Critical Care & Titration (Part 2) — practice set (Q451–500)

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50 review questions from the chapter. Try each one, then open the answer.

1. Question 451. Scenario: A 68-year-old patient in cardiogenic shock weighs 82 kg. Order: Dopamine 5 mcg/kg/min IV infusion, titrate to maintain mean arterial pressure (MAP) ≥ 65 mmHg. Available: Dopamine 400 mg in 250 mL D5W. Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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   Correct answer: 15.4 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 5 mcg/kg/min × 82 kg = 410 mcg/min Rate (mL/hr) = 410 mcg/min × (60 min/1 hr) × (1 mL/1600 mcg) Raw calculation: 410 × 60 ÷ 1600 = 15.375 mL/hr Rounding: 15.375 rounds to 15.4 mL/hr (nearest tenth). Final answer: 15.4 mL/hr Rationale: Convert the ordered mcg/kg/min to mcg/min by multiplying by weight, then to mcg/hr, then divide by the bag concentration (400 mg = 400,000 mcg ÷ 250 mL = 1600 mcg/mL) to obtain mL/hr. Clinical pearl: Dopamine 400 mg/250 mL always yields 1600 mcg/mL — a common "standard" concentration; memorizing the standard concentrations of critical-care drips speeds verification.

2. Question 452. Scenario: A 70 kg patient with septic shock requires a vasopressor. Order: Norepinephrine 0.1 mcg/kg/min IV infusion, titrate to MAP ≥ 65 mmHg. Available: Norepinephrine 4 mg in 250 mL D5W (16 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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   Correct answer: 26.3 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 0.1 mcg/kg/min × 70 kg = 7 mcg/min Rate (mL/hr) = 7 mcg/min × (60 min/1 hr) × (1 mL/16 mcg) Raw calculation: 7 × 60 ÷ 16 = 26.25 mL/hr Rounding: 26.25 rounds up to 26.3 mL/hr (nearest tenth; half-way values round up). Final answer: 26.3 mL/hr Rationale: Norepinephrine 4 mg in 250 mL = 4000 mcg ÷ 250 mL = 16 mcg/mL. The ordered 0.1 mcg/kg/min for 70 kg delivers 7 mcg/min = 420 mcg/hr, which at 16 mcg/mL requires 26.25 mL/hr. Clinical pearl: Norepinephrine 4 mg/250 mL = 16 mcg/mL and the 8 mg/250 mL "double" = 32 mcg/mL; always confirm which concentration is hanging before programming the pump.

3. Question 453. Scenario: A 91 kg patient is started on an inotrope for decompensated heart failure. Order: Dobutamine 5 mcg/kg/min IV infusion. Available: Dobutamine 250 mg in 250 mL D5W (1000 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth. A. 22.8 mL/hr B. 27.3 mL/hr C. 31.9 mL/hr D. 45.5 mL/hr

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   Correct answer: B. 27.3 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 5 mcg/kg/min × 91 kg = 455 mcg/min Rate (mL/hr) = 455 mcg/min × (60 min/1 hr) × (1 mL/1000 mcg) Raw calculation: 455 × 60 ÷ 1000 = 27.3 mL/hr Rounding: 27.3 mL/hr (already at the tenth). Final answer: 27.3 mL/hr Rationale: Dobutamine 250 mg in 250 mL = 1000 mcg/mL. The ordered 5 mcg/kg/min for 91 kg = 27,300 mcg/hr ÷ 1000 mcg/mL = 27.3 mL/hr. Clinical pearl: When the bag concentration is a "round" 1000 mcg/mL, the mL/hr equals mcg/min ÷ 1000 × 60 — spot-check with a quick mental estimate (≈ 5 × 90 = 450 mcg/min → about 27 mL/hr).

4. Question 454. Scenario: A 68 kg patient needs an escalating vasopressor after fluid resuscitation. Order: Dopamine 10 mcg/kg/min IV infusion. Available: Dopamine 800 mg in 500 mL D5W (1600 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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   Correct answer: 25.5 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 10 mcg/kg/min × 68 kg = 680 mcg/min Rate (mL/hr) = 680 mcg/min × (60 min/1 hr) × (1 mL/1600 mcg) Raw calculation: 680 × 60 ÷ 1600 = 25.5 mL/hr Rounding: 25.5 mL/hr (already at the tenth). Final answer: 25.5 mL/hr Rationale: Dopamine 800 mg in 500 mL = 800,000 mcg ÷ 500 mL = 1600 mcg/mL (same as 400 mg/250 mL). 10 mcg/kg/min × 68 kg = 680 mcg/min = 40,800 mcg/hr ÷ 1600 mcg/mL = 25.5 mL/hr. Clinical pearl: 400 mg/250 mL and 800 mg/500 mL are the SAME concentration (1600 mcg/mL) — recognizing equivalent concentrations prevents a tenfold dosing error.

5. Question 455. Scenario: A 75 kg patient has been on a dobutamine infusion and the nurse must document the delivered dose. Order: Dobutamine continuous infusion (verify the delivered dose in mcg/kg/min). Available: Dobutamine 500 mg in 250 mL D5W (2000 mcg/mL) infusing at 18 mL/hr. Question: What dose in mcg/kg/min is the patient receiving? Round to the nearest tenth.

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   Correct answer: 8 mcg/kg/min Setup (dimensional analysis): mcg/hr = 18 mL/hr × 2000 mcg/mL = 36,000 mcg/hr mcg/min = 36,000 mcg/hr ÷ 60 min/hr = 600 mcg/min mcg/kg/min = 600 mcg/min ÷ 75 kg Raw calculation: 18 × 2000 ÷ 60 ÷ 75 = 8 mcg/kg/min Rounding: 8 mcg/kg/min (already a whole number). Final answer: 8 mcg/kg/min Rationale: Dobutamine 500 mg in 250 mL = 2000 mcg/mL (double concentration). At 18 mL/hr the patient receives 36,000 mcg/hr = 600 mcg/min; divided by 75 kg = 8 mcg/kg/min. Clinical pearl: To back-calculate a drip, multiply rate (mL/hr) × concentration (mcg/mL) ÷ 60 ÷ weight (kg) — do this whenever the ordered dose is not documented.

6. Question 456. Scenario: A 80 kg patient is on a double-concentration norepinephrine infusion; the nurse must verify the delivered dose during handoff. Order: Norepinephrine continuous infusion (verify the delivered dose in mcg/kg/min). Available: Norepinephrine 8 mg in 250 mL D5W (32 mcg/mL) infusing at 15 mL/hr. Question: What dose in mcg/kg/min is the patient receiving? Round to the nearest hundredth.

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   Correct answer: 0.1 mcg/kg/min Setup (dimensional analysis): mcg/hr = 15 mL/hr × 32 mcg/mL = 480 mcg/hr mcg/min = 480 mcg/hr ÷ 60 min/hr = 8 mcg/min mcg/kg/min = 8 mcg/min ÷ 80 kg Raw calculation: 15 × 32 ÷ 60 ÷ 80 = 0.1 mcg/kg/min Rounding: 0.1 mcg/kg/min (already at the hundredth). Final answer: 0.1 mcg/kg/min Rationale: Norepinephrine 8 mg in 250 mL = 8000 mcg ÷ 250 mL = 32 mcg/mL. At 15 mL/hr the patient receives 480 mcg/hr = 8 mcg/min; ÷ 80 kg = 0.1 mcg/kg/min. Clinical pearl: Norepinephrine doses are small (typically 0.01–0.5 mcg/kg/min); carry enough decimal places through the calculation and only round at the end.

7. Question 457. Scenario: During rounds, a 60 kg patient's dopamine infusion is questioned because the rate looks high for the documented weight. Order: Dopamine continuous infusion (verify the delivered dose in mcg/kg/min). Available: Dopamine 400 mg in 250 mL D5W (1600 mcg/mL) infusing at 22.5 mL/hr. Question: What dose in mcg/kg/min is the patient receiving? A. 5 mcg/kg/min B. 7.5 mcg/kg/min C. 10 mcg/kg/min D. 15 mcg/kg/min

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   Correct answer: C. 10 mcg/kg/min Setup (dimensional analysis): mcg/hr = 22.5 mL/hr × 1600 mcg/mL = 36,000 mcg/hr mcg/min = 36,000 ÷ 60 = 600 mcg/min mcg/kg/min = 600 ÷ 60 kg Raw calculation: 22.5 × 1600 ÷ 60 ÷ 60 = 10 mcg/kg/min Rounding: 10 mcg/kg/min (already a whole number). Final answer: 10 mcg/kg/min Rationale: Dopamine 400 mg/250 mL = 1600 mcg/mL. At 22.5 mL/hr the patient receives 36,000 mcg/hr = 600 mcg/min ÷ 60 kg = 10 mcg/kg/min. Clinical pearl: A rate that "looks high" may simply reflect a higher mcg/kg/min because of a lower body weight — always back-calculate before questioning an order.

