. Clinical pearl: Cefazolin's labeled concentration is approximate (~330 mg/mL); carry the division to the tenth for a syringe-drawable volume.
Question 185. Scenario: A nurse reconstitutes a multi-dose vial of ampicillin and is unsure how long it may be stored after mixing. Order: ampicillin 500 mg IM q6h. Available: Ampicillin 1 g powder vial, reconstituted to 250 mg/mL. The nurse cannot locate beyond-use information on the vial label. Question: To determine the correct storage conditions and beyond-use date/time for the reconstituted vial, what must the nurse do?
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Correct answer: Consult the manufacturer's package insert/labeling and pharmacy policy for the specific product's storage conditions and beyond-use date/time. Setup (dimensional analysis): N/A Raw calculation: N/A Rounding: N/A Final answer: Determine beyond-use from the manufacturer's labeling (and pharmacy), never from a general rule. Rationale: Beyond-use times after reconstitution are product-specific and depend on the drug, diluent, and storage temperature. The nurse must locate the manufacturer's directions (package insert) or pharmacy guidance rather than assuming a universal expiry period. Clinical pearl: "How long is a reconstituted vial good for?" always has a product-specific answer — check the label, not memory.
Question 186. Scenario: A nurse is reconstituting a cephalosporin and needs to account for the powder volume. Order: ceftriaxone 1 g IV. Available: Ceftriaxone 1 g powder vial. The package insert states the powder displaces 0.4 mL, and the nurse needs a final volume of 10 mL. Question: How many mL of Sterile Water for Injection should the nurse add to reach a final volume of 10 mL? Round to the nearest tenth.
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Correct answer: 9.6 mL Setup (dimensional analysis): diluent = final volume − displacement = 10 mL − 0.4 mL Raw calculation: 10 − 0.4 = 9.6 Rounding: Exact to the tenth. Final answer: 9.6 mL Rationale: To achieve a 10 mL final volume when the powder occupies 0.4 mL, the nurse adds 9.6 mL of diluent. Clinical pearl: When a specific final volume is required, subtract the powder's displacement volume from the target to find the diluent volume.
Question 187. Scenario: A nurse is preparing an intramuscular penicillin dose for a patient with streptococcal pharyngitis. Order: penicillin G potassium 1,500,000 units IM. Available: Penicillin G potassium 5,000,000 unit powder vial, reconstituted to 500,000 units/mL. Question: How many mL should the nurse administer? Round to the nearest tenth. A) 2 mL B) 3 mL C) 4 mL D) 6 mL
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Correct answer: B) 3 mL Setup (dimensional analysis): 1,500,000 units × (1 mL / 500,000 units) = ? mL Raw calculation: 1,500,000 ÷ 500,000 = 3 Rounding: Exact value. Final answer: 3 mL Rationale: The reconstituted vial contains 500,000 units/mL, so 1,500,000 units requires 3 mL. Clinical pearl: Keep units in the dimensional-analysis chain just as you would mg — units cancel to leave mL.
Question 188. Scenario: A nurse is giving a dose of reconstituted oral amoxicillin suspension to a child. Order: amoxicillin 250 mg PO. Available: Amoxicillin 250 mg/5 mL oral suspension, already reconstituted per label. Question: How many mL should the nurse administer? Round to the nearest tenth.
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Correct answer: 5 mL Setup (dimensional analysis): 250 mg × (5 mL / 250 mg) = ? mL Raw calculation: 250 × 5 ÷ 250 = 5 Rounding: Exact value. Final answer: 5 mL Rationale: The suspension is 250 mg per 5 mL, so a 250 mg dose is 5 mL. Clinical pearl: Oral suspension doses are usually expressed as "mg per 5 mL"; set up the ratio so the volume matches the measuring device.
Question 189. Scenario: A nurse reconstitutes a large antibiotic vial and needs the resulting concentration. Order: ampicillin 2 g IV. Available: Ampicillin 2 g powder vial. The nurse adds 6.8 mL Sterile Water for Injection; the final volume is 8 mL. Question: What is the resulting concentration (mg/mL)?
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Correct answer: 250 mg/mL Setup (dimensional analysis): concentration = 2 g ÷ 8 mL = 2000 mg ÷ 8 mL Raw calculation: 2000 ÷ 8 = 250 Rounding: Exact value. Final answer: 250 mg/mL Rationale: A 2 g (2000 mg) vial reconstituted to 8 mL yields 250 mg/mL. Clinical pearl: Large vials often reconstitute to the same concentration as smaller vials of the same drug (here 250 mg/mL), which simplifies cross-checks.
