A lab worker dilutes 3.0 mL of a 4.0 mg/mL solution to a final concentration of 1.0 mg/mL. What final volume is required?

• A. 9 mL
• B. 12 mL
• C. 6 mL
• D. 3 mL

Answer: (B)

Dilution keeps the same amount of solute while increasing the volume, so the concentration drops as volume rises. Use the relationship C1V1 = C2V2.

First find how much solute you start with: 4.0 mg/mL × 3.0 mL = 12 mg of solute. You want a final concentration of 1.0 mg/mL, so the final volume must be V2 = (C1V1) / C2 = 12 mg / (1.0 mg/mL) = 12 mL.

So, the final volume required is 12 mL. The amount of diluent added would be 12 mL − 3 mL = 9 mL. If you test the other volumes, they’d yield higher concentrations (for example, 9 mL would give 12 mg / 9 mL = 1.333 mg/mL, 6 mL would give 2 mg/mL, and 3 mL would keep 4 mg/mL), which doesn’t meet the target concentration.