A nurse is caring for a client with a hypertensive crisis. The provider prescribes a conti… — NCLEX-RN

A nurse is caring for a client with a hypertensive crisis. The provider prescribes a continuous intravenous (IV) infusion of sodium nitroprusside at $3 \text{ mcg/kg/min}$ . The client weighs $176 \text{ lbs}$ . The medication is supplied as $50 \text{ mg}$ of sodium nitroprusside in $250 \text{ mL}$ of $5\% \text{ Dextrose}$ in water ( $D_5W$ ). At what rate should the nurse set the IV infusion pump in $\text{mL/hr}$ ? (Round the answer to the nearest whole number.)

Answer: 72 mL/hr

Answer

The correct infusion rate is 72 mL/hr.

To solve this calculation correctly, multiple conversions are required. First, the client's weight of

176 \text{ lbs}

is converted to

80 \text{ kg}

. The total per-minute dose is

80 \text{ kg} \times 3 \text{ mcg/kg/min} = 240 \text{ mcg/min}

. This equals

14,400 \text{ mcg/hr}

(

240 \times 60

). Converting to milligrams gives

14.4 \text{ mg/hr}

(

14,400 \div 1,000

). The concentration of the supplied bag is

50 \text{ mg} / 250 \text{ mL} = 0.2 \text{ mg/mL}

. Dividing the hourly dose by the concentration (

14.4 \div 0.2

) yields exactly

72 \text{ mL/hr}

Step-by-Step Solution

Convert weight to kilograms

176 \text{ lbs} \div 2.2 \text{ lbs/kg} = 80 \text{ kg}

The prescribed dose is weight-based in kg.

Calculate dose per minute

80 \text{ kg} \times 3 \text{ mcg/kg/min} = 240 \text{ mcg/min}

To determine the total micrograms the client receives each minute.

Calculate dose per hour

240 \text{ mcg/min} \times 60 \text{ min/hr} = 14,400 \text{ mcg/hr}

Infusion pumps are set in mL/hr, requiring an hourly dose.

Convert dose to milligrams

14,400 \text{ mcg/hr} \div 1,000 \text{ mcg/mg} = 14.4 \text{ mg/hr}

The supplied medication is measured in milligrams, so the units must match.

Calculate the infusion rate in mL/hr

14.4 \text{ mg/hr} \div (50 \text{ mg} / 250 \text{ mL}) = 14.4 \text{ mg/hr} \div 0.2 \text{ mg/mL} = 72 \text{ mL/hr}

To find the final volume to be infused per hour based on the drug's concentration.

Key Concept

Weight-based continuous intravenous (IV) infusion calculations requiring multi-step unit conversions.

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