A client weighing 78\text{ kg} is admitted to the progressive care unit with a hypertensiv… — NCLEX-RN

A client weighing $78\text{ kg}$ is admitted to the progressive care unit with a hypertensive crisis. The healthcare provider prescribes a continuous intravenous infusion of sodium nitroprusside at a rate of $3\text{ mcg/kg/min}$ . The medication is supplied as sodium nitroprusside $50\text{ mg}$ mixed in $250\text{ mL}$ of $5\%$ dextrose in water (D5W). At what rate should the nurse set the infusion pump in $\text{mL/hr}$ ? Round your answer to the nearest tenth.

Answer: 70.2 mL/hr

Answer

70.2

To determine the correct infusion pump rate, the nurse must first calculate the total hourly dose based on the client's weight (

78\text{ kg} \times 3\text{ mcg/kg/min} \times 60\text{ min/hr} = 14,040\text{ mcg/hr}

). Next, this dose must be converted to match the supplied medication unit (

14,040\text{ mcg} = 14.04\text{ mg}

). Finally, dividing the hourly dose by the concentration of the IV solution (

14.04\text{ mg/hr} \div 0.2\text{ mg/mL}

) yields exactly

70.2\text{ mL/hr}

Step-by-Step Solution

Calculate the required dose in micrograms per minute.

234\text{ mcg/min}

The prescription is weight-based, so the client's total body weight must be multiplied by the ordered rate of

3\text{ mcg/kg/min}

Convert the minute dose to an hourly dose.

14,040\text{ mcg/hr}

Intravenous infusion pumps are programmed in milliliters per hour, so the total medication dose must be determined on an hourly basis.

Convert the hourly dose from micrograms to milligrams.

14.04\text{ mg/hr}

The supplied medication is measured in milligrams, so units must match the supply before calculating the final volume.

Calculate the concentration of the supplied intravenous medication.

0.2\text{ mg/mL}

Dividing the total drug mass (

50\text{ mg}

) by the total fluid volume (

250\text{ mL}

) yields the amount of active drug in each milliliter of solution.

Calculate the final pump infusion rate in mL/hr.

70.2\text{ mL/hr}

Dividing the required hourly dose (

14.04\text{ mg/hr}

) by the drug concentration (

0.2\text{ mg/mL}

) determines the exact fluid volume needed per hour.

Key Concept

Weight-based continuous intravenous medication calculations

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