The child is diagnosed with bacterial meningitis and is to be given a course of antibiotics every 4 hours for 5 days. He will receive ampicillin 150mg/kg/day IVPB in divided doses every 6 hours. Patient weight is 40lbs. The pharmacy sends a vial labeled ampicillin 1g. Instructions on the label state that the medication must be reconstituted with 10 ml of sterile water and then further diluted in 50 ml before administering. What is the rx? S? C? Show all worl
To calculate the proper dosage, we'll need to use the following formula:
Dose (in mg) = Patient weight (in lbs) * Dose (in mg/kg)
First, let's convert the patient's weight from pounds to kilograms:
40 lbs = 40 / 2.205 = 18.14 kg (rounded to two decimal places)
Next, let's calculate the appropriate dosage:
Dose = 18.14 kg * 150 mg/kg = 2721 mg (rounded to the nearest whole number)
Now let's determine the number of ampoules needed. Each ampoule contains 1g (1000 mg) of ampicillin.
Number of ampoules = Dose needed (mg) / Amount per ampoule (mg)
Number of ampoules = 2721 mg / 1000 mg/ampoule = 2.721 ampoules (rounded to three decimal places)
Since we cannot administer a fraction of an ampoule, we need to round up to ensure we have enough medication. Therefore, we'll need to dispense 3 ampoules of ampicillin.
Now let's calculate the total amount of sterile water needed for reconstitution.
Total amount of sterile water needed = Number of ampoules * Amount per ampoule
Total amount of sterile water needed = 3 ampoules * 10 ml/ampoule = 30 ml
The instructions state that the medication should be reconstituted with 10 ml of sterile water. Therefore, we'll use the entire 30 ml of sterile water to reconstitute the 3 ampoules.
Next, we need to calculate the total volume of the reconstituted solution, including the dilution.
Total volume of reconstituted solution = Total amount of sterile water + Dilution volume
Total volume of reconstituted solution = 30 ml + 50 ml = 80 ml
Therefore, the final answer is:
Rx: Ampicillin 2721 mg (3 ampoules) to be reconstituted with 30 ml of sterile water, and further diluted to a total volume of 80 ml before administering.
S: 2721 mg
C: 3 ampoules
Sure, let's break down the steps to find the required prescription (rx), the supply (S), and the calculation (C):
1. Determine the patient's weight in kilograms:
Patient weight: 40 lbs
1 lb = 0.45 kg
Patient weight in kg = 40 lbs * 0.45 kg/lb = 18 kg
2. Calculate the total amount of ampicillin required per day:
Ampicillin dose: 150 mg/kg/day
Patient weight in kg: 18 kg
Total ampicillin dose per day = 150 mg/kg/day * 18 kg = 2700 mg/day
3. Calculate the amount of ampicillin required per dose:
The patient will receive the dose every 6 hours.
Total ampicillin dose per day: 2700 mg
Total doses per day = 24 hours / 6 hours = 4 doses
Amount of ampicillin per dose = Total ampicillin dose per day / Total doses per day
Amount of ampicillin per dose = 2700 mg / 4 doses = 675 mg/dose
4. Calculate the volume of reconstituted ampicillin required:
Each vial contains 1 g (1000 mg) of ampicillin.
The vial must be reconstituted with 10 ml of sterile water.
Therefore, the concentration of reconstituted ampicillin = 1000 mg / 10 ml = 100 mg/ml
Amount of ampicillin required per dose = 675 mg (from step 3)
Volume of reconstituted ampicillin required = Amount of ampicillin required per dose / Concentration of reconstituted ampicillin
Volume of reconstituted ampicillin required = 675 mg / 100 mg/ml = 6.75 ml
5. Calculate the final volume of diluted ampicillin required:
The reconstituted ampicillin needs to be further diluted in 50 ml.
Final volume of diluted ampicillin required = Volume of reconstituted ampicillin + Volume for dilution
Final volume of diluted ampicillin required = 6.75 ml + 50 ml = 56.75 ml
Now let's summarize the prescription:
Rx: Ampicillin 675 mg IVPB every 6 hours
S: Ampicillin 1g vial, sterile water for reconstitution, 50 ml diluent
C: Reconstitute the 1g vial with 10 ml of sterile water. Then further dilute the reconstituted solution in 50 ml before administering.