Dopamine 5 mcg/kg/minute IV is prescribed for a client who weighs 132 pounds. The pharmacy dispenses a 500 mL IV solution of 0.9% normal saline with dopamine 1600 mg. The nurse should program the infusion pump to deliver how many ml/hour? (Enter numeric value only. If rounding is required, round to the nearest tenth)
The Correct answer and Explanation is:
To solve this problem, we need to calculate the rate at which the infusion pump should deliver the dopamine solution in milliliters per hour (mL/hour). Here’s the step-by-step breakdown:
Step 1: Convert the client’s weight to kilograms
Since the dosage is given in mcg/kg/min, we first convert the client’s weight from pounds to kilograms.
[
132 \, \text{lbs} \times \frac{1 \, \text{kg}}{2.2 \, \text{lbs}} = 60 \, \text{kg}
]
Step 2: Calculate the dose in mcg/minute
The prescribed dose is 5 mcg/kg/min. Multiply the client’s weight by this dosage to get the total dose in mcg/minute.
[
5 \, \text{mcg} \times 60 \, \text{kg} = 300 \, \text{mcg/minute}
]
Step 3: Convert the dose to mg/hour
Since we need the infusion rate in mL/hour and the available solution is in mg, we must first convert the dose from mcg/minute to mg/hour.
1 mg = 1000 mcg, so:
[
300 \, \text{mcg/min} \times \frac{1 \, \text{mg}}{1000 \, \text{mcg}} = 0.3 \, \text{mg/minute}
]
Now, convert this to mg/hour by multiplying by 60 minutes:
[
0.3 \, \text{mg/min} \times 60 \, \text{minutes} = 18 \, \text{mg/hour}
]
Step 4: Calculate the infusion rate in mL/hour
The pharmacy has dispensed a solution with 1600 mg of dopamine in 500 mL of saline. To find out how many mL contain 1 mg of dopamine, divide the volume by the total amount of dopamine:
[
\frac{500 \, \text{mL}}{1600 \, \text{mg}} = 0.3125 \, \text{mL/mg}
]
Now, multiply this by the dosage in mg/hour:
[
18 \, \text{mg/hour} \times 0.3125 \, \text{mL/mg} = 5.625 \, \text{mL/hour}
]
Step 5: Round to the nearest tenth
The final infusion rate is 5.6 mL/hour.
Explanation
The dopamine dosage is calculated based on the patient’s weight, making accurate weight conversion essential. The prescription requires 5 mcg/kg/min, and this value must be adjusted for the client’s specific body mass, converted to mL/hour using the concentration of dopamine in the dispensed solution. By breaking the problem into clear steps—starting with unit conversions and progressing through dose calculations—we ensure precise dosing, critical for medications like dopamine where incorrect dosing can lead to significant clinical outcomes.