Final answer:
The nurse should administer 0.2 ml of the hydromorphone solution, based on the dosage concentration formula and the provided medication concentration.
Step-by-step explanation:
When a client with terminal bone cancer needs to receive 2 mg of hydromorphone intravenously (IV) for severe breakthrough pain, and the vial contains 10 mg/ml, we need to calculate how much solution the nurse would administer. To find the volume of the solution, use the dosage concentration formula:
Dosage (mg) = Volume (ml) × Concentration (mg/ml)
So, rearranging the formula to solve for the volume (ml):
Volume (ml) = Dosage (mg) / Concentration (mg/ml)
Substituting the given values:
Volume (ml) = 2 mg / 10 mg/ml = 0.2 ml
Therefore, the nurse should administer 0.2 ml of the hydromorphone solution.