8. Question 458. Scenario: A 65 kg intubated patient requires sedation for mechanical ventilation. Order: Fentanyl 1.5 mcg/kg/hr IV infusion. Available: Fentanyl 2500 mcg in 250 mL 0.9% sodium chloride (10 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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   Correct answer: 9.8 mL/hr Setup (dimensional analysis): Dose (mcg/hr) = 1.5 mcg/kg/hr × 65 kg = 97.5 mcg/hr Rate (mL/hr) = 97.5 mcg/hr × (1 mL/10 mcg) Raw calculation: 97.5 ÷ 10 = 9.75 mL/hr Rounding: 9.75 rounds up to 9.8 mL/hr (nearest tenth). Final answer: 9.8 mL/hr Rationale: Fentanyl 2500 mcg in 250 mL = 10 mcg/mL. The ordered 1.5 mcg/kg/hr for 65 kg = 97.5 mcg/hr ÷ 10 mcg/mL = 9.75 mL/hr. Clinical pearl: For mcg/kg/hr drugs, no ×60 conversion is needed (the dose is already per hour) — a frequent source of tenfold errors when confused with mcg/kg/min.

9. Question 459. Scenario: A 60 kg patient on a fentanyl infusion is being transferred to another unit. Order: Fentanyl continuous infusion (verify the delivered dose in mcg/kg/hr). Available: Fentanyl 2500 mcg in 250 mL (10 mcg/mL) infusing at 12 mL/hr. Question: What dose in mcg/kg/hr is the patient receiving? Round to the nearest tenth.

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   Correct answer: 2 mcg/kg/hr Setup (dimensional analysis): mcg/hr = 12 mL/hr × 10 mcg/mL = 120 mcg/hr mcg/kg/hr = 120 mcg/hr ÷ 60 kg Raw calculation: 12 × 10 ÷ 60 = 2 mcg/kg/hr Rounding: 2 mcg/kg/hr (already a whole number). Final answer: 2 mcg/kg/hr Rationale: Fentanyl 2500 mcg/250 mL = 10 mcg/mL. At 12 mL/hr the patient receives 120 mcg/hr ÷ 60 kg = 2 mcg/kg/hr. Clinical pearl: Fentanyl 2500 mcg/250 mL is the standard 10 mcg/mL concentration; use it to rapidly verify mcg/kg/hr sedation orders during handoff.

10. Question 460. Scenario: A 75 kg patient is receiving a midazolam infusion; the receiving nurse must confirm the rate is consistent with the documented mcg/kg/hr dose. Order: Midazolam continuous infusion (verify the delivered dose in mcg/kg/hr). Available: Midazolam 100 mg in 100 mL 0.9% sodium chloride (1000 mcg/mL) infusing at 6 mL/hr. Question: What dose in mcg/kg/hr is the patient receiving? A. 60 mcg/kg/hr B. 75 mcg/kg/hr C. 80 mcg/kg/hr D. 100 mcg/kg/hr

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    Correct answer: C. 80 mcg/kg/hr Setup (dimensional analysis): mcg/hr = 6 mL/hr × 1000 mcg/mL = 6,000 mcg/hr mcg/kg/hr = 6,000 mcg/hr ÷ 75 kg Raw calculation: 6 × 1000 ÷ 75 = 80 mcg/kg/hr Rounding: 80 mcg/kg/hr (already a whole number). Final answer: 80 mcg/kg/hr Rationale: Midazolam 100 mg in 100 mL = 100,000 mcg ÷ 100 mL = 1000 mcg/mL. At 6 mL/hr the patient receives 6,000 mcg/hr ÷ 75 kg = 80 mcg/kg/hr. Clinical pearl: A 1 mg/mL midazolam drip delivers 1000 mcg/mL; converting the concentration to mcg/mL up front makes the mcg/kg/hr arithmetic straightforward.

11. Question 461. Scenario: A pharmacist teaches a new nurse that adding drug to a diluent increases the total volume, which changes the final concentration. Order: Prepare the dobutamine admixture and determine its final concentration in mcg/mL. Available: Dobutamine 250 mg/20 mL vial (12.5 mg/mL). The entire 20 mL is added to a 250 mL bag of D5W. Question: What is the final concentration of the admixture in mcg/mL? Round to the nearest tenth.

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    Correct answer: 925.9 mcg/mL Setup (dimensional analysis): Total volume = 250 mL + 20 mL = 270 mL Concentration = 250 mg × (1000 mcg/1 mg) ÷ 270 mL Raw calculation: 250,000 ÷ 270 = 925.926 mcg/mL Rounding: 925.926 rounds to 925.9 mcg/mL (nearest tenth). Final answer: 925.9 mcg/mL Rationale: Adding the full 20 mL of the 250 mg/20 mL vial increases the total volume to 270 mL, so the true concentration is 250,000 mcg ÷ 270 mL = 925.9 mcg/mL — NOT 1000 mcg/mL. Clinical pearl: Always account for the additive volume when compounding; ignoring it overestimates the concentration and underdoses the patient.

12. Question 462. Scenario: A critical-care nurse must compound a custom norepinephrine concentration for a fluid-restricted patient. Order: Norepinephrine 0.05 mcg/kg/min for a 70 kg patient, to be delivered at exactly 5 mL/hr. Available: Norepinephrine 1 mg/mL (4 mg/4 mL ampules) to be diluted in D5W to a total final volume of 250 mL (QS to 250 mL). Question: How many milligrams of norepinephrine must be added to the bag? Round to the nearest tenth. How many mL of the 1 mg/mL solution does this represent?

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    Correct answer: 10.5 mg (10.5 mL of the 1 mg/mL solution) Setup (dimensional analysis): Required mcg/hr = 0.05 mcg/kg/min × 70 kg × 60 min/hr = 210 mcg/hr Required concentration = 210 mcg/hr ÷ 5 mL/hr = 42 mcg/mL Total drug = 42 mcg/mL × 250 mL = 10,500 mcg = 10.5 mg Volume to add = 10.5 mg × (1 mL/1 mg) = 10.5 mL Raw calculation: 0.05 × 70 × 60 = 210; 210 ÷ 5 = 42; 42 × 250 = 10,500 mcg = 10.5 mg Rounding: 10.5 mg (already at the tenth); 10.5 mL of the 1 mg/mL solution. Final answer: Add 10.5 mg (10.5 mL) of norepinephrine, then QS to a total of 250 mL Rationale: A 70 kg patient at 0.05 mcg/kg/min needs 210 mcg/hr. Delivering that at 5 mL/hr requires 42 mcg/mL; a 250 mL bag therefore needs 10,500 mcg = 10.5 mg. Because the ampules are 1 mg/mL, 10.5 mg = 10.5 mL. Clinical pearl: When compounding a custom concentration, always specify "QS to final volume" so the added drug volume does not silently change the concentration.

13. Question 463. Scenario: A nurse prepares a standard dopamine infusion. Order: Prepare dopamine 400 mg in 250 mL D5W (QS to 250 mL). Available: Dopamine concentrate 40 mg/mL. Question: How many mL of dopamine concentrate must be drawn up? Round to the nearest tenth.

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    Correct answer: 10 mL Setup (dimensional analysis): Volume = 400 mg × (1 mL/40 mg) Raw calculation: 400 ÷ 40 = 10 mL Rounding: 10 mL (already a whole number). Final answer: 10 mL Rationale: Dopamine concentrate is 40 mg/mL, so 400 mg requires 400 ÷ 40 = 10 mL. Clinical pearl: Dopamine 400 mg in 250 mL is the classic "standard concentration" (1600 mcg/mL); drawing up 10 mL of 40 mg/mL concentrate into a 250 mL bag reproduces it.

14. Question 464. Scenario: A 90 kg patient is started on a weight-based heparin protocol for an acute coronary syndrome. Order: (HYPOTHETICAL protocol) Heparin IV bolus 80 units/kg, then continuous infusion 18 units/kg/hr. Available: Heparin 5,000 units/mL vial (for bolus); heparin 25,000 units in 250 mL D5W (100 units/mL) for infusion. Question: Calculate (a) the bolus dose in units, (b) the bolus volume in mL (round to the nearest tenth), and (c) the initial infusion rate in mL/hr (round to the nearest tenth).

