Final answer:
To calculate the infusion time, first find the patient's dosage rate at 1560mcg/min, translate that to volume based on the solution concentration, resulting in 0.975 mL/min. Then divide the total volume of the bag by the flow rate, giving approximately 256.41 minutes for the bag to completely infuse.
Step-by-step explanation:
The doctor has ordered a Dopamine infusion at a rate of 20mcg/kg/min for a patient who weighs 78kg. The solution available is 250mL of Dopamine at a concentration of 1600 mcg/mL. To calculate how long it will take for the bag to completely infuse, you must first determine the total dosage required per minute for the patient, then calculate the number of minutes the 250mL bag will last.
The dosage per minute for the patient is 20mcg/kg/min × 78kg, which equals 1560mcg/min. This is the amount of Dopamine the patient requires in one minute. Next, we need to find out how many mL this corresponds to by using the concentration of the Dopamine solution. We know that 1mL of the solution contains 1600mcg of Dopamine, so 1560mcg of Dopamine equals 1560mcg/1600mcg/mL, which is 0.975 mL/min.
Now that we have the flow rate (0.975 mL/min), to find out how long the 250mL bag will last, we divide the total volume of the bag by the flow rate. Therefore, 250mL ÷ 0.975 mL/min equals approximately 256.41 minutes for the bag to completely infuse.