Final answer:
To administer 50 micrograms of fentanyl from a solution that has a concentration of 0.1 mg per 2 mL, the nurse should give 1 mL of the solution.
Step-by-step explanation:
The student is asking for assistance in converting medication dosage units from micrograms to milliliters, using the provided concentration of the drug fentanyl. To find the correct amount to administer, one must first convert 50 micrograms to milligrams. Since there are 1,000 micrograms in a milligram, the calculation is as follows: 50 mcg ÷ 1,000 = 0.05 mg.
Now, using the provided concentration of fentanyl (0.1 mg/2 mL), we determine the appropriate volume to administer to achieve a dose of 0.05 mg. If 0.1 mg is in 2 mL, then 0.05 mg will be in 1 mL, because the amount of fentanyl is directly proportional to the volume. The nurse should therefore administer 1 mL of fentanyl to deliver a dose of 50 micrograms.