Question 190. Scenario: A nurse is preparing an intramuscular cephalosporin and must convert the ordered dose. Order: ceftriaxone 0.5 g IM. Available: Ceftriaxone 1 g vial, reconstituted to 100 mg/mL. Question: How many mL should the nurse administer? Round to the nearest tenth.
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Correct answer: 5 mL Setup (dimensional analysis): 0.5 g = 500 mg; 500 mg × (1 mL / 100 mg) = ? mL Raw calculation: 500 ÷ 100 = 5 Rounding: Exact value. Final answer: 5 mL Rationale: Convert 0.5 g to 500 mg, then divide by 100 mg/mL to get 5 mL. Clinical pearl: Always convert the ordered dose to the same units as the concentration before dividing.
Question 191. Scenario: A nurse is planning vancomycin doses from a single vial across a day. Order: vancomycin 250 mg IV q8h. Available: Vancomycin 1 g powder vial, reconstituted to 50 mg/mL (20 mL total). Question: How many mL should be given per dose, and how many complete 250 mg doses can be obtained from one vial? Round mL to the nearest tenth.
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Correct answer: 5 mL per dose; 4 doses per vial Setup (dimensional analysis): 250 mg × (1 mL / 50 mg) = 5 mL; doses = 1000 mg ÷ 250 mg = 4 Raw calculation: 250 ÷ 50 = 5; 1000 ÷ 250 = 4 Rounding: Exact values. Final answer: 5 mL per dose; 4 complete doses per vial Rationale: At 50 mg/mL, 250 mg = 5 mL. A 1 g (1000 mg) vial provides four 250 mg doses. Clinical pearl: The number of doses per vial equals the vial's total drug divided by the dose amount.
Question 192. Scenario: A nurse must dilute a reconstituted vancomycin dose to a safe infusion concentration. Order: vancomycin 1 g IV. Available: Vancomycin 1 g powder vial, reconstituted to 50 mg/mL (20 mL). Institutional protocol requires vancomycin to be diluted to a concentration of 5 mg/mL or less before infusion. Question: What is the minimum total volume (mL) to which the nurse must dilute the full 1 g dose to achieve 5 mg/mL?
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Correct answer: 200 mL Setup (dimensional analysis): minimum total volume = total drug ÷ max concentration = 1000 mg ÷ 5 mg/mL Raw calculation: 1000 ÷ 5 = 200 Rounding: Exact value. Final answer: 200 mL Rationale: To achieve no more than 5 mg/mL, the full 1 g (1000 mg) must be diluted to at least 200 mL. The 20 mL of reconstituted drug is added to enough saline to reach 200 mL total. Clinical pearl: For "concentration ≤ X mg/mL" limits, divide the total mg by X to find the minimum total volume.
Question 193. Scenario: A nurse is verifying a concentration after administration. Order: ampicillin 1 g IV. Available: A reconstituted ampicillin vial. The nurse drew 4 mL and administered the full 1 g dose with that volume. Question: What was the concentration (mg/mL) of the reconstituted ampicillin?
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Correct answer: 250 mg/mL Setup (dimensional analysis): concentration = dose ÷ volume = 1000 mg ÷ 4 mL Raw calculation: 1000 ÷ 4 = 250 Rounding: Exact value. Final answer: 250 mg/mL Rationale: The full 1 g (1000 mg) was contained in 4 mL, so the concentration was 250 mg/mL. Clinical pearl: Concentration can be back-calculated from the administered dose and volume (mg ÷ mL).
Question 194. Scenario: A nurse reviews a handwritten provider order for an antibiotic. Order: "ampicillin 1.0 g IM now." Available: Ampicillin 1 g powder vial. Question: What error does this order contain, and how should it be corrected?
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Correct answer: Trailing zero ("1.0 g"); correct to "1 g". Setup (dimensional analysis): N/A Raw calculation: N/A Rounding: N/A Final answer: Remove the trailing zero — write "ampicillin 1 g IM now." Rationale: "1.0 g" contains a trailing zero, which is on The Joint Commission "Do Not Use" list because the decimal point can be missed and the dose misread as 10. The order should be written "1 g." Clinical pearl: Never use trailing zeros (1.0 → 1) and always use a leading zero before a decimal fraction (0.5, not .5).
