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Reconstitution & Powder Volume Practice

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Reconstituting a powdered drug adds diluent to reach a target concentration, but the dry powder occupies space of its own. That space is the powder volume, or displacement volume, and it makes the final volume greater than the diluent added.

Formulapowder (displacement) volume = final reconstituted volume − volume of diluent added
Worked example

A 1 g vial reconstituted to 100 mg/mL needs a final volume of 10 mL. If the label says to add 9.5 mL diluent, the powder volume = 10 − 9.5 = 0.5 mL.

Add the displacement volume to the diluent when finding concentration. Leave it out and you overestimate the strength.

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Reconstitution
A vial contains 3 g of powdered drug. Adding 11.5 mL of diluent yields a final concentration of 250 mg/mL. What is the powder (displacement) volume? Round your answer to two decimal places.
mL

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How to set up a reconstitution problem

A powdered drug for injection has to be dissolved before use, and the volume you get after dissolving is not the volume of diluent you added, because the powder itself takes up space. That space is the powder volume, also called displacement volume. Every reconstitution question is built on one relationship, and knowing which of the three quantities is unknown tells you how to rearrange it.

final volume = diluent added + powder volume   •   concentration = drug amount ÷ final volume

Worked example 1: find the powder volume

A 1 g vial reconstituted with 9.6 mL of diluent gives 100 mg/mL. What is the powder volume?

final volume = 1,000 ÷ 100 = 10 mL

powder volume = 10 − 9.6 = 0.4 mL

The label usually states the diluent volume and the resulting concentration, and leaves the powder volume for you to work out. Get the final volume from the concentration first, then subtract.

Worked example 2: find the concentration

A 2 g vial has a powder volume of 0.5 mL. You add 9.5 mL of diluent. What is the concentration?

final volume = 9.5 + 0.5 = 10 mL

concentration = 2,000 ÷ 10 = 200 mg/mL

Leaving the powder volume out gives 2,000 ÷ 9.5:

2,000 ÷ 9.5 = 210.53 mg/mL

which is 5% too strong. Every dose drawn from that vial would then be 5% short. Small powder volumes matter more, not less, in small vials, because they're a larger share of the final volume.

Worked example 3: find the dose volume

From the vial in example 2, an order calls for 500 mg.

volume = 500 ÷ 200 = 2.5 mL

Once the concentration is right, the dose volume is a proportion like any other.

Choosing the diluent volume for a target concentration

Questions also run the relationship backwards: what volume of diluent gives a target concentration? Work out the final volume needed (drug amount ÷ target concentration), then subtract the powder volume. A 1 g vial with a 0.4 mL powder volume, to be made 50 mg/mL: final volume 1,000 ÷ 50 = 20 mL, so add 19.6 mL of diluent. Adding 20 mL would give 1,000 ÷ 20.4, about 49 mg/mL, which is close but not the target and not what the label would say.

Where students lose the points

10 Reconstitution & Powder Volume practice problems with worked solutions

Every problem below is worked start to finish. Try it yourself first, then check the steps. For a fresh problem every time, use the practice box above. It generates unlimited variations of these same question types.

Problem 1: Reconstitution

A vial contains 0.5 g of drug with a powder displacement volume of 0.4 mL. If you add 4.5 mL of diluent, what is the final concentration in mg/mL? Round your answer to the nearest whole number.

Answer 102 mg/mL

Solution
  1. Final volume = diluent + powder displacement = 4.5 mL + 0.4 mL = 4.9 mL.
  2. Concentration = 500 mg ÷ 4.9 mL ≈ 102.04 mg/mL.
  3. Rounded as the question asks: 102 mg/mL.

Add the powder's displacement volume to the diluent. Leave it out and you overestimate the concentration.

Problem 2: Reconstitution

A vial contains 2 g of drug with a powder displacement volume of 0.7 mL. If you add 4.6 mL of diluent, what is the final concentration in mg/mL? Round your answer to the nearest whole number.

Answer 377 mg/mL

Solution
  1. Final volume = diluent + powder displacement = 4.6 mL + 0.7 mL = 5.3 mL.
  2. Concentration = 2000 mg ÷ 5.3 mL ≈ 377.36 mg/mL.
  3. Rounded as the question asks: 377 mg/mL.

Add the powder's displacement volume to the diluent. Leave it out and you overestimate the concentration.

Problem 3: Reconstitution

A vial contains 0.25 g of drug with a powder displacement volume of 0.5 mL. If you add 1.8 mL of diluent, what is the final concentration in mg/mL? Round your answer to the nearest whole number.

Answer 109 mg/mL

Solution
  1. Final volume = diluent + powder displacement = 1.8 mL + 0.5 mL = 2.3 mL.
  2. Concentration = 250 mg ÷ 2.3 mL ≈ 108.7 mg/mL.
  3. Rounded as the question asks: 109 mg/mL.