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    Correct answer: (a) 7,200 units; (b) 1.4 mL; (c) 16.2 mL/hr Setup (dimensional analysis): (a) Bolus = 80 units/kg × 90 kg = 7,200 units (b) Bolus volume = 7,200 units × (1 mL/5,000 units) = 1.44 mL (c) Infusion = 18 units/kg/hr × 90 kg = 1,620 units/hr Rate = 1,620 units/hr × (1 mL/100 units) = 16.2 mL/hr Raw calculation: 80 × 90 = 7,200; 7,200 ÷ 5,000 = 1.44; 18 × 90 = 1,620; 1,620 ÷ 100 = 16.2 Rounding: Bolus volume 1.44 → 1.4 mL (nearest tenth); infusion 16.2 mL/hr (already at the tenth). Final answer: Bolus 7,200 units (1.4 mL); infusion 16.2 mL/hr Rationale: The protocol is weight-based, so both the bolus and the maintenance rate scale with the 90 kg weight. The 25,000 units/250 mL bag = 100 units/mL, so 1,620 units/hr = 16.2 mL/hr. Clinical pearl: Heparin boluses are drawn from a concentrated vial (5,000 units/mL) while the infusion uses a dilute bag (100 units/mL) — use the correct concentration for each calculation.

15. Question 465. Scenario: A 76 kg patient begins a heparin infusion for a venous thromboembolism. Order: (HYPOTHETICAL protocol) Heparin IV bolus 70 units/kg, then continuous infusion 15 units/kg/hr. Available: Heparin 5,000 units/mL vial (for bolus); heparin 25,000 units in 250 mL D5W (100 units/mL) for infusion. Question: Calculate (a) the bolus dose in units, (b) the bolus volume in mL (round to the nearest tenth), and (c) the initial infusion rate in mL/hr (round to the nearest tenth).

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    Correct answer: (a) 5,320 units; (b) 1.1 mL; (c) 11.4 mL/hr Setup (dimensional analysis): (a) Bolus = 70 units/kg × 76 kg = 5,320 units (b) Bolus volume = 5,320 units × (1 mL/5,000 units) = 1.064 mL (c) Infusion = 15 units/kg/hr × 76 kg = 1,140 units/hr Rate = 1,140 units/hr × (1 mL/100 units) = 11.4 mL/hr Raw calculation: 70 × 76 = 5,320; 5,320 ÷ 5,000 = 1.064; 15 × 76 = 1,140; 1,140 ÷ 100 = 11.4 Rounding: Bolus volume 1.064 → 1.1 mL (nearest tenth); infusion 11.4 mL/hr (already at the tenth). Final answer: Bolus 5,320 units (1.1 mL); infusion 11.4 mL/hr Rationale: Both the bolus and maintenance rate are computed from the 76 kg weight per the hypothetical protocol. The bag is 100 units/mL, so 1,140 units/hr = 11.4 mL/hr. Clinical pearl: Even a small difference in protocol (70 vs. 80 units/kg) meaningfully changes the dose — always confirm the specific protocol your institution uses.

16. Question 466. Scenario: A 82 kg patient has been on a heparin infusion at 16 units/kg/hr. The 6-hour aPTT returns at 42 seconds (therapeutic range 60–85 seconds). Order: (HYPOTHETICAL nomogram) - aPTT < 55 s → give a re-bolus of 40 units/kg AND increase the infusion by 2 units/kg/hr. - aPTT 55–59 s → increase the infusion by 1 unit/kg/hr (no bolus). - aPTT 60–85 s → therapeutic, no change. - aPTT 86–100 s → decrease the infusion by 1 unit/kg/hr. - aPTT > 100 s → hold 1 hour, then decrease the infusion by 2 unit/kg/hr. Available: Heparin 5,000 units/mL vial (for bolus); heparin 25,000 units in 250 mL D5W (100 units/mL) for infusion. Question: Calculate (a) the additional bolus in units and (b) the new infusion rate in mL/hr (round to the nearest tenth).

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    Correct answer: (a) 3,280 units; (b) 14.8 mL/hr Setup (dimensional analysis): (a) Re-bolus = 40 units/kg × 82 kg = 3,280 units (b) New rate = (16 + 2) units/kg/hr × 82 kg = 18 units/kg/hr × 82 kg = 1,476 units/hr New mL/hr = 1,476 units/hr × (1 mL/100 units) = 14.76 mL/hr Raw calculation: 40 × 82 = 3,280; 18 × 82 = 1,476; 1,476 ÷ 100 = 14.76 Rounding: 14.76 rounds to 14.8 mL/hr (nearest tenth); bolus 3,280 units (whole number). Final answer: Re-bolus 3,280 units; increase infusion to 14.8 mL/hr Rationale: An aPTT of 42 seconds is below 55 seconds, so the nomogram calls for a 40 units/kg re-bolus and a 2 units/kg/hr increase (16 → 18 units/kg/hr). At 82 kg and 100 units/mL, the new rate is 14.76 mL/hr. Clinical pearl: When a nomogram specifies both a re-bolus and a rate change, compute and administer BOTH; the bolus addresses current under-anticoagulation while the rate change prevents recurrence.

17. Question 467. Scenario: A patient with diabetic ketoacidosis begins an insulin infusion. Order: Regular insulin IV infusion at 6 units/hr. Available: Regular insulin 100 units in 100 mL 0.9% sodium chloride (1 unit/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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    Correct answer: 6 mL/hr Setup (dimensional analysis): Rate (mL/hr) = 6 units/hr × (1 mL/1 unit) Raw calculation: 6 ÷ 1 = 6 mL/hr Rounding: 6 mL/hr (already a whole number). Final answer: 6 mL/hr Rationale: The standard insulin infusion is 1 unit/mL (100 units in 100 mL), so units/hr and mL/hr are numerically identical. Clinical pearl: A 1 unit/mL insulin infusion makes units/hr = mL/hr; the danger is assuming every insulin bag is 1 unit/mL — always read the label.

18. Question 468. Scenario: A patient on an insulin infusion has a fingerstick glucose of 260 mg/dL. Order: (HYPOTHETICAL titration scale) For glucose 251–300 mg/dL, increase the insulin infusion by 2 units/hr. The current rate is 6 units/hr. Available: Regular insulin 100 units in 100 mL 0.9% sodium chloride (1 unit/mL). Question: What is the new infusion rate in mL/hr? Round to the nearest tenth.

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    Correct answer: 8 mL/hr Setup (dimensional analysis): New dose = 6 units/hr + 2 units/hr = 8 units/hr Rate (mL/hr) = 8 units/hr × (1 mL/1 unit) = 8 mL/hr Raw calculation: 6 + 2 = 8; 8 ÷ 1 = 8 mL/hr Rounding: 8 mL/hr (whole number). Final answer: 8 mL/hr Rationale: A glucose of 260 mg/dL falls in the 251–300 bracket, so the infusion increases by 2 units/hr (6 → 8 units/hr). At 1 unit/mL, that is 8 mL/hr. Clinical pearl: Titration adjustments are ADDED to (or subtracted from) the current rate — compute the new rate, then re-check the glucose per protocol rather than titrating repeatedly on guesswork.

19. Question 469. Scenario: A 90 kg patient is placed on an insulin infusion for hyperglycemia in critical illness. Order: (HYPOTHETICAL protocol) - IV bolus: 0.1 units/kg. - Start infusion at 0.1 units/kg/hr. - Hourly glucose scale: < 70 mg/dL → hold infusion, give 25 g D50W; 70–150 → decrease 1 unit/hr; 151–200 → no change; 201–250 → increase 1 unit/hr; 251–300 → increase 2 units/hr; > 300 → increase 3 units/hr and notify provider. Available: Regular insulin 100 units in 100 mL 0.9% sodium chloride (1 unit/mL). Question: Calculate (a) the bolus dose in units, (b) the initial infusion rate in mL/hr, and (c) the infusion rate after the first hourly glucose of 285 mg/dL (mL/hr). Round to the nearest tenth.

