A nurse is caring for a client in the intensive care unit who is experiencing severe hypot… — NCLEX-RN

A nurse is caring for a client in the intensive care unit who is experiencing severe hypotension and weighs $87\text{ kg}$ . The healthcare provider prescribes a continuous intravenous (IV) infusion of norepinephrine at $0.05\text{ mcg/kg/min}$ . The pharmacy dispenses norepinephrine $4\text{ mg}$ in $250\text{ mL}$ of $5\%$ dextrose in water ( $\text{D}_5\text{W}$ ). At what rate should the nurse set the IV infusion pump in $\text{mL/hr}$ ? (Round the answer to the nearest tenth. Do not use a trailing zero.)

Answer: 16.3 mL/hr

Answer

16.3

The correct infusion rate is calculated by first determining the total hourly dose required for the client's specific weight (

0.05\text{ mcg/kg/min} \times 87\text{ kg} \times 60\text{ min/hr} = 261\text{ mcg/hr}

). Next, the concentration of the IV bag is found by converting milligrams to micrograms (

4\text{ mg} = 4000\text{ mcg}

) and dividing by the total volume (

4000\text{ mcg} / 250\text{ mL} = 16\text{ mcg/mL}

). Finally, dividing the hourly dose by the concentration gives the pump rate (

261\text{ mcg/hr} \div 16\text{ mcg/mL} = 16.3125\text{ mL/hr}

), which rounds to

16.3

Step-by-Step Solution

Calculate the prescribed dose per minute based on the client's weight.

0.05\text{ mcg/kg/min} \times 87\text{ kg} = 4.35\text{ mcg/min}

The prescription is weight-based, so the total microgram dose per minute must be determined first.

Convert the prescribed dose per minute to the prescribed dose per hour.

4.35\text{ mcg/min} \times 60\text{ min/hr} = 261\text{ mcg/hr}

IV infusion pumps deliver medication at an hourly rate (

\text{mL/hr}

), requiring the dose to be converted from minutes to hours.

Determine the concentration of the dispensed IV solution in

\text{mcg/mL}

4\text{ mg} \times 1000\text{ mcg/mg} = 4000\text{ mcg}

. Then,

4000\text{ mcg} / 250\text{ mL} = 16\text{ mcg/mL}

The prescribed dose is in micrograms, so the medication supplied in milligrams must be converted to match the units before calculating the volume.

Calculate the final infusion rate in

\text{mL/hr}

and round to the nearest tenth.

261\text{ mcg/hr} \div 16\text{ mcg/mL} = 16.3125\text{ mL/hr}

. Rounded to the nearest tenth is

16.3

Dividing the required hourly dose by the concentration yields the exact volume needed per hour. Rounding to the nearest tenth is standard for critical care infusions.

Key Concept

Weight-based continuous intravenous (IV) medication calculation and infusion pump programming.

Alternative Method

Dimensional analysis can be used to solve this in a single equation:

X\text{ mL/hr} = (250\text{ mL} / 4\text{ mg}) \times (1\text{ mg} / 1000\text{ mcg}) \times (0.05\text{ mcg} / 1\text{ kg} \times 1\text{ min}) \times (87\text{ kg} / 1) \times (60\text{ min} / 1\text{ hr}) = 16.3125\text{ mL/hr}

Estimated Time:2m 0s

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