A nurse is preparing to administer dopamine 5 mcg/kg/min by continuous IV infusion to a client who weighs 220 lb. Available is 400 mg of dopamine in 250 mL of 0.9% sodium chloride. The nurse should set the IV pump to deliver how many mi/hr? (Round the answer to the nearest tenth. Use a leading zero if it applies. Do not use a trailing zero.)
The Correct Answer and Explanation is:
To calculate the rate at which the IV pump should be set to deliver the dopamine infusion, we need to follow these steps:
Step 1: Convert the client’s weight from pounds to kilograms.
Since 1 kilogram (kg) equals 2.2 pounds (lb), the conversion is:Weight in kg=220 lb2.2=100 kg\text{Weight in kg} = \frac{220 \, \text{lb}}{2.2} = 100 \, \text{kg}Weight in kg=2.2220lb=100kg
Step 2: Calculate the dose in micrograms per minute.
The prescribed dose is 5 mcg/kg/min. Therefore:Dose in mcg/min=5 mcg×100 kg=500 mcg/min\text{Dose in mcg/min} = 5 \, \text{mcg} \times 100 \, \text{kg} = 500 \, \text{mcg/min}Dose in mcg/min=5mcg×100kg=500mcg/min
Step 3: Convert the dose from micrograms to milligrams.
Since 1 milligram (mg) equals 1000 micrograms (mcg), the dose in milligrams per minute is:Dose in mg/min=500 mcg/min1000=0.5 mg/min\text{Dose in mg/min} = \frac{500 \, \text{mcg/min}}{1000} = 0.5 \, \text{mg/min}Dose in mg/min=1000500mcg/min=0.5mg/min
Step 4: Calculate the concentration of the solution.
The available solution contains 400 mg of dopamine in 250 mL of 0.9% sodium chloride. To find the concentration:Concentration=400 mg250 mL=1.6 mg/mL\text{Concentration} = \frac{400 \, \text{mg}}{250 \, \text{mL}} = 1.6 \, \text{mg/mL}Concentration=250mL400mg=1.6mg/mL
Step 5: Determine the IV pump rate in mL/hr.
To find out how many mL/hr to administer, use the formula:Rate in mL/hr=Dose in mg/min×60 min/hrConcentration in mg/mL\text{Rate in mL/hr} = \frac{\text{Dose in mg/min} \times 60 \, \text{min/hr}}{\text{Concentration in mg/mL}}Rate in mL/hr=Concentration in mg/mLDose in mg/min×60min/hr
Substitute the values:Rate in mL/hr=0.5 mg/min×60 min/hr1.6 mg/mL=30 mg/hr1.6 mg/mL=18.75 mL/hr\text{Rate in mL/hr} = \frac{0.5 \, \text{mg/min} \times 60 \, \text{min/hr}}{1.6 \, \text{mg/mL}} = \frac{30 \, \text{mg/hr}}{1.6 \, \text{mg/mL}} = 18.75 \, \text{mL/hr}Rate in mL/hr=1.6mg/mL0.5mg/min×60min/hr=1.6mg/mL30mg/hr=18.75mL/hr
Step 6: Round the answer to the nearest tenth.
Rounded Rate=18.8 mL/hr\text{Rounded Rate} = 18.8 \, \text{mL/hr}Rounded Rate=18.8mL/hr
Final Answer:
The nurse should set the IV pump to deliver 18.8 mL/hr.
Explanation:
Administering dopamine via continuous IV infusion requires precise calculation to ensure the correct dose is delivered to the patient. First, the patient’s weight was converted from pounds to kilograms to match the dosing units (mcg/kg/min). Next, the required dose in micrograms per minute was calculated based on the prescribed 5 mcg/kg/min. This value was then converted to milligrams per minute, which is more practical for use with available drug concentrations. The concentration of dopamine in the IV solution (1.6 mg/mL) was calculated using the total amount of drug and the volume of diluent provided. The infusion rate was derived by dividing the desired dose by the concentration, converting to an hourly rate, and rounding to the nearest tenth. This step ensures the nurse accurately programs the IV pump to deliver the correct medication dosage to the patient, minimizing the risk of under- or over-dosing, which could lead to ineffective treatment or adverse effects.