Final answer:
To determine how long a 100 ml bag of 2% lidocaine solution at a dose of 4 mg/min will last, calculate the total lidocaine in the bag, divide by the rate, and convert minutes to hours. The bag will last for approximately 8 hours when rounded to the nearest whole number.
Step-by-step explanation:
To calculate the number of hours a 100 ml bag of 2% lidocaine solution will last when administered at a rate of 4 mg/min, we need to first determine the total amount of lidocaine in milligrams in the bag. Since the concentration of the solution is 2%, this means that there are 2 grams of lidocaine per 100 ml of solution. To convert grams to milligrams, we must multiply by 1000:
2 grams × 1000 mg/gram = 2000 mg
Now that we know the total amount of lidocaine in the bag is 2000 mg, we divide this by the dose rate of 4 mg/min to find out how many minutes the bag will last:
2000 mg ÷ 4 mg/min = 500 min
To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):
500 min ÷ 60 min/hour ≈ 8.33 hours
Rounding to the nearest whole number, the 100 ml bag will last approximately 8 hours.