The correct volume to administer is 50 mL.

Step-by-step setup

  • Order: 100 mg is prescribed.
  • Supply: 1,000 mcg per 0.5 mL.
  • First, convert mg to mcg, since the vial is labeled in mcg. There are 1,000 mcg in 1 mg.

So:

  • 100 mg=100×1,000=100,000 mcg100\text{ mg}=100\times 1{,}000=100{,}000\text{ mcg}100 mg=100×1,000=100,000 mcg.

Finding the volume

  • The solution contains 1,000 mcg in 0.5 mL. That is a concentration of:
    • 1,000 mcg/0.5 mL=2,000 mcg/mL1{,}000\text{ mcg}/0.5\text{ mL}=2{,}000\text{ mcg/mL}1,000 mcg/0.5 mL=2,000 mcg/mL.
  • Required dose: 100,000 mcg.

Use the formula:

  • Volume === Dose ÷ Concentration.
  • Volume =100,000textmcg2,000textmcg/mL=50 mL=\dfrac{100{,}000\\text{mcg}}{2{,}000\\text{mcg/mL}}=50\text{ mL}=2,000textmcg/mL100,000textmcg​=50 mL.

So, 50 mL should be administered (mathematically). Always confirm such an unusually large volume with a pharmacist or prescriber before administration, as a 100 mg dose at this concentration is clinically suspicious.