Question 195. Scenario: A nurse is drawing up a cefazolin dose for intravenous administration. Order: cefazolin 400 mg IV. Available: Cefazolin 1 g powder vial, reconstituted to 3 mL (≈330 mg/mL). Question: How many mL should the nurse administer? Round to the nearest tenth. A) 1.2 mL B) 1.5 mL C) 2 mL D) 3 mL
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Correct answer: A) 1.2 mL Setup (dimensional analysis): 400 mg × (1 mL / 330 mg) = ? mL Raw calculation: 400 ÷ 330 = 1.212… Rounding: 1.212 → 1.2 mL (nearest tenth). Final answer: 1.2 mL Rationale: The reconstituted cefazolin is ≈330 mg/mL. A 400 mg dose is 400 ÷ 330 = 1.2 mL. Clinical pearl: With an approximate labeled concentration, round the final volume to the precision of the syringe (tenths for a 3 mL syringe).
Question 196. Scenario: A nurse is preparing an oral cephalosporin suspension for a child. Order: cefdinir 125 mg PO. Available: Cefdinir 125 mg/5 mL powder for oral suspension, 60 mL bottle. Label: "Add 40 mL water to make 60 mL total." Question: How many mL of water should the nurse add to reconstitute the bottle, and how many mL of the finished suspension should be given for a 125 mg dose?
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Correct answer: add 40 mL water; give 5 mL per dose Setup (dimensional analysis): water = 40 mL (label); dose = 125 mg × (5 mL / 125 mg) Raw calculation: 125 × 5 ÷ 125 = 5 Rounding: Exact values. Final answer: Add 40 mL water; administer 5 mL per 125 mg dose Rationale: The label directs 40 mL of water to make 60 mL of suspension. The suspension is 125 mg/5 mL, so a 125 mg dose is 5 mL. Clinical pearl: Oral suspension reconstitution is a two-part task: add the directed water, then measure doses from the final concentration.
Question 197. Scenario: A nurse reconstitutes a multi-dose vial of ceftriaxone and needs to determine when it must be discarded. Order: ceftriaxone 1 g IV. Available: Ceftriaxone 1 g powder vial. Manufacturer's label: "After reconstitution, refrigerate and discard 24 hours after reconstitution." The nurse reconstitutes the vial at 0800. Question: At what time must the reconstituted vial be discarded?
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Correct answer: 0800 the following day (discard at 24 hours after reconstitution) Setup (dimensional analysis): beyond-use = reconstitution time + 24 hours = 0800 + 24 h Raw calculation: 0800 + 24 h = 0800 next day Rounding: N/A Final answer: Discard at 0800 the next day Rationale: The manufacturer's label states the vial must be refrigerated and discarded 24 hours after reconstitution. Reconstituted at 0800, it must be discarded at 0800 the following day. Clinical pearl: Beyond-use counts from the time of reconstitution (not first use), and is product-specific per the label.
Question 198. Scenario: A nurse is preparing an intravenous penicillin dose for a patient with neurosyphilis. Order: penicillin G potassium 3,000,000 units IV. Available: Penicillin G potassium 5,000,000 unit powder vial, reconstituted to 500,000 units/mL. Question: How many mL should the nurse withdraw from the vial for this dose? Round to the nearest tenth.
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Correct answer: 6 mL Setup (dimensional analysis): 3,000,000 units × (1 mL / 500,000 units) = ? mL Raw calculation: 3,000,000 ÷ 500,000 = 6 Rounding: Exact value. Final answer: 6 mL Rationale: The vial is 500,000 units/mL; 3,000,000 units requires 6 mL. Clinical pearl: Large unit doses are easy to misplace by a factor of 10 — count the zeros carefully.
Question 199. Scenario: A nurse needs to reconstitute ampicillin to a specific concentration. Order: ampicillin 1 g IV. Available: Ampicillin 1 g powder vial. The powder displaces 0.5 mL, and the nurse needs a final concentration of 200 mg/mL. Question: What total volume is needed for the 200 mg/mL concentration, and how many mL of diluent should the nurse add? Round to the nearest tenth.
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Correct answer: total volume 5 mL; add 4.5 mL diluent Setup (dimensional analysis): total volume = 1000 mg ÷ 200 mg/mL = 5 mL; diluent = 5 mL − 0.5 mL = 4.5 mL Raw calculation: 1000 ÷ 200 = 5; 5 − 0.5 = 4.5 Rounding: Exact values. Final answer: Total volume 5 mL; add 4.5 mL of diluent Rationale: To make 200 mg/mL from 1000 mg, the final volume must be 5 mL. Since the powder displaces 0.5 mL, only 4.5 mL of diluent is added. Clinical pearl: To hit a target concentration, first find the required total volume, then subtract the displacement volume to get the diluent volume.