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    Correct answer: (a) 9 units; (b) 9 mL/hr; (c) 11 mL/hr Setup (dimensional analysis): (a) Bolus = 0.1 units/kg × 90 kg = 9 units (b) Initial = 0.1 units/kg/hr × 90 kg = 9 units/hr × (1 mL/1 unit) = 9 mL/hr (c) Glucose 285 → increase 2 units/hr: 9 + 2 = 11 units/hr × (1 mL/1 unit) = 11 mL/hr Raw calculation: 0.1 × 90 = 9; 9 ÷ 1 = 9; 9 + 2 = 11; 11 ÷ 1 = 11 Rounding: All whole numbers. Final answer: Bolus 9 units; initial 9 mL/hr; after first glucose 11 mL/hr Rationale: Both the bolus and the starting infusion are weight-based (0.1 units/kg and 0.1 units/kg/hr for 90 kg = 9 units and 9 units/hr). A glucose of 285 falls in the 251–300 bracket, adding 2 units/hr → 11 units/hr = 11 mL/hr. Clinical pearl: Insulin protocols combine a weight-based start with a glucose-based adjustment — compute the starting rate from weight, then apply each hourly glucose bracket to the CURRENT rate.

20. Question 470. Scenario: A 70 kg patient's norepinephrine is being titrated upward. Order: Increase the norepinephrine infusion from 0.06 mcg/kg/min to 0.08 mcg/kg/min. Available: Norepinephrine 4 mg in 250 mL D5W (16 mcg/mL). Question: What is the new infusion rate in mL/hr? Round to the nearest tenth.

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    Correct answer: 21 mL/hr Setup (dimensional analysis): New dose (mcg/min) = 0.08 mcg/kg/min × 70 kg = 5.6 mcg/min Rate (mL/hr) = 5.6 mcg/min × (60 min/1 hr) × (1 mL/16 mcg) = 21 mL/hr Raw calculation: 0.08 × 70 × 60 ÷ 16 = 21 mL/hr Rounding: 21 mL/hr (already a whole number). Final answer: 21 mL/hr Rationale: The new ordered dose of 0.08 mcg/kg/min for 70 kg delivers 5.6 mcg/min = 336 mcg/hr ÷ 16 mcg/mL = 21 mL/hr. Clinical pearl: Titration changes are expressed in mcg/kg/min; each step must be re-converted to mL/hr using the current bag concentration before reprogramming the pump.

21. Question 471. Scenario: A fluid-restricted 70 kg patient requires a double-concentration norepinephrine preparation. Order: Norepinephrine 0.1 mcg/kg/min IV infusion. Available: Norepinephrine 8 mg in 250 mL D5W (32 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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    Correct answer: 13.1 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 0.1 mcg/kg/min × 70 kg = 7 mcg/min Rate (mL/hr) = 7 mcg/min × (60 min/1 hr) × (1 mL/32 mcg) Raw calculation: 7 × 60 ÷ 32 = 13.125 mL/hr Rounding: 13.125 rounds to 13.1 mL/hr (nearest tenth). Final answer: 13.1 mL/hr Rationale: The double-concentration bag (8 mg/250 mL = 32 mcg/mL) delivers the same 0.1 mcg/kg/min at half the volume of the standard 16 mcg/mL bag (13.1 vs. 26.3 mL/hr). Clinical pearl: Doubling the concentration halves the required rate for the same dose — a key strategy to conserve fluid volume, but it demands extra vigilance to avoid dosing errors.

22. Question 472. Scenario: A 85 kg patient's dopamine infusion is reviewed to determine whether it is being used at a "renal-dose" or "pressor-dose" range. Order: Dopamine continuous infusion (determine the delivered dose and its clinical range). Available: Dopamine 800 mg in 500 mL D5W (1600 mcg/mL) infusing at 12 mL/hr. Question: What dose in mcg/kg/min is the patient receiving (round to the nearest tenth), and into which HYPOTHETICAL range does it fall: renal-dose (2–5 mcg/kg/min) or pressor-dose (5–20 mcg/kg/min)?

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    Correct answer: 3.8 mcg/kg/min (renal-dose range) Setup (dimensional analysis): mcg/hr = 12 mL/hr × 1600 mcg/mL = 19,200 mcg/hr mcg/min = 19,200 ÷ 60 = 320 mcg/min mcg/kg/min = 320 ÷ 85 kg = 3.76 mcg/kg/min Raw calculation: 12 × 1600 ÷ 60 ÷ 85 = 3.765 mcg/kg/min Rounding: 3.765 rounds to 3.8 mcg/kg/min (nearest tenth). Final answer: 3.8 mcg/kg/min — falls in the HYPOTHETICAL renal-dose range (2–5 mcg/kg/min) Rationale: Dopamine 800 mg/500 mL = 1600 mcg/mL. At 12 mL/hr the patient receives 19,200 mcg/hr = 320 mcg/min ÷ 85 kg = 3.76 mcg/kg/min, which sits within the hypothetical renal-dose range. Clinical pearl: "Renal-dose dopamine" is a low-dose strategy historically used for renal protection; current evidence does not support routine use, so verify the indication rather than the label alone.

23. Question 473. Scenario: A patient's vasopressin infusion is titrated because the MAP remains below 65 mmHg. Order: (HYPOTHETICAL protocol) If MAP < 65 mmHg, increase vasopressin by 0.01 units/min. The current dose is 0.03 units/min. Available: Vasopressin 20 units in 100 mL 0.9% sodium chloride (0.2 units/mL). Question: What is the new infusion rate in mL/hr after the increase? Round to the nearest whole number.

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    Correct answer: 12 mL/hr Setup (dimensional analysis): New dose = 0.03 units/min + 0.01 units/min = 0.04 units/min units/hr = 0.04 units/min × 60 min/hr = 2.4 units/hr Rate (mL/hr) = 2.4 units/hr × (1 mL/0.2 units) = 12 mL/hr Raw calculation: 0.04 × 60 = 2.4; 2.4 ÷ 0.2 = 12 Rounding: 12 mL/hr (whole number). Final answer: 12 mL/hr Rationale: Vasopressin 20 units/100 mL = 0.2 units/mL. The new dose of 0.04 units/min = 2.4 units/hr ÷ 0.2 units/mL = 12 mL/hr. Clinical pearl: Vasopressin is ordered in units/min (not mcg/kg/min); convert units/min → units/hr (×60) before dividing by the 0.2 units/mL concentration.

24. Question 474. Scenario: A 70 kg patient with acute decompensated heart failure is started on milrinone. Order: (HYPOTHETICAL protocol) Loading dose 50 mcg/kg IV over 10 minutes, then maintenance infusion 0.375 mcg/kg/min. Available: Milrinone 20 mg in 100 mL D5W (200 mcg/mL). Question: Calculate (a) the loading-dose volume in mL and (b) the maintenance infusion rate in mL/hr. Round each to the nearest tenth.

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    Correct answer: (a) 17.5 mL; (b) 7.9 mL/hr Setup (dimensional analysis): (a) Load = 50 mcg/kg × 70 kg = 3,500 mcg Load volume = 3,500 mcg × (1 mL/200 mcg) = 17.5 mL (b) Maintenance = 0.375 mcg/kg/min × 70 kg = 26.25 mcg/min mcg/hr = 26.25 × 60 = 1,575 mcg/hr Rate = 1,575 mcg/hr × (1 mL/200 mcg) = 7.875 mL/hr Raw calculation: 50 × 70 = 3,500; 3,500 ÷ 200 = 17.5; 0.375 × 70 × 60 = 1,575; 1,575 ÷ 200 = 7.875 Rounding: Load 17.5 mL (exact tenth); maintenance 7.875 → 7.9 mL/hr (nearest tenth). Final answer: Loading dose 17.5 mL; maintenance 7.9 mL/hr Rationale: Milrinone 20 mg/100 mL = 200 mcg/mL. The 50 mcg/kg load = 3,500 mcg = 17.5 mL; the 0.375 mcg/kg/min maintenance = 1,575 mcg/hr = 7.875 mL/hr. Clinical pearl: Loading and maintenance doses use the SAME concentration but are delivered at very different rates — label the pump and the line to avoid running the load at the maintenance rate.

