A nurse is preparing to administer gentamicin 1 mg/kg IM to a client who weighs 154 lb. Available is gentamicin solution 40 mg/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 determine the correct amount of gentamicin solution to administer, follow these steps:
Step-by-Step Solution
- Convert the client’s weight from pounds to kilograms: The weight of the client is given as 154 lb. To convert pounds to kilograms, use the conversion factor 1 kg = 2.20462 lb.Weight (kg)=Weight (lb)2.20462=154 lb2.20462≈70 kg\text{Weight (kg)} = \frac{\text{Weight (lb)}}{2.20462} = \frac{154 \text{ lb}}{2.20462} \approx 70 \text{ kg}Weight (kg)=2.20462Weight (lb)=2.20462154 lb≈70 kg
- Calculate the required dose in milligrams: The prescribed dose is 1 mg/kg. Multiply the weight in kilograms by the dose per kilogram.Dose (mg)=Weight (kg)×Dose (mg/kg)=70 kg×1 mg/kg=70 mg\text{Dose (mg)} = \text{Weight (kg)} \times \text{Dose (mg/kg)} = 70 \text{ kg} \times 1 \text{ mg/kg} = 70 \text{ mg}Dose (mg)=Weight (kg)×Dose (mg/kg)=70 kg×1 mg/kg=70 mg
- Determine the volume of gentamicin solution needed: The available gentamicin solution is 40 mg/mL. To find out how many milliliters are needed to administer 70 mg, use the formula:Volume (mL)=Dose (mg)Concentration (mg/mL)=70 mg40 mg/mL=1.75 mL\text{Volume (mL)} = \frac{\text{Dose (mg)}}{\text{Concentration (mg/mL)}} = \frac{70 \text{ mg}}{40 \text{ mg/mL}} = 1.75 \text{ mL}Volume (mL)=Concentration (mg/mL)Dose (mg)=40 mg/mL70 mg=1.75 mL
- Round the volume to the nearest tenth: The calculated volume is 1.75 mL. When rounding to the nearest tenth, this becomes 1.8 mL.
Summary
The nurse should administer 1.8 mL of gentamicin solution.
Explanation
To accurately prepare the medication, it’s essential to perform several calculations, starting with converting the client’s weight into kilograms since dosages are often based on weight in kilograms. Next, calculating the total dose needed helps in determining the exact volume of medication to draw. Finally, converting this dose into the volume of solution based on its concentration ensures the client receives the correct amount of medication. Proper rounding practices ensure the medication volume is practical for administration and aligns with standard dosage protocols.