Question 200. Scenario: A nurse is preparing a large ceftriaxone dose for intravenous infusion. Order: ceftriaxone 600 mg IV. Available: Ceftriaxone 2 g powder vial, reconstituted to 100 mg/mL (20 mL total). Question: How many mL should the nurse withdraw for the dose? Round to the nearest tenth. A) 3 mL B) 5 mL C) 6 mL D) 8 mL
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Correct answer: C) 6 mL Setup (dimensional analysis): 600 mg × (1 mL / 100 mg) = ? mL Raw calculation: 600 ÷ 100 = 6 Rounding: Exact value. Final answer: 6 mL Rationale: The 2 g vial reconstituted to 100 mg/mL means a 600 mg dose is 6 mL. Clinical pearl: The reconstituted concentration (mg/mL) is the single number you need to convert an ordered mg dose to mL.
Question 201. Scenario: A nurse reconstitutes cefazolin and plans to use the same vial for two doses. Order: cefazolin 500 mg IM now and 500 mg IM in 8 hours. Available: Cefazolin 1 g powder vial, reconstituted to 3 mL (≈330 mg/mL). Manufacturer's label: "After reconstitution, discard 12 hours after reconstitution." The nurse reconstitutes the vial at 0900. Question: May the nurse use the same vial for the second dose at 1700? Explain using the time interval and the label's beyond-use limit.
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Correct answer: Yes — 8 hours is within the 12-hour limit; give 1.5 mL at 1700. Setup (dimensional analysis): elapsed = 1700 − 0900 = 8 h (≤ 12 h limit); dose = 500 mg ÷ 330 mg/mL = 1.5 mL Raw calculation: 8 h elapsed; 500 ÷ 330 = 1.515 → 1.5 mL Rounding: 1.5 mL (nearest tenth). Final answer: Yes, the vial may be used; administer 1.5 mL at 1700. Rationale: The second dose is due 8 hours after reconstitution, which is within the label's 12-hour beyond-use limit. The vial must be stored according to the label in the meantime. Clinical pearl: Compare the elapsed time since reconstitution to the label's beyond-use limit before reusing a multi-dose vial.
Question 202. Scenario: A nurse reconstitutes and then further dilutes a proton-pump inhibitor for infusion. Order: omeprazole 40 mg IV. Available: Omeprazole 40 mg powder vial. Label: "Add 10 mL Sterile Water for Injection to yield 4 mg/mL." The nurse adds the entire 10 mL to a 40 mL bag of normal saline. Question: What is the concentration (mg/mL) of the diluted omeprazole in the bag? Round to the nearest hundredth.
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Correct answer: 0.8 mg/mL Setup (dimensional analysis): concentration = total drug ÷ total volume = 40 mg ÷ (10 mL + 40 mL) Raw calculation: 40 ÷ 50 = 0.8 Rounding: Exact to the hundredth. Final answer: 0.8 mg/mL Rationale: The 40 mg is now in 50 mL total, giving 0.8 mg/mL. Clinical pearl: After further dilution, divide the total drug by the total (combined) volume.
Question 203. Scenario: A nurse prepares a vancomycin infusion and sets the pump rate. Order: vancomycin 1 g IV over 90 minutes. Available: Vancomycin 1 g powder vial, reconstituted to 50 mg/mL (20 mL). The nurse adds the full 20 mL to normal saline to a total volume of 250 mL. Question: At what rate (mL/hr) should the infusion pump be set? Round to the nearest whole number.
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Correct answer: 167 mL/hr Setup (dimensional analysis): rate = total volume ÷ time = 250 mL ÷ 1.5 hr Raw calculation: 250 ÷ 1.5 = 166.67 Rounding: 166.67 → 167 mL/hr (nearest whole number). Final answer: 167 mL/hr Rationale: The full 1 g (20 mL) is diluted to 250 mL and infused over 90 minutes (1.5 hours), so the pump runs at about 167 mL/hr. Clinical pearl: Convert minutes to hours before dividing for mL/hr (90 min = 1.5 hr).
Question 204. Scenario: A nurse prepares an intravenous penicillin dose and sets the infusion rate. Order: penicillin G potassium 4,000,000 units IV q4h over 30 minutes. Available: Penicillin G potassium 5,000,000 unit powder vial, reconstituted to 500,000 units/mL. The nurse withdraws the ordered dose and adds it to a 50 mL bag of normal saline. Question: How many mL should the nurse withdraw from the vial, and at what rate (mL/hr) should the infusion be run? Round mL/hr to the nearest whole number.
