Order: Cefazolin 25 mg/kg/30 min IVPB for otitis media
Available: 500 mg in 50 mL 0.9% NS
Drop factor: 10 gtts/mL
Client's weight: 40 lbs
Calculate the flow rate_ Show all work using dimensional analysis
To calculate the flow rate, we need to find the total volume of Cefazolin that needs to be infused and the time it takes to infuse that volume.
Step 1: Convert the client's weight from pounds to kilograms.
40 lbs ÷ 2.2 = 18.18 kg (rounded to two decimal places)
Step 2: Calculate the total dose of Cefazolin required.
25 mg/kg x 18.18 kg = 454.5 mg
Step 3: Calculate the total volume of the Cefazolin solution needed.
The concentration of the solution is 500 mg in 50 mL, so the concentration can be expressed as 10 mg/mL.
454.5 mg ÷ 10 mg/mL = 45.45 mL
Step 4: Calculate the flow rate.
Time = 30 minutes
Volume = 45.45 mL
Flow rate = Volume / Time
Flow rate = 45.45 mL / 30 minutes
To ensure consistent units, we convert minutes to hours:
Flow rate = 45.45 mL / 0.5 hours
Flow rate = 90.9 mL/hour
Step 5: Convert the flow rate to drops per minute.
We know that 1 mL = 10 gtts (drop factor given)
90.9 mL/hour * 10 gtts/mL = 909 gtts/hour
To ensure consistent units, we convert hours to minutes:
909 gtts/hour ÷ 60 minutes/hour = 15.15 gtts/minute (rounded to two decimal places)
The flow rate is approximately 15.15 gtts/minute.
To calculate the flow rate, we will use dimensional analysis to convert the weight of the client from pounds to kilograms.
Step 1: Convert the weight from pounds to kilograms.
1 kg = 2.2 lbs
Weight in kg = Weight in lbs / 2.2
Weight in kg = 40 lbs / 2.2
Weight in kg ≈ 18.18 kg
Step 2: Calculate the total dose.
Total dose = Weight in kg * Dose (mg/kg)
Total dose = 18.18 kg * 25 mg/kg
Total dose = 454.5 mg
Step 3: Calculate the volume to be infused.
Volume to be infused = Total dose / Concentration
Volume to be infused = 454.5 mg / 500 mg
Volume to be infused ≈ 0.909 mL
Step 4: Calculate the time for infusion.
Time for infusion = Volume to be infused / Flow rate
Time for infusion = 0.909 mL / (Flow rate / 60 min/hr)
Time for infusion = 0.909 mL / (Flow rate / 60)
Time for infusion = 0.909 * 60 / Flow rate
Time for infusion = 54.54 / Flow rate
Step 5: Substitute the given values and solve for the flow rate.
Flow rate = 54.54 / Time for infusion
Since we have not been given the desired infusion time, we cannot calculate the flow rate.