A patient with a weight of 166 lbs is suffering from bacterial pneumonia. The doctor prescribes the antibiotic, Cefaclor, with a total of 45 mg/kg each day. If the drug is divided into 3 doses and is available in a solution of 125 mg/mL, how many mL would the nurse administer per dose? (1 kg = 2.2 lbs)
The Correct Answer and Explanation is :
Step-by-Step Solution:
Step 1: Convert the patient’s weight from pounds to kilograms.
We are given that the patient weighs 166 lbs, and we know that:
[
1 \, \text{kg} = 2.2 \, \text{lbs}
]
To convert the weight to kilograms, we divide the weight by 2.2:
[
\text{Weight in kg} = \frac{166 \, \text{lbs}}{2.2} = 75.45 \, \text{kg}
]
Step 2: Calculate the total dose of Cefaclor the patient needs each day.
The doctor prescribed 45 mg of Cefaclor per kilogram of body weight each day. So, we multiply the weight in kilograms by the dosage:
[
\text{Total daily dose} = 45 \, \text{mg/kg} \times 75.45 \, \text{kg} = 3395.25 \, \text{mg}
]
Step 3: Divide the total dose by the number of doses.
The prescription specifies that the total daily dose is divided into 3 doses. To find the dose per administration, we divide the total daily dose by 3:
[
\text{Dose per administration} = \frac{3395.25 \, \text{mg}}{3} = 1131.75 \, \text{mg}
]
Step 4: Convert the dose to milliliters.
The medication is available in a solution of 125 mg/mL. To find out how many mL correspond to 1131.75 mg, we divide the dose by the concentration of the solution:
[
\text{Volume per dose (mL)} = \frac{1131.75 \, \text{mg}}{125 \, \text{mg/mL}} = 9.05 \, \text{mL}
]
Final Answer:
The nurse should administer 9.05 mL of the solution per dose.
Explanation:
- Weight Conversion: We need the weight in kilograms because the dosage is prescribed per kilogram. The conversion factor is straightforward: 1 kg = 2.2 lbs. This conversion ensures that we apply the correct amount of medication based on the patient’s weight.
- Dosage Calculation: The doctor specifies 45 mg of the drug per kg of body weight. By multiplying the patient’s weight by this value, we determine how much Cefaclor is required each day. Dividing by 3 doses ensures that each dose is appropriate for the prescribed regimen.
- Volume Calculation: Given the concentration of the drug in the solution, we can convert the required dose (in mg) into the volume (in mL) by dividing by the concentration (mg/mL). This step allows the nurse to prepare the correct volume of the medication for administration.
By breaking down the problem into manageable steps, we ensure the patient receives the proper dosage of Cefaclor in a safe and effective manner.