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Correct answer: 8 mL from the vial; 116 mL/hr Setup (dimensional analysis): volume = 4,000,000 units ÷ 500,000 units/mL = 8 mL; rate = (8 mL + 50 mL) ÷ 0.5 hr Raw calculation: 4,000,000 ÷ 500,000 = 8; (8 + 50) ÷ 0.5 = 58 ÷ 0.5 = 116 Rounding: 116 mL/hr (exact). Final answer: Withdraw 8 mL; run at 116 mL/hr Rationale: 4,000,000 units is 8 mL of the 500,000 units/mL solution. Added to 50 mL of saline, the total 58 mL runs over 30 minutes, i.e., 116 mL/hr. Clinical pearl: Include the drug volume in the total infusion volume when calculating the rate.
Question 205. Scenario: A nurse plans several vancomycin doses from one multi-dose vial and wants to know how much will remain. Order: vancomycin 400 mg IV q6h. Available: Vancomycin 1 g powder vial, reconstituted to 50 mg/mL (20 mL total). Question: How many complete 400 mg doses can be obtained from one vial, and how many mg (and mL) of vancomycin remain after those doses?
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Correct answer: 2 complete doses; 200 mg (4 mL) remains Setup (dimensional analysis): mL/dose = 400 mg ÷ 50 mg/mL = 8 mL; doses = 1000 mg ÷ 400 mg = 2.5 Raw calculation: 400 ÷ 50 = 8; 1000 ÷ 400 = 2.5; remainder = 1000 − (2 × 400) = 200 mg = 4 mL Rounding: Exact values. Final answer: 2 complete 400 mg doses; 200 mg (4 mL) remaining Rationale: The 1 g vial provides 2.5 doses, so only 2 complete 400 mg doses can be given, leaving 200 mg (4 mL at 50 mg/mL) unused. Clinical pearl: "Complete doses per vial" is a floor — a partial dose does not count as a usable full dose.
Question 206. Scenario: A nurse is preparing a corticosteroid dose from a high-strength vial. Order: methylprednisolone 100 mg IV. Available: Methylprednisolone 500 mg powder vial, reconstituted to 62.5 mg/mL. Question: How many mL should the nurse administer? Round to the nearest hundredth.
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Correct answer: 1.6 mL Setup (dimensional analysis): 100 mg × (1 mL / 62.5 mg) = ? mL Raw calculation: 100 ÷ 62.5 = 1.6 Rounding: Exact to the hundredth. Final answer: 1.6 mL Rationale: The 500 mg vial reconstituted to 62.5 mg/mL gives 100 mg in 1.6 mL. Clinical pearl: For non-whole-number concentrations, multiply/divide precisely and round only the final volume.
Question 207. Scenario: A nurse is calculating the gravity infusion rate for a vancomycin infusion. Order: vancomycin 1 g IV in 250 mL normal saline over 90 minutes. Available: Vancomycin 1 g powder vial (reconstituted and added to the 250 mL bag). IV tubing drop factor: 15 gtt/mL. Question: How many gtt/min should the nurse set the gravity flow to? Round to the nearest whole drop.
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Correct answer: 42 gtt/min Setup (dimensional analysis): gtt/min = (volume mL × drop factor gtt/mL) ÷ time min = (250 × 15) ÷ 90 Raw calculation: (250 × 15) ÷ 90 = 3750 ÷ 90 = 41.67 Rounding: 41.67 → 42 gtt/min (nearest whole drop). Final answer: 42 gtt/min Rationale: With a 15 gtt/mL set and 250 mL over 90 minutes, the flow is about 42 drops per minute. Clinical pearl: Drops are always rounded to the nearest whole drop — you cannot count a fraction of a drop.
Question 208. Scenario: A nurse double-checks a drawn-up corticosteroid dose before administration. Order: methylprednisolone 100 mg IV. Available: Methylprednisolone 500 mg powder vial, reconstituted to 62.5 mg/mL. The nurse drew 1.6 mL into the syringe. Question: What dose (mg) does the 1.6 mL in the syringe contain, and is this the correct ordered dose?
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Correct answer: 100 mg; yes, correct dose Setup (dimensional analysis): dose = 62.5 mg/mL × 1.6 mL Raw calculation: 62.5 × 1.6 = 100 Rounding: Exact value. Final answer: 100 mg — correct dose Rationale: The syringe contains 1.6 mL × 62.5 mg/mL = 100 mg, exactly matching the order. Clinical pearl: Verify a drawn dose by multiplying volume by concentration before administering.
Question 209. Scenario: A nurse is planning the use of a reconstituted cephalosporin vial near its beyond-use limit. Order: ceftriaxone 1 g IV now and 1 g IV the next morning. Available: Ceftriaxone 1 g powder vial. Manufacturer's label: "After reconstitution, discard 24 hours after reconstitution." The nurse reconstitutes the first vial at 0800; the next dose is due at 0800 the following day. Question: May the nurse use the same vial for the 0800 dose the next day? Explain using the label's beyond-use limit.