25. Question 475. Scenario: A 90 kg patient requires rate control for rapid atrial fibrillation. Order: Esmolol 50 mcg/kg/min IV infusion, titrate to a heart rate < 110 beats/min. Available: Esmolol 2500 mg in 250 mL (10 mg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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    Correct answer: 27 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 50 mcg/kg/min × 90 kg = 4,500 mcg/min mcg/hr = 4,500 × 60 = 270,000 mcg/hr Rate (mL/hr) = 270,000 mcg/hr × (1 mL/10,000 mcg) = 27 mL/hr Raw calculation: 50 × 90 × 60 = 270,000; 270,000 ÷ 10,000 = 27 Rounding: 27 mL/hr (whole number). Final answer: 27 mL/hr Rationale: Esmolol 2500 mg/250 mL = 10 mg/mL = 10,000 mcg/mL. The ordered 50 mcg/kg/min for 90 kg = 270,000 mcg/hr ÷ 10,000 mcg/mL = 27 mL/hr. Clinical pearl: Esmolol is a 10 mg/mL (10,000 mcg/mL) infusion; its large numbers make a unit-conversion error (mg vs. mcg) especially dangerous — always convert to mcg/mL first.

26. Question 476. Scenario: A 70 kg patient is started on a norepinephrine titration protocol. Order: (HYPOTHETICAL protocol) Start norepinephrine at 0.05 mcg/kg/min. If MAP < 65 mmHg, increase by 0.05 mcg/kg/min every 5 minutes to a maximum of 0.2 mcg/kg/min. Available: Norepinephrine 4 mg in 250 mL D5W (16 mcg/mL). Question: Calculate (a) the starting infusion rate in mL/hr, and (b) the infusion rate in mL/hr after two upward titrations (i.e., at 0.15 mcg/kg/min). Round each to the nearest tenth.

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    Correct answer: (a) 13.1 mL/hr; (b) 39.4 mL/hr Setup (dimensional analysis): (a) Start = 0.05 mcg/kg/min × 70 kg = 3.5 mcg/min × 60 = 210 mcg/hr ÷ 16 mcg/mL = 13.125 mL/hr (b) After 2 increases = 0.05 + 0.05 + 0.05 = 0.15 mcg/kg/min × 70 kg = 10.5 mcg/min × 60 = 630 mcg/hr ÷ 16 = 39.375 mL/hr Raw calculation: 0.05 × 70 × 60 ÷ 16 = 13.125; 0.15 × 70 × 60 ÷ 16 = 39.375 Rounding: 13.125 → 13.1 mL/hr; 39.375 → 39.4 mL/hr (nearest tenth). Final answer: Start at 13.1 mL/hr; after two titrations, 39.4 mL/hr Rationale: Each 0.05 mcg/kg/min increment for a 70 kg patient adds 3.5 mcg/min = 210 mcg/hr, i.e., 13.125 mL/hr per step. Starting at 13.1 mL/hr and adding two steps reaches 0.15 mcg/kg/min = 39.4 mL/hr. Clinical pearl: A fixed increment produces a fixed mL/hr change per step — learn the "mL/hr per 0.05 mcg/kg/min" for your bag concentration to titrate quickly and safely.

27. Question 477. Scenario: A norepinephrine infusion is running and the nurse plans when to hang the next bag. Order: Norepinephrine continuous infusion (determine how long the bag will last). Available: Norepinephrine 4 mg in 250 mL D5W infusing at 15 mL/hr. Question: How many hours will the 250 mL bag last? Round to the nearest tenth.

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    Correct answer: 16.7 hours Setup (dimensional analysis): Duration (hr) = 250 mL × (1 hr/15 mL) = 16.67 hr Raw calculation: 250 ÷ 15 = 16.667 hr Rounding: 16.667 rounds to 16.7 hours (nearest tenth). Final answer: 16.7 hours (about 16 hours 40 minutes) Rationale: A 250 mL bag at 15 mL/hr will run 250 ÷ 15 = 16.67 hours. Clinical pearl: Infusion duration = bag volume ÷ rate; use it to plan the next bag well before the pump alarms "air in line" or "occlusion."

28. Question 478. Scenario: A 80 kg patient has been on a dopamine infusion for 4 hours; the nurse must document the total drug delivered. Order: Dopamine continuous infusion (determine the total dose delivered). Available: Dopamine 400 mg in 250 mL D5W (1600 mcg/mL) infusing at 15 mL/hr for 4 hours. Question: Calculate (a) the total dose of dopamine delivered in mg over 4 hours, and (b) the delivered dose in mcg/kg/min. Round to the nearest tenth.

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    Correct answer: (a) 96 mg; (b) 5 mcg/kg/min Setup (dimensional analysis): (a) mcg/hr = 15 mL/hr × 1600 mcg/mL = 24,000 mcg/hr Total mcg = 24,000 mcg/hr × 4 hr = 96,000 mcg = 96 mg (b) mcg/min = 24,000 ÷ 60 = 400 mcg/min; 400 ÷ 80 kg = 5 mcg/kg/min Raw calculation: 15 × 1600 = 24,000; 24,000 × 4 = 96,000 mcg = 96 mg; 24,000 ÷ 60 ÷ 80 = 5 Rounding: 96 mg (whole number); 5 mcg/kg/min (whole number). Final answer: 96 mg delivered over 4 hours; delivered dose 5 mcg/kg/min Rationale: Dopamine 400 mg/250 mL = 1600 mcg/mL. At 15 mL/hr the patient receives 24,000 mcg/hr = 96 mg over 4 hours, which is 400 mcg/min ÷ 80 kg = 5 mcg/kg/min. Clinical pearl: Total drug delivered = rate × concentration × time; documenting cumulative mcg or mg helps detect cumulative dosing issues on long-running titratable drips.

29. Question 479. Scenario: A provider writes a new norepinephrine order for a patient in the ICU. Order: (as written) "Norepinephrine 4.0 mg in 250 mL D5W, titrate to MAP ≥ 65 mmHg." Available: N/A — order-safety item (no calculation required). Question: Identify the medication-order error in this order and rewrite it correctly.

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    Correct answer: Trailing zero ("4.0 mg"); rewrite as "4 mg" Setup (dimensional analysis): N/A (order-safety item, not a computation). Raw calculation: N/A Rounding: N/A Final answer: "Norepinephrine 4 mg in 250 mL D5W, titrate to MAP ≥ 65 mmHg." Rationale: "4.0 mg" 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 "40 mg" — a 10-fold overdose. Clinical pearl: Trailing zeros (4.0 mg) are dangerous; write "4 mg," not "4.0 mg." (A leading zero IS required: 0.5 mg, never .5 mg.)

30. Question 480. Scenario: A nurse must draw up a heparin bolus. Order: Heparin 6,400 units IV bolus. Available: Heparin 5,000 units/mL vial. Question: What volume must be drawn up (round to the nearest hundredth), and which syringe is most appropriate: 1 mL, 3 mL, 5 mL, or 10 mL?

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    Correct answer: 1.28 mL; use a 3 mL syringe Setup (dimensional analysis): Volume = 6,400 units × (1 mL/5,000 units) = 1.28 mL Raw calculation: 6,400 ÷ 5,000 = 1.28 mL Rounding: 1.28 mL (nearest hundredth). Final answer: 1.28 mL drawn up in a 3 mL syringe Rationale: Heparin 5,000 units/mL, so 6,400 units = 1.28 mL. A 1 mL syringe cannot hold 1.28 mL; a 3 mL syringe is the smallest that accurately measures it. A 5 or 10 mL syringe would hold it but with poorer small-volume accuracy. Clinical pearl: Select the smallest syringe that safely holds the dose to maximize measurement accuracy — but never force an oversize volume into an undersized syringe.

31. Question 481. Scenario: During a pump failure, a dopamine infusion must be run by gravity using a microdrip set. Order: Dopamine 5 mcg/kg/min for a 82 kg patient. Available: Dopamine 400 mg in 250 mL D5W (1600 mcg/mL); microdrip tubing 60 gtt/mL. Question: Calculate the flow rate in gtt/min. Round to the nearest whole drop.

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    Correct answer: 15 gtt/min Setup (dimensional analysis): mcg/min = 5 mcg/kg/min × 82 kg = 410 mcg/min mL/min = 410 mcg/min × (1 mL/1600 mcg) = 0.25625 mL/min gtt/min = 0.25625 mL/min × 60 gtt/mL = 15.375 gtt/min Raw calculation: 5 × 82 ÷ 1600 × 60 = 15.375 gtt/min Rounding: 15.375 rounds to 15 gtt/min (nearest whole drop). Final answer: 15 gtt/min Rationale: Dopamine 400 mg/250 mL = 1600 mcg/mL. The patient needs 410 mcg/min = 0.25625 mL/min; with 60 gtt/mL microdrip tubing that is 15.375 gtt/min. Clinical pearl: Gravity delivery of vasoactive drugs is a temporary emergency measure — titratable vasopressors should be on a smart pump whenever possible, and the drip must be frequently re-counted.

