If you need to prepare 50 mL of a 10 mg/mL solution, stock is 50 mg/mL. How many mL of stock are needed, and what is the final volume?

• A. 10 mL stock; final volume 50 mL
• B. 5 mL stock; final volume 50 mL
• C. 20 mL stock; final volume 50 mL
• D. 15 mL stock; final volume 60 mL

Answer: (A)

When you dilute a solution to a desired concentration, use the relation C1V1 = C2V2, which keeps the amount of drug the same before and after dilution. Here, the stock concentration is 50 mg/mL (C1), the desired final concentration is 10 mg/mL (C2), and the final volume you want is 50 mL (V2). Solve for the volume of stock to use: V1 = (C2 × V2) / C1 = (10 mg/mL × 50 mL) / (50 mg/mL) = 10 mL.

So, measure 10 mL of the stock solution and dilute it with solvent to reach a total final volume of 50 mL. This gives 10 mL × 50 mg/mL = 500 mg in 50 mL, which is 500 mg / 50 mL = 10 mg/mL.