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Correct answer: No — discard at 0800 (24-hour limit); prepare a new vial. Setup (dimensional analysis): beyond-use = 0800 + 24 h = 0800 next day Raw calculation: 0800 + 24 h = 0800 next day Rounding: N/A Final answer: No; the vial expires at 0800 the next day and must not be used for that dose. Rationale: The label requires discarding 24 hours after reconstitution. The next-morning dose falls exactly at the 24-hour mark, which is beyond use; the nurse must reconstitute a fresh vial. Clinical pearl: At the beyond-use time the vial is expired — it is not "still good" at the boundary.
Question 210. Scenario: A nurse dilutes vancomycin to a specific final concentration in an IV bag. Order: vancomycin 1 g IV. Available: Vancomycin 1 g powder vial, reconstituted to 50 mg/mL (20 mL). The nurse needs a final bag concentration of 4 mg/mL. Question: What total volume is needed for a 4 mg/mL concentration, and how many mL of normal saline should the nurse add to the 20 mL of drug? Round to the nearest whole mL.
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Correct answer: total volume 250 mL; add 230 mL of saline Setup (dimensional analysis): total volume = 1000 mg ÷ 4 mg/mL = 250 mL; saline = 250 mL − 20 mL = 230 mL Raw calculation: 1000 ÷ 4 = 250; 250 − 20 = 230 Rounding: Exact values. Final answer: Total volume 250 mL; add 230 mL of normal saline to the 20 mL of drug Rationale: To reach 4 mg/mL, the 1000 mg must occupy 250 mL. Since 20 mL is already drug solution, 230 mL of saline is added. Clinical pearl: When diluting to a target concentration, subtract the drug volume from the target total to find the diluent volume.
Question 211. Scenario: A nurse is determining how long a bottle of reconstituted oral antibiotic will last. Order: amoxicillin 250 mg PO q8h. Available: Amoxicillin 250 mg/5 mL powder for oral suspension, 100 mL bottle, reconstituted per label to 100 mL total. Question: What is the total amount of amoxicillin (mg) in the bottle, and how many complete 24-hour days (3 doses per day) will one bottle provide?
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Correct answer: 5000 mg total; 6 complete days (18 doses) Setup (dimensional analysis): total mg = 100 mL × 50 mg/mL = 5000 mg; daily = 250 mg × 3 = 750 mg; days = 5000 ÷ 750 Raw calculation: 100 × 50 = 5000; 250 × 3 = 750; 5000 ÷ 750 = 6.67; doses = 5000 ÷ 250 = 20 Rounding: 6.67 days → 6 complete 24-hour days (18 doses; 2 doses remain). Final answer: 5000 mg total; 6 complete days (18 doses), with 2 doses remaining Rationale: The 100 mL bottle at 50 mg/mL holds 5000 mg. Three 250 mg doses per day consume 750 mg/day, so the bottle lasts 6 full days (5000 ÷ 750 = 6.67). Clinical pearl: For multi-day oral courses, compute total drug in the bottle and divide by the daily total to find the days supplied.
Question 212. Scenario: A nurse must choose the correct reconstitution for the route of administration. Order: ampicillin 500 mg IM. Available: Ampicillin 1 g powder vial. Label: "For IM: add 3.5 mL Sterile Water for Injection to yield 250 mg/mL. For IV: add 7.2 mL Sterile Water for Injection to yield 125 mg/mL." Question: Which concentration should the nurse use for the IM route, and how many mL should be administered for the 500 mg dose?
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Correct answer: 250 mg/mL (IM concentration); 2 mL Setup (dimensional analysis): 500 mg × (1 mL / 250 mg) = ? mL Raw calculation: 500 ÷ 250 = 2 Rounding: Exact value. Final answer: Use 250 mg/mL; administer 2 mL Rationale: The order is IM, so the nurse uses the IM reconstitution (3.5 mL → 250 mg/mL). A 500 mg dose is 2 mL. Clinical pearl: Match the reconstitution concentration to the ordered route on dual-purpose labels.
Question 213. Scenario: A nurse identifies a reconstitution error before giving a dose. Order: ampicillin 500 mg IM. Available: Ampicillin 1 g powder vial with dual reconstitution directions (IM: 250 mg/mL; IV: 125 mg/mL). A colleague reconstituted the vial using the IV directions (7.2 mL → 125 mg/mL) and prepared the dose. Question: What error was made, and how many mL should the nurse actually administer for the 500 mg IM dose? (Assume the IM concentration of 250 mg/mL should have been used.)