32. Question 482. Scenario: A 70 kg patient is started on a low-dose dopamine infusion. Order: Dopamine 2.5 mcg/kg/min IV infusion. Available: Dopamine 400 mg in 250 mL D5W (1600 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth. A. 4.4 mL/hr B. 6.6 mL/hr C. 8.8 mL/hr D. 13.1 mL/hr

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    Correct answer: B. 6.6 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 2.5 mcg/kg/min × 70 kg = 175 mcg/min Rate (mL/hr) = 175 mcg/min × (60 min/1 hr) × (1 mL/1600 mcg) Raw calculation: 175 × 60 ÷ 1600 = 6.5625 mL/hr Rounding: 6.5625 rounds to 6.6 mL/hr (nearest tenth). Final answer: 6.6 mL/hr Rationale: Dopamine 400 mg/250 mL = 1600 mcg/mL. The ordered 2.5 mcg/kg/min for 70 kg = 175 mcg/min = 10,500 mcg/hr ÷ 1600 mcg/mL = 6.56 mL/hr. Clinical pearl: Low-dose drips yield small, easy-to-miss pump rates; always independent-double-check low rates on critical-care drugs.

33. Question 483. Scenario: A 65 kg patient's norepinephrine infusion is checked during shift change. Order: Norepinephrine continuous infusion (verify the delivered dose in mcg/kg/min). Available: Norepinephrine 4 mg in 250 mL D5W (16 mcg/mL) infusing at 13 mL/hr. Question: What dose in mcg/kg/min is the patient receiving? Round to the nearest hundredth.

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    Correct answer: 0.05 mcg/kg/min Setup (dimensional analysis): mcg/hr = 13 mL/hr × 16 mcg/mL = 208 mcg/hr mcg/min = 208 ÷ 60 = 3.467 mcg/min mcg/kg/min = 3.467 ÷ 65 kg = 0.0533 mcg/kg/min Raw calculation: 13 × 16 ÷ 60 ÷ 65 = 0.05333 mcg/kg/min Rounding: 0.0533 rounds to 0.05 mcg/kg/min (nearest hundredth). Final answer: 0.05 mcg/kg/min Rationale: Norepinephrine 4 mg/250 mL = 16 mcg/mL. At 13 mL/hr the patient receives 208 mcg/hr = 3.467 mcg/min ÷ 65 kg = 0.053 mcg/kg/min. Clinical pearl: When the back-calculated dose (0.053) is close to a standard order (0.05), the small difference is rounding — confirm the pump rate matches the documented order.

34. Question 484. Scenario: A patient in hypertensive crisis is started on sodium nitroprusside. Order: Nitroprusside 0.5 mcg/kg/min IV infusion for a 70 kg patient. Available: Nitroprusside 50 mg in 250 mL D5W (200 mcg/mL). Protect from light. Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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    Correct answer: 10.5 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 0.5 mcg/kg/min × 70 kg = 35 mcg/min mcg/hr = 35 × 60 = 2,100 mcg/hr Rate (mL/hr) = 2,100 mcg/hr × (1 mL/200 mcg) = 10.5 mL/hr Raw calculation: 0.5 × 70 × 60 ÷ 200 = 10.5 mL/hr Rounding: 10.5 mL/hr (already at the tenth). Final answer: 10.5 mL/hr Rationale: Nitroprusside 50 mg/250 mL = 50,000 mcg ÷ 250 mL = 200 mcg/mL. The ordered 0.5 mcg/kg/min for 70 kg = 35 mcg/min = 2,100 mcg/hr ÷ 200 mcg/mL = 10.5 mL/hr. Clinical pearl: Nitroprusside is light-sensitive and requires arterial-line monitoring; protect the bag and tubing from light and titrate in small increments.

35. Question 485. Scenario: A 70 kg patient requires light sedation to tolerate mechanical ventilation. Order: Dexmedetomidine 0.5 mcg/kg/hr IV infusion. Available: Dexmedetomidine 400 mcg in 100 mL 0.9% sodium chloride (4 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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    Correct answer: 8.8 mL/hr Setup (dimensional analysis): Dose (mcg/hr) = 0.5 mcg/kg/hr × 70 kg = 35 mcg/hr Rate (mL/hr) = 35 mcg/hr × (1 mL/4 mcg) = 8.75 mL/hr Raw calculation: 35 ÷ 4 = 8.75 mL/hr Rounding: 8.75 rounds up to 8.8 mL/hr (nearest tenth). Final answer: 8.8 mL/hr Rationale: Dexmedetomidine 400 mcg/100 mL = 4 mcg/mL. The ordered 0.5 mcg/kg/hr for 70 kg = 35 mcg/hr ÷ 4 mcg/mL = 8.75 mL/hr. Clinical pearl: Dexmedetomidine is dosed in mcg/kg/hr (not per minute) — check the time unit on the order to avoid a 60-fold error.

36. Question 486. Scenario: A 84 kg patient on dexmedetomidine is transferred to the step-down unit. Order: Dexmedetomidine continuous infusion (verify the delivered dose in mcg/kg/hr). Available: Dexmedetomidine 400 mcg in 100 mL (4 mcg/mL) infusing at 10.5 mL/hr. Question: What dose in mcg/kg/hr is the patient receiving? Round to the nearest hundredth.

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    Correct answer: 0.5 mcg/kg/hr Setup (dimensional analysis): mcg/hr = 10.5 mL/hr × 4 mcg/mL = 42 mcg/hr mcg/kg/hr = 42 mcg/hr ÷ 84 kg Raw calculation: 10.5 × 4 ÷ 84 = 0.5 mcg/kg/hr Rounding: 0.5 mcg/kg/hr (already at the hundredth). Final answer: 0.5 mcg/kg/hr Rationale: Dexmedetomidine 400 mcg/100 mL = 4 mcg/mL. At 10.5 mL/hr the patient receives 42 mcg/hr ÷ 84 kg = 0.5 mcg/kg/hr. Clinical pearl: Dexmedetomidine orders are commonly written to a target range (e.g., 0.2–0.7 mcg/kg/hr); back-calculate to confirm the drip is within the intended range.

37. Question 487. Scenario: A patient's heparin infusion is ordered by units per hour. Order: Heparin 1,200 units/hr IV infusion. Available: Heparin 25,000 units in 500 mL D5W (50 units/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest whole number.

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    Correct answer: 24 mL/hr Setup (dimensional analysis): Rate (mL/hr) = 1,200 units/hr × (1 mL/50 units) = 24 mL/hr Raw calculation: 1,200 ÷ 50 = 24 mL/hr Rounding: 24 mL/hr (whole number). Final answer: 24 mL/hr Rationale: Heparin 25,000 units/500 mL = 50 units/mL. The ordered 1,200 units/hr ÷ 50 units/mL = 24 mL/hr. Clinical pearl: 25,000 units/500 mL = 50 units/mL and 25,000 units/250 mL = 100 units/mL — the "same" vial label hides a 2× concentration difference; always verify the bag volume.

38. Question 488. Scenario: A 80 kg patient's heparin infusion rate is reviewed to confirm the dose in units/kg/hr. Order: Heparin continuous infusion (verify the delivered dose in units/kg/hr). Available: Heparin 25,000 units in 500 mL D5W (50 units/mL) infusing at 32 mL/hr. Question: Calculate (a) the dose in units/hr and (b) the dose in units/kg/hr. Round to the nearest whole number.

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    Correct answer: (a) 1,600 units/hr; (b) 20 units/kg/hr Setup (dimensional analysis): (a) units/hr = 32 mL/hr × 50 units/mL = 1,600 units/hr (b) units/kg/hr = 1,600 units/hr ÷ 80 kg = 20 units/kg/hr Raw calculation: 32 × 50 = 1,600; 1,600 ÷ 80 = 20 Rounding: Both whole numbers. Final answer: 1,600 units/hr = 20 units/kg/hr Rationale: Heparin 25,000 units/500 mL = 50 units/mL. At 32 mL/hr the patient receives 1,600 units/hr, which for 80 kg is 20 units/kg/hr — a typical initial weight-based heparin rate. Clinical pearl: Expressing heparin in units/kg/hr lets you compare the running rate against your protocol's weight-based range independent of bag size.

