A nurse is preparing to administer fentanyl 0.5 mcg/kg via IV bolus to a client who weighs 187 lb. Available is fentanyl 50 mcg/mL. How many mL should the nurse administer? (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 solve this problem, we need to follow these steps:
Step 1: Convert the client’s weight from pounds (lb) to kilograms (kg).
Since 1 kg = 2.2 lb, we divide the weight in pounds by 2.2:
[
187 \, \text{lb} \div 2.2 = 85 \, \text{kg}
]
Step 2: Calculate the fentanyl dose in micrograms (mcg).
The order is to administer 0.5 mcg/kg. Therefore, multiply the client’s weight in kg by 0.5 mcg/kg:
[
85 \, \text{kg} \times 0.5 \, \text{mcg/kg} = 42.5 \, \text{mcg}
]
Step 3: Determine how many milliliters (mL) of fentanyl to administer.
The available concentration of fentanyl is 50 mcg/mL. To find the volume in mL, use the formula:
[
\frac{\text{Dose ordered}}{\text{Concentration}} = \frac{42.5 \, \text{mcg}}{50 \, \text{mcg/mL}} = 0.85 \, \text{mL}
]
Step 4: Round the answer to the nearest tenth.
The final volume is 0.85 mL. Rounding to the nearest tenth gives 0.9 mL.
Explanation:
In this calculation, the client weighs 187 pounds, which converts to 85 kg. The prescribed dose is 0.5 mcg per kg of body weight, which equals 42.5 mcg for this client. Since the concentration of fentanyl available is 50 mcg/mL, dividing the prescribed dose (42.5 mcg) by the concentration (50 mcg/mL) results in a volume of 0.85 mL. After rounding, the nurse should administer 0.9 mL of fentanyl.
This step-by-step approach ensures accurate dosing, which is crucial for safety when administering potent medications like fentanyl, a strong opioid used for pain management. Proper dose calculations prevent underdosing (leading to inadequate pain control) or overdosing (leading to potential respiratory depression and other side effects).