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Correct answer: Wrong concentration used for IM; should be 2 mL (not 4 mL). Setup (dimensional analysis): correct volume = 500 mg ÷ 250 mg/mL = 2 mL; incorrect volume = 500 mg ÷ 125 mg/mL = 4 mL Raw calculation: 500 ÷ 250 = 2; 500 ÷ 125 = 4 Rounding: Exact values. Final answer: The vial was reconstituted to the IV concentration (125 mg/mL) instead of the IM concentration (250 mg/mL); the correct IM volume is 2 mL. Rationale: Using the IV concentration for an IM order would require 4 mL — double the intended volume and the wrong formulation strength for the route. The nurse must reconstitute a fresh vial to 250 mg/mL and give 2 mL. Clinical pearl: Reconstituting to the wrong concentration doubles (or halves) the dose volume — always match concentration to route before drawing.
Question 214. Scenario: A nurse calculates the completion time of a vancomycin infusion. Order: vancomycin 1 g IV at 60 mL/hr. Available: Vancomycin 1 g powder vial, reconstituted and diluted to a total volume of 250 mL. Infusion started at 0900. Question: At what time will the infusion be complete?
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Correct answer: 1310 (1:10 PM) Setup (dimensional analysis): duration = 250 mL ÷ 60 mL/hr = 4.17 hr = 4 hr 10 min Raw calculation: 250 ÷ 60 = 4.1667 hr; 0.1667 hr × 60 = 10 min; 0900 + 4 hr 10 min = 1310 Rounding: N/A Final answer: 1310 (1:10 PM) Rationale: At 60 mL/hr, 250 mL infuses in 4 hours 10 minutes, so an infusion started at 0900 completes at 1310. Clinical pearl: Convert the fractional hour (0.17 hr) to minutes (× 60) before adding to the start time.
Question 215. Scenario: A nurse is preparing a large daily ceftriaxone dose from multiple vials. Order: ceftriaxone 2.25 g IV daily. Available: Ceftriaxone 1 g powder vials, each reconstituted to 100 mg/mL (10 mL total per vial). Question: How many vials are needed, and how many total mL should the nurse withdraw for the 2.25 g dose? Round mL to the nearest tenth.
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Correct answer: 3 vials; 22.5 mL Setup (dimensional analysis): 2.25 g = 2250 mg; 2250 mg × (1 mL / 100 mg) = ? mL; vials = ceil(2250 ÷ 1000) = 3 Raw calculation: 2250 ÷ 100 = 22.5; vials = 3 Rounding: 22.5 mL (exact to the tenth). Final answer: 3 vials; withdraw 22.5 mL total Rationale: 2.25 g = 2250 mg, which exceeds two 1 g vials, so three vials are needed. At 100 mg/mL the dose is 22.5 mL, drawn across the vials. Clinical pearl: Convert the total dose to mg, then compare with the vial size to determine how many vials to open.
Question 216. Scenario: A nurse reconstitutes and then further dilutes a proton-pump inhibitor for infusion. Order: pantoprazole 40 mg IV. Available: Pantoprazole 40 mg powder vial. Label: "Add 10 mL 0.9% sodium chloride to yield 4 mg/mL." The nurse adds the entire 10 mL to a 100 mL bag of normal saline. Question: What is the concentration (mg/mL) of the diluted pantoprazole in the bag? Round to the nearest hundredth.
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Correct answer: 0.36 mg/mL Setup (dimensional analysis): concentration = 40 mg ÷ (10 mL + 100 mL) = 40 mg ÷ 110 mL Raw calculation: 40 ÷ 110 = 0.3636… Rounding: 0.3636 → 0.36 mg/mL (nearest hundredth). Final answer: 0.36 mg/mL Rationale: The 40 mg is now in 110 mL total, giving about 0.36 mg/mL. Clinical pearl: Include both the drug volume and the bag volume in the total when calculating a diluted concentration.
Question 217. Scenario: A nurse reverses a reconstitution to find the powder volume and drug mass. Order: ceftriaxone 1 g IV. Available: A powder vial. The nurse adds 4.6 mL of Sterile Water for Injection, and the resulting final volume is 5 mL with a concentration of 200 mg/mL. Question: What volume (mL) does the powder displace, and what is the total amount of drug (mg) in the vial?