39. Question 489. Scenario: A patient's insulin infusion rate is being converted back to units per hour for documentation. Order: Regular insulin continuous infusion (document the dose in units/hr). Available: Regular insulin 100 units in 100 mL (1 unit/mL) infusing at 7.5 mL/hr. Question: How many units/hr is the patient receiving? Round to the nearest tenth.

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    Correct answer: 7.5 units/hr Setup (dimensional analysis): units/hr = 7.5 mL/hr × 1 unit/mL = 7.5 units/hr Raw calculation: 7.5 × 1 = 7.5 units/hr Rounding: 7.5 units/hr (already at the tenth). Final answer: 7.5 units/hr Rationale: The standard insulin infusion is 1 unit/mL, so mL/hr and units/hr are equal. Clinical pearl: Insulin is a high-alert medication — when the concentration is 1 unit/mL the numbers coincide, but never skip reading the concentration label.

40. Question 490. Scenario: A 85 kg patient is started on a weight-based insulin infusion. Order: (HYPOTHETICAL protocol) Regular insulin IV infusion at 0.1 units/kg/hr. Available: Regular insulin 100 units in 100 mL 0.9% sodium chloride (1 unit/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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    Correct answer: 8.5 mL/hr Setup (dimensional analysis): Dose (units/hr) = 0.1 units/kg/hr × 85 kg = 8.5 units/hr Rate (mL/hr) = 8.5 units/hr × (1 mL/1 unit) = 8.5 mL/hr Raw calculation: 0.1 × 85 = 8.5; 8.5 ÷ 1 = 8.5 Rounding: 8.5 mL/hr (already at the tenth). Final answer: 8.5 mL/hr Rationale: The hypothetical weight-based insulin order (0.1 units/kg/hr) for 85 kg = 8.5 units/hr, which is 8.5 mL/hr at 1 unit/mL. Clinical pearl: Weight-based insulin protocols are used in some DKA/HHS pathways; calculate the rate from weight first, then apply the glucose scale to the result.

41. Question 491. Scenario: A patient's vasopressin infusion rate is documented in units/min for the critical-care flow sheet. Order: Vasopressin continuous infusion (document the dose in units/min). Available: Vasopressin 20 units in 100 mL (0.2 units/mL) infusing at 9 mL/hr. Question: What dose in units/min is the patient receiving? Round to the nearest hundredth.

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    Correct answer: 0.03 units/min Setup (dimensional analysis): units/hr = 9 mL/hr × 0.2 units/mL = 1.8 units/hr units/min = 1.8 units/hr ÷ 60 min/hr = 0.03 units/min Raw calculation: 9 × 0.2 ÷ 60 = 0.03 units/min Rounding: 0.03 units/min (already at the hundredth). Final answer: 0.03 units/min Rationale: Vasopressin 20 units/100 mL = 0.2 units/mL. At 9 mL/hr the patient receives 1.8 units/hr = 0.03 units/min. Clinical pearl: Vasopressin is titrated in 0.01–0.04 units/min increments — documenting in units/min keeps the flow sheet consistent with the order.

42. Question 492. Scenario: A 80 kg patient requires a double-concentration dobutamine infusion to limit fluid volume. Order: Dobutamine 5 mcg/kg/min IV infusion. Available: Dobutamine 500 mg in 250 mL D5W (2000 mcg/mL). Question: Calculate the infusion rate in mL/hr. Round to the nearest tenth.

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    Correct answer: 12 mL/hr Setup (dimensional analysis): Dose (mcg/min) = 5 mcg/kg/min × 80 kg = 400 mcg/min mcg/hr = 400 × 60 = 24,000 mcg/hr Rate (mL/hr) = 24,000 mcg/hr × (1 mL/2000 mcg) = 12 mL/hr Raw calculation: 5 × 80 × 60 ÷ 2000 = 12 mL/hr Rounding: 12 mL/hr (whole number). Final answer: 12 mL/hr Rationale: Dobutamine 500 mg/250 mL = 2000 mcg/mL (double concentration). The ordered 5 mcg/kg/min for 80 kg = 400 mcg/min = 24,000 mcg/hr ÷ 2000 mcg/mL = 12 mL/hr. Clinical pearl: The 500 mg/250 mL dobutamine bag delivers the same dose at half the standard volume — useful for fluid-restricted patients but easy to confuse with the standard 250 mg/250 mL bag.

43. Question 493. Scenario: A 90 kg patient in refractory shock is receiving two vasoactive infusions; the nurse verifies the dose of each during handoff. Order: Norepinephrine and vasopressin continuous infusions (verify each delivered dose). Available: Norepinephrine 8 mg in 250 mL D5W (32 mcg/mL) infusing at 12 mL/hr; vasopressin 20 units in 100 mL (0.2 units/mL) infusing at 6 mL/hr. Question: Calculate (a) the norepinephrine dose in mcg/kg/min (round to the nearest hundredth) and (b) the vasopressin dose in units/min (round to the nearest hundredth).

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    Correct answer: (a) 0.07 mcg/kg/min; (b) 0.02 units/min Setup (dimensional analysis): (a) NE mcg/hr = 12 mL/hr × 32 mcg/mL = 384 mcg/hr; mcg/min = 384 ÷ 60 = 6.4 mcg/min; ÷ 90 kg = 0.0711 mcg/kg/min (b) Vasopressin units/hr = 6 mL/hr × 0.2 units/mL = 1.2 units/hr; units/min = 1.2 ÷ 60 = 0.02 units/min Raw calculation: 12 × 32 ÷ 60 ÷ 90 = 0.0711; 6 × 0.2 ÷ 60 = 0.02 Rounding: 0.0711 → 0.07 mcg/kg/min (nearest hundredth); 0.02 units/min (exact). Final answer: Norepinephrine 0.07 mcg/kg/min; vasopressin 0.02 units/min Rationale: Each vasoactive drug uses a different concentration and dose unit. Norepinephrine (32 mcg/mL) at 12 mL/hr delivers 0.071 mcg/kg/min; vasopressin (0.2 units/mL) at 6 mL/hr delivers 0.02 units/min. Clinical pearl: When multiple vasopressors run concurrently, treat each with its own units and concentration — a mcg/kg/min dose for one drug is meaningless for another dosed in units/min.

44. Question 494. Scenario: A dopamine infusion was started at 1400. Order: Dopamine continuous infusion (determine when the bag empties). Available: Dopamine 400 mg in 250 mL D5W infusing at 25 mL/hr. Question: At what time will the 250 mL bag empty and the next bag need to be hung?

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    Correct answer: 0000 (midnight) Setup (dimensional analysis): Duration (hr) = 250 mL × (1 hr/25 mL) = 10 hr Empty time = 1400 + 10 hr = 2400 Raw calculation: 250 ÷ 25 = 10 hr; 14:00 + 10:00 = 00:00 Rounding: N/A (time). Final answer: The bag empties at midnight (0000); hang the next bag then Rationale: A 250 mL bag at 25 mL/hr lasts 10 hours; started at 1400, it empties at 2400 (0000). Clinical pearl: Use the 24-hour clock and "volume ÷ rate" to schedule bag changes during busy shifts, avoiding both empty-bag alarms and premature waste.

45. Question 495. Scenario: A patient has been on a double-concentration norepinephrine infusion for 6 hours; the nurse documents the total drug delivered. Order: Norepinephrine continuous infusion (determine the total dose delivered). Available: Norepinephrine 8 mg in 250 mL D5W (32 mcg/mL) infusing at 13.1 mL/hr for 6 hours. Question: How many milligrams of norepinephrine were delivered over 6 hours? Round to the nearest tenth.

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    Correct answer: 2.5 mg Setup (dimensional analysis): mcg/hr = 13.1 mL/hr × 32 mcg/mL = 419.2 mcg/hr Total mcg = 419.2 mcg/hr × 6 hr = 2,515.2 mcg = 2.5152 mg Raw calculation: 13.1 × 32 × 6 = 2,515.2 mcg = 2.5152 mg Rounding: 2.5152 rounds to 2.5 mg (nearest tenth). Final answer: 2.5 mg delivered over 6 hours Rationale: Norepinephrine 8 mg/250 mL = 32 mcg/mL. At 13.1 mL/hr the patient receives 419.2 mcg/hr, or 2,515.2 mcg (2.5 mg) over 6 hours. Clinical pearl: Total vasopressor delivered can be surprisingly small in mg even over many hours — document cumulative dose to support titration and weaning decisions.

46. Question 496. Scenario: A provider writes an order for breakthrough pain in a postoperative patient. Order: (as written) "Hydromorphone .5 mg IV push q4h PRN pain." Available: N/A — order-safety item (no calculation required). Question: Identify the medication-order error in this order and rewrite it correctly.

