An adult whose weight is 108.4 kg is to receive a dosage of 2 mg/kg/hr. The solution strength is 1 g in 500 mL.
The Correct Answer and Explanation is:
Correct Answer:
To calculate the infusion rate in mL/hr:
- Determine the dosage in mg/hr:
108.4 kg×2 mgkg⋅hr=216.8 mg/hr108.4 \, \text{kg} \times 2 \, \frac{\text{mg}}{\text{kg} \cdot \text{hr}} = 216.8 \, \text{mg/hr}108.4kg×2kg⋅hrmg=216.8mg/hr
- Convert solution strength from g to mg:
1 g=1000 mg⇒Solution strength=1000 mg in 500 mL1 \, \text{g} = 1000 \, \text{mg} \Rightarrow \text{Solution strength} = 1000 \, \text{mg in 500 mL}1g=1000mg⇒Solution strength=1000mg in 500 mL
- Determine how many mg are in 1 mL:
1000 mg500 mL=2 mg/mL\frac{1000 \, \text{mg}}{500 \, \text{mL}} = 2 \, \text{mg/mL}500mL1000mg=2mg/mL
- Find the volume in mL that delivers 216.8 mg/hr:
216.8 mg/hr2 mg/mL=108.4 mL/hr\frac{216.8 \, \text{mg/hr}}{2 \, \text{mg/mL}} = 108.4 \, \text{mL/hr}2mg/mL216.8mg/hr=108.4mL/hr
Final Answer: 108.4 mL/hr
Explanation (without using the word “we”):
To determine the correct infusion rate for a patient, it is essential to convert the body weight-based dosage into a volume that matches the concentration of the prepared solution. In this situation, a weight of 108.4 kilograms is multiplied by the prescribed dosage rate of 2 milligrams per kilogram per hour, which results in 216.8 milligrams per hour.
The prepared medication solution contains 1 gram in 500 milliliters. Since 1 gram equals 1000 milligrams, the concentration of the solution is 2 milligrams per milliliter. This is found by dividing 1000 milligrams by 500 milliliters.
With the desired dosage now known to be 216.8 milligrams per hour and the solution concentration at 2 milligrams per milliliter, the next step involves dividing the dosage by the concentration. The result of this calculation is 108.4 milliliters per hour. This is the rate at which the infusion pump must be set to deliver the correct dosage of the drug continuously over time.
Such dosage calculations are critical in clinical settings, especially when drugs are dosed by weight and administered intravenously. Ensuring accuracy prevents underdosing or overdosing, both of which could have serious consequences for patient safety and treatment effectiveness.
