Dilution calculations: conserve the amount of solute

To calculate 250 mL of a hypothetical 12% w/v solution from a 40% w/v stock, first find the target solute amount: 12 g/100 mL × 250 mL = 30 g. The stock contains 0.4 g/mL, so 30 g requires 75 mL of stock. The compact calculation is V1 = 12 × 250 ÷ 40 = 75 mL.

The two methods agree because both express conservation of solute. In an idealized additive-volume problem, the diluent amount would be 250 - 75 = 175 mL. In a preparation described as quantity sufficient to a final volume, measure the stock and bring the final mixture to 250 mL; do not assume exact liquid volume additivity.

You cannot place 2% w/v and 5 mg/mL into the formula as the numbers 2 and 5. Convert 2% w/v to 20 mg/mL first. To calculate 100 mL at 5 mg/mL from that stock, V1 = 5 × 100 ÷ 20 = 25 mL. The units are now consistent.

For a concentration expressed by mass, use corresponding masses rather than forcing a volume formula. A w/w stock and a w/v target cannot be interchanged without additional density information. The formula works because the units describe the same conserved amount, not because all percentage symbols are equivalent.

A 2 mg/mL stock cannot become a 5 mg/mL solution by adding only solute-free diluent. The final concentration would have to stay the same or fall. If your computed stock volume exceeds the requested final volume in a simple dilution, check whether the requested preparation is impossible under the supplied conditions.

Removing solvent or adding solute would be a different process, not the dilution operation described here. The exam may test whether you recognize the constraint rather than simply entering a large answer. Explain which assumption failed.

These hypothetical exercises assume that the stated substance remains dissolved, the solute is conserved and the diluent contains none of it. They do not establish compatibility, sterility, stability, route suitability or clinical dosing. Actual preparation requires the relevant verified product and procedural information.

In your review notes, record whether a wrong answer came from mixed units, using the diluent volume as V2, confusing stock volume with final volume or overlooking an impossible target. Then re-test that specific mistake using different numbers. NABP's outline includes calculations, but this resource does not predict their count on your exam.

Try it before reading the answer

Write your setup, units and check first. These are original practice exercises, not recalled exam items.

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