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    Correct answer: Missing leading zero (".5 mg"); rewrite as "0.5 mg" Setup (dimensional analysis): N/A (order-safety item). Raw calculation: N/A Rounding: N/A Final answer: "Hydromorphone 0.5 mg IV push q4h PRN pain." Rationale: ".5 mg" lacks a leading zero, which is on The Joint Commission "Do Not Use" list because the decimal point may be overlooked and the dose misread as "5 mg" — a 10-fold overdose of a potent opioid. Clinical pearl: Always write a leading zero before a decimal less than 1 (0.5 mg), and never a trailing zero (0.50 mg).

47. Question 497. Scenario: A nurse reviews a new order for a postoperative patient. Order: (as written) "MS 2 mg IV q4h PRN pain." Available: N/A — order-safety item (no calculation required). Question: Which medication-order error is present? A. Trailing zero (2.0 mg) B. Use of an ambiguous abbreviation ("MS") C. Use of "U" for units D. Missing leading zero

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    Correct answer: B. Use of an ambiguous abbreviation ("MS") Setup (dimensional analysis): N/A (order-safety item). Raw calculation: N/A Rounding: N/A Final answer: B — "MS" is an ambiguous abbreviation Rationale: "MS" can mean morphine sulfate OR magnesium sulfate and appears on ISMP's list of error-prone abbreviations. It should be written out ("morphine sulfate" or "magnesium sulfate"). This is an ISMP recommendation, distinct from the Joint Commission "Do Not Use" list. Clinical pearl: The Joint Commission "Do Not Use" list and ISMP's error-prone abbreviation list overlap but are not identical — "MS" is an ISMP item, while "U," "IU," and trailing/leading-zero errors are Joint Commission items.

48. Question 498. Scenario: A 70 kg patient is ordered a dopamine infusion that the nurse suspects exceeds the pressor range. Order: Dopamine 25 mcg/kg/min IV infusion. Available: Dopamine 400 mg in 250 mL D5W (1600 mcg/mL). HYPOTHETICAL educational pressor range: 2–20 mcg/kg/min. Question: Calculate the ordered infusion rate in mL/hr (round to the nearest tenth), compare it with the minimum and maximum rates of the safe range, and state whether the order is SAFE or UNSAFE.

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    Correct answer: UNSAFE — 65.6 mL/hr exceeds the hypothetical maximum (52.5 mL/hr) Setup (dimensional analysis): Ordered rate = 25 mcg/kg/min × 70 kg = 1,750 mcg/min × 60 = 105,000 mcg/hr ÷ 1600 mcg/mL = 65.625 mL/hr Minimum (2 mcg/kg/min) = 2 × 70 × 60 ÷ 1600 = 5.25 mL/hr Maximum (20 mcg/kg/min) = 20 × 70 × 60 ÷ 1600 = 52.5 mL/hr Raw calculation: 25 × 70 × 60 ÷ 1600 = 65.625; 2 × 70 × 60 ÷ 1600 = 5.25; 20 × 70 × 60 ÷ 1600 = 52.5 Rounding: 65.625 → 65.6 mL/hr; 5.25 → 5.3 mL/hr (nearest tenth); 52.5 mL/hr exact. Final answer: Ordered 25 mcg/kg/min = 65.6 mL/hr; safe range 5.3–52.5 mL/hr → UNSAFE Rationale: The ordered 25 mcg/kg/min exceeds the hypothetical educational maximum of 20 mcg/kg/min. The corresponding rate (65.6 mL/hr) is above the maximum range rate (52.5 mL/hr). The nurse should NOT start this rate as written and must clarify the order. Clinical pearl: When an ordered rate falls outside the (hypothetical) safe range, hold the infusion and clarify — computing the mL/hr equivalent first makes the discrepancy concrete for the provider.

49. Question 499. Scenario: A 70 kg patient is managed on a heparin nomogram; the nurse calculates each step. Order: (HYPOTHETICAL protocol) - Initial: bolus 80 units/kg, then infusion 18 units/kg/hr. - Check aPTT at 6 hours, then every 6 hours. - Nomogram (therapeutic aPTT 60–85 s): - aPTT < 55 s → re-bolus 40 units/kg AND increase infusion 2 units/kg/hr. - aPTT 55–59 s → increase infusion 1 unit/kg/hr. - aPTT 60–85 s → therapeutic, no change. - aPTT 86–100 s → decrease infusion 1 unit/kg/hr. - aPTT > 100 s → hold 1 hour, then decrease 2 units/kg/hr. Available: Heparin 5,000 units/mL vial (for bolus); heparin 25,000 units in 250 mL D5W (100 units/mL) for infusion. Question: The 6-hour aPTT is 40 seconds and the 12-hour aPTT is 66 seconds. Calculate (a) the initial bolus in units, (b) the initial infusion rate in mL/hr, (c) the additional bolus after the 6-hour aPTT, and (d) the infusion rate in mL/hr after the 12-hour aPTT. Round rates to the nearest tenth.

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    Correct answer: (a) 5,600 units; (b) 12.6 mL/hr; (c) 2,800 units; (d) 14 mL/hr Setup (dimensional analysis): (a) Bolus = 80 units/kg × 70 kg = 5,600 units (b) Initial = 18 units/kg/hr × 70 kg = 1,260 units/hr × (1 mL/100 units) = 12.6 mL/hr (c) 6-hr aPTT 40 s (< 55) → re-bolus 40 units/kg × 70 kg = 2,800 units AND increase 2 units/kg/hr (d) After increase = 20 units/kg/hr × 70 kg = 1,400 units/hr = 14 mL/hr; 12-hr aPTT 66 s is therapeutic → no change (stays 14 mL/hr) Raw calculation: 80 × 70 = 5,600; 18 × 70 = 1,260; 1,260 ÷ 100 = 12.6; 40 × 70 = 2,800; 20 × 70 = 1,400; 1,400 ÷ 100 = 14 Rounding: 12.6 and 14 mL/hr (nearest tenth); boluses are whole units. Final answer: Bolus 5,600 units; start 12.6 mL/hr; re-bolus 2,800 units at 6 hr; after 12-hr aPTT the rate remains 14 mL/hr Rationale: The first aPTT (40 s) is subtherapeutic, triggering a 40 units/kg re-bolus and a 2 units/kg/hr increase (18 → 20 units/kg/hr = 14 mL/hr). The 12-hour aPTT (66 s) is therapeutic, so no further change. Clinical pearl: Track the cumulative heparin response over multiple aPTT draws — each result drives BOTH a bolus and a rate change per the nomogram, and therapeutic readings mean "hold steady," not "keep titrating."

50. Question 500. Scenario: A 88 kg patient is started on a dopamine infusion; the nurse computes the rate and plans the infusion duration. Order: Dopamine 7.5 mcg/kg/min IV infusion. Available: Dopamine 400 mg in 250 mL D5W (1600 mcg/mL). Question: Calculate (a) the infusion rate in mL/hr (round to the nearest tenth) and (b) how long the 250 mL bag will last in hours (round to the nearest tenth).

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    Correct answer: (a) 24.8 mL/hr; (b) 10.1 hours Setup (dimensional analysis): (a) Dose (mcg/min) = 7.5 mcg/kg/min × 88 kg = 660 mcg/min mcg/hr = 660 × 60 = 39,600 mcg/hr Rate (mL/hr) = 39,600 ÷ 1600 = 24.75 mL/hr (b) Duration = 250 mL ÷ 24.75 mL/hr = 10.10 hr Raw calculation: 7.5 × 88 × 60 ÷ 1600 = 24.75; 250 ÷ 24.75 = 10.101 Rounding: 24.75 → 24.8 mL/hr (nearest tenth); 10.101 → 10.1 hours (nearest tenth). Final answer: Infuse at 24.8 mL/hr; the 250 mL bag lasts about 10.1 hours Rationale: Dopamine 400 mg/250 mL = 1600 mcg/mL. The ordered 7.5 mcg/kg/min for 88 kg = 660 mcg/min = 39,600 mcg/hr ÷ 1600 mcg/mL = 24.75 mL/hr, which runs a 250 mL bag for 250 ÷ 24.75 = 10.1 hours. Clinical pearl: Compute the rate first, then use volume ÷ rate for duration — but schedule the change using the UNROUNDED rate (24.75) where practical so the bag does not run dry early.