Calculating a 30-Day Supply of a Multiple-Dose Opioid Vial
A hospice nurse is calculating the supply needed for a 30-day period for a patient prescribed hydromorphone 3 mg subcutaneously every 6 hours. The pharmacy dispenses 10-mL multiple-dose vials labeled 2.5 mg/mL. Agency policy allows a vial to be used for 28 days after the first puncture, any vial opened longer must be discarded, and a new vial must be started whenever the remaining volume cannot deliver one full dose. The nurse also schedules the four daily doses at 06:00, 12:00, 18:00, and 00:00, and the patient's daughter will record each dose on a log that the nurse reviews at every visit. The nurse currently has 6 unopened vials on hand, and the next pharmacy delivery is in 10 days. The nurse must report the total volume to be administered over the 30 days for the pharmacy's controlled-substance reconciliation.
1. How many milliliters are drawn per dose, per day, and over the full 30 days?
Read the worked answer
Per dose: 3 mg ÷ 2.5 mg/mL = 1.2 mL.
Per day: 4 doses × 1.2 mL = 4.8 mL.
Total doses: 4 × 30 = 120 doses.
Total volume: 120 × 1.2 mL = 144 mL, which matches 4.8 mL/day × 30 days = 144 mL.
Answer: 1.2 mL per dose, 4.8 mL per day, 144 mL over 30 days. This 144 mL figure is what the nurse reports for reconciliation; it is the volume actually administered, not the volume dispensed, and the difference is the documented wastage.
2. How many usable days does one 10-mL vial provide, and what fraction of the vial is discarded?
Read the worked answer
Days per vial: 10 mL ÷ 4.8 mL/day = 2.083 days, so 2 complete days.
Volume used in 2 days: 2 × 4.8 = 9.6 mL.
Remainder: 10 − 9.6 = 0.4 mL. As a fraction of a dose: 0.4 ÷ 1.2 = 1/3 of a dose, which cannot deliver a full 3-mg dose, so policy requires a new vial and the 0.4 mL is wasted.
Waste: 0.4 ÷ 10 = 0.04, or 4% of each vial.
Answer: 2 usable days per vial, with 0.4 mL (one-third of a dose, 4% of the vial) discarded. The 28-day puncture limit never comes into play because each vial is exhausted in about 2.5 days.
3. How many vials are needed for the 30-day period, and are the 6 vials on hand enough to reach the delivery in 10 days?
Read the worked answer
Vials needed: because each vial yields only 2 usable days, 30 ÷ 2 = 15 vials. Cross-check by volume: 144 mL ÷ 10 mL per vial = 14.4, which rounds up to 15 - the same answer, since the 0.4-mL remnants cannot be pooled.
Coverage with 6 vials: 6 × 2 days = 12 usable days, which covers the 10-day gap with about one vial (2 days) to spare. Five vials would cover exactly 10 days, leaving no margin for a dropped or contaminated vial.
Answer: 15 vials for 30 days; the 6 on hand are sufficient until delivery, but barely. The nurse should request the full 15-vial supply at the next delivery and document the 0.4-mL wastage on each vial for the controlled-substance record.