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Med math · 5 free problems

Reconstitution practice: powder vials and concentrations

Once a powder is reconstituted, the label states a concentration. Treat that concentration exactly like a liquid label: ordered amount times one mL over the mg per mL.

Fictional labels. Round as each question says. How to round

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Reconstitution: work through the set

Question 1 of 5

Volume from a reconstituted concentration

A fictional powder vial is reconstituted according to its practice label to a concentration of 250 mg/mL. The exercise requests 500 mg. What volume contains 500 mg? Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 2 mL.

500 mg × (1 mL / 250 mg) = 2 mL. The mg units cancel.

Check: 2 mL × 250 mg/mL = 500 mg.

If you got 0.5: You divided the concentration by the requested amount. Start with the requested amount.

Question 2 of 5

A volume with a decimal

A fictional powder vial is reconstituted according to its practice label to 100 mg/mL. The exercise requests 350 mg. What volume contains 350 mg? Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 3.5 mL.

350 mg × (1 mL / 100 mg) = 3.5 mL.

Check: 3.5 mL × 100 mg/mL = 350 mg.

If you got 35: You moved the decimal the wrong way. Dividing by 100 makes the number smaller.

Question 3 of 5

Convert grams before using the concentration

A fictional powder vial is reconstituted according to its practice label to 200 mg/mL. The exercise requests 1.5 g. What volume contains 1.5 g? Use 1 g = 1,000 mg. Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 7.5 mL.

First 1.5 g × (1,000 mg / 1 g) = 1,500 mg. Then 1,500 mg × (1 mL / 200 mg) = 7.5 mL.

Check: 7.5 mL × 200 mg/mL = 1,500 mg = 1.5 g.

If you got 0.0075: You used 1.5 as milligrams. Convert grams to milligrams first.

Question 4 of 5

Find the concentration

A fictional practice label states that a vial contains 1,000 mg once reconstituted to a total volume of 10 mL. What is the concentration in mg/mL? Give the exact answer; no rounding is needed.

Worked solution and answer

Answer: 100 mg/mL.

1,000 mg ÷ 10 mL = 100 mg/mL.

Check: 100 mg/mL × 10 mL = 1,000 mg.

If you got 0.01: You divided volume by amount. Concentration is amount per volume, so put mg in the numerator.

Question 5 of 5

Use a stated concentration

A fictional practice label states a reconstituted concentration of 50 mg/mL. The exercise requests 125 mg. What volume contains 125 mg? Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 2.5 mL.

125 mg × (1 mL / 50 mg) = 2.5 mL.

Check: 2.5 mL × 50 mg/mL = 125 mg.

If you got 0.4: You divided 50 by 125. The requested amount belongs in the numerator.

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