Add the powder's displacement volume to the diluent. Leave it out and you overestimate the concentration.

Problem 4: Reconstitution

A vial contains 1 g of drug with a powder displacement volume of 0.7 mL. If you add 9.5 mL of diluent, what is the final concentration in mg/mL? Round your answer to the nearest whole number.

Answer 98 mg/mL

Solution
  1. Final volume = diluent + powder displacement = 9.5 mL + 0.7 mL = 10.2 mL.
  2. Concentration = 1000 mg ÷ 10.2 mL ≈ 98.04 mg/mL.
  3. Rounded as the question asks: 98 mg/mL.

Add the powder's displacement volume to the diluent. Leave it out and you overestimate the concentration.

Problem 5: Reconstitution

A vial contains 2 g of drug with a powder displacement volume of 0.4 mL. If you add 4.6 mL of diluent, what is the final concentration in mg/mL? Round your answer to the nearest whole number.

Answer 400 mg/mL

Solution
  1. Final volume = diluent + powder displacement = 4.6 mL + 0.4 mL = 5 mL.
  2. Concentration = 2000 mg ÷ 5 mL = 400 mg/mL.
  3. Rounded as the question asks: 400 mg/mL.

Add the powder's displacement volume to the diluent. Leave it out and you overestimate the concentration.

Problem 6: Reconstitution

A vial contains 1 g of powdered drug. Adding 2.1 mL of diluent yields a final concentration of 400 mg/mL. What is the powder (displacement) volume? Round your answer to two decimal places.

Answer 0.40 mL

Solution
  1. Final volume needed: 1 g = 1000 mg; 1000 mg ÷ 400 mg/mL = 2.5 mL.
  2. Powder volume = final volume − diluent added = 2.5 − 2.1 = 0.4 mL.
  3. Rounded as the question asks: 0.40 mL.

The dry powder occupies space (displacement). Powder volume = final reconstituted volume − volume of diluent added.

Problem 7: Reconstitution

A vial contains 2 g of powdered drug. Adding 4.6 mL of diluent yields a final concentration of 400 mg/mL. What is the powder (displacement) volume? Round your answer to two decimal places.

Answer 0.40 mL

Solution
  1. Final volume needed: 2 g = 2000 mg; 2000 mg ÷ 400 mg/mL = 5 mL.
  2. Powder volume = final volume − diluent added = 5 − 4.6 = 0.4 mL.
  3. Rounded as the question asks: 0.40 mL.

The dry powder occupies space (displacement). Powder volume = final reconstituted volume − volume of diluent added.

Problem 8: Reconstitution

A vial contains 3 g of powdered drug. Adding 23.4 mL of diluent yields a final concentration of 125 mg/mL. What is the powder (displacement) volume? Round your answer to two decimal places.

Answer 0.60 mL

Solution
  1. Final volume needed: 3 g = 3000 mg; 3000 mg ÷ 125 mg/mL = 24 mL.
  2. Powder volume = final volume − diluent added = 24 − 23.4 = 0.6 mL.
  3. Rounded as the question asks: 0.60 mL.

The dry powder occupies space (displacement). Powder volume = final reconstituted volume − volume of diluent added.

Problem 9: Reconstitution

A vial contains 1 g of powdered drug. Adding 3.6 mL of diluent yields a final concentration of 250 mg/mL. What is the powder (displacement) volume? Round your answer to two decimal places.

Answer 0.40 mL

Solution
  1. Final volume needed: 1 g = 1000 mg; 1000 mg ÷ 250 mg/mL = 4 mL.
  2. Powder volume = final volume − diluent added = 4 − 3.6 = 0.4 mL.
  3. Rounded as the question asks: 0.40 mL.

The dry powder occupies space (displacement). Powder volume = final reconstituted volume − volume of diluent added.

Problem 10: Reconstitution

A vial contains 1 g of drug with a powder displacement volume of 0.7 mL. If you add 2.5 mL of diluent, what is the final concentration in mg/mL? Round your answer to the nearest whole number.

Answer 313 mg/mL

Solution
  1. Final volume = diluent + powder displacement = 2.5 mL + 0.7 mL = 3.2 mL.
  2. Concentration = 1000 mg ÷ 3.2 mL = 312.5 mg/mL.
  3. Rounded as the question asks: 313 mg/mL.

Add the powder's displacement volume to the diluent. Leave it out and you overestimate the concentration.

Sources and how far they go

Where a convention on this page comes from a published standard, the standard is named. Where it comes from a textbook or from ordinary practice instead, the entry says so. That difference matters when a preceptor or an exam disagrees with you.

Citations are to the source of the method. They are not a review of this page, and none of these bodies has reviewed or endorsed it.

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