Questions: Question 25 of 54 A client who weights 176 pounds is receiving an IV infusion with esmolol hydrochloride (Brevibloc) at 48 ml / hour. The IV solution is labeled with the concentration of Brevibloc 10 mg / ml. How many mcg / kg / minute is the client receiving? (Enter numeric value only. Round to nearest whole number.)

Solution Steps

To solve this problem, we need to convert the infusion rate from milliliters per hour to micrograms per kilogram per minute. First, calculate the total milligrams of the drug being infused per hour using the concentration. Then, convert this to micrograms per minute. Finally, divide by the client's weight in kilograms to find the rate in micrograms per kilogram per minute.

The client's weight is given as 176 pounds. To convert this to kilograms, use the conversion factor \(1 \, \text{pound} = 0.453592 \, \text{kg}\).

\[ \text{Weight in kg} = 176 \times 0.453592 = 79.8322 \, \text{kg} \]

The infusion rate is 48 ml/hour, and the concentration of the drug is 10 mg/ml. Therefore, the total drug infusion per hour is:

\[ \text{Total mg per hour} = 48 \, \text{ml/hour} \times 10 \, \text{mg/ml} = 480 \, \text{mg/hour} \]

Convert the total drug infusion from mg/hour to mcg/minute using the conversion factors \(1 \, \text{mg} = 1000 \, \text{mcg}\) and \(1 \, \text{hour} = 60 \, \text{minutes}\).

\[ \text{Total mcg per minute} = \frac{480 \, \text{mg/hour} \times 1000 \, \text{mcg/mg}}{60 \, \text{minutes/hour}} = 8000 \, \text{mcg/minute} \]

To find the infusion rate in mcg/kg/minute, divide the total mcg per minute by the client's weight in kg.

\[ \text{mcg/kg/minute} = \frac{8000 \, \text{mcg/minute}}{79.8322 \, \text{kg}} = 100.2102 \, \text{mcg/kg/minute} \]

Round the result to the nearest whole number.

\[ \text{Rounded mcg/kg/minute} = 100 \]

Final Answer