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Correct answer: 0.4 mL displacement; 1000 mg (1 g) total drug Setup (dimensional analysis): displacement = 5 mL − 4.6 mL; drug mass = 200 mg/mL × 5 mL Raw calculation: 5 − 4.6 = 0.4; 200 × 5 = 1000 Rounding: Exact values. Final answer: Powder displaces 0.4 mL; the vial contains 1000 mg (1 g) Rationale: The final volume (5 mL) minus the diluent (4.6 mL) is the powder volume (0.4 mL). Multiplying the concentration by the total volume gives the total drug: 200 × 5 = 1000 mg. Clinical pearl: You can recover both displacement and total drug mass from the diluent volume, final volume, and concentration.
Question 218. Scenario: A nurse completes a full vancomycin workflow — reconstitution, dilution, and gravity rate. Order: vancomycin 1.5 g IV over 120 minutes. Available: Vancomycin 1 g powder vials, each reconstituted to 50 mg/mL (20 mL per vial). The nurse withdraws the needed volume, adds it to normal saline to a total volume of 250 mL, and hangs it with tubing that delivers 20 gtt/mL. Question: How many mL of drug should the nurse withdraw from the vials, and what drip rate (gtt/min) should be set? Round gtt/min to the nearest whole drop.
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Correct answer: 30 mL from vials; 42 gtt/min Setup (dimensional analysis): volume = 1.5 g = 1500 mg ÷ 50 mg/mL = 30 mL; gtt/min = (250 × 20) ÷ 120 Raw calculation: 1500 ÷ 50 = 30; (250 × 20) ÷ 120 = 5000 ÷ 120 = 41.67 Rounding: 41.67 → 42 gtt/min (nearest whole drop). Final answer: Withdraw 30 mL (from 2 vials); set 42 gtt/min Rationale: 1.5 g requires 30 mL of the 50 mg/mL solution (one full 1 g vial = 20 mL, plus 10 mL from a second). Diluted to 250 mL and run over 120 minutes with a 20 gtt/mL set, the rate is 42 gtt/min. Clinical pearl: Chain the steps: reconstitute → withdraw the dose → dilute to final volume → compute the drip rate.
Question 219. Scenario: A nurse plans a full-day course of intravenous corticosteroids from one vial. Order: methylprednisolone 250 mg IV q6h × 4 doses. Available: Methylprednisolone 1 g powder vial, reconstituted to 62.5 mg/mL (16 mL total). Question: How many mL should be given per dose, how many 250 mg doses does one vial contain, and does a single vial cover the entire 4-dose course?
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Correct answer: 4 mL per dose; 4 doses per vial; yes, one vial covers the course Setup (dimensional analysis): mL/dose = 250 mg ÷ 62.5 mg/mL = 4 mL; doses = 1000 mg ÷ 250 mg = 4 Raw calculation: 250 ÷ 62.5 = 4; 1000 ÷ 250 = 4 Rounding: Exact values. Final answer: 4 mL per dose; 4 doses per vial; one vial is sufficient for all 4 doses Rationale: Each 250 mg dose is 4 mL of the 62.5 mg/mL solution, and the 1 g (1000 mg) vial contains exactly four 250 mg doses, matching the 4-dose course. Clinical pearl: Verify a multi-dose plan by confirming (dose × number of doses) ≤ total drug in the vial.
Question 220. Scenario: A nurse prepares a weight-based antibiotic for a pediatric patient. Order: cefepime 50 mg/kg/dose IV q8h for a child weighing 20 kg. Available: Cefepime 1 g powder vial. Label: "Add 10 mL Sterile Water for Injection to yield 100 mg/mL." Each dose is further diluted in 50 mL normal saline and infused over 30 minutes. Question: What is the dose (mg), how many mL should be withdrawn from the reconstituted vial, and at what rate (mL/hr) should the infusion be run? Round mL/hr to the nearest whole number.
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Correct answer: 1000 mg; 10 mL; 120 mL/hr Setup (dimensional analysis): dose = 50 mg/kg × 20 kg = 1000 mg; volume = 1000 mg ÷ 100 mg/mL = 10 mL; rate = (10 mL + 50 mL) ÷ 0.5 hr Raw calculation: 50 × 20 = 1000; 1000 ÷ 100 = 10; 60 ÷ 0.5 = 120 Rounding: 120 mL/hr (exact). Final answer: Dose 1000 mg; withdraw 10 mL; run at 120 mL/hr Rationale: The weight-based order gives 1000 mg (1 g). The reconstituted cefepime is 100 mg/mL, so 10 mL is withdrawn, added to 50 mL of saline (60 mL total), and infused over 30 minutes at 120 mL/hr. Clinical pearl: Weight-based orders are solved first in mg, then converted to volume from the reconstituted concentration, then to an infusion rate.
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