Dilution calculations with C1V1 = C2V2
When you dilute a stock solution, the amount of drug stays the same, so concentration × volume before equals concentration × volume after.
Method
- Write C1 × V1 = C2 × V2.
- Fill in the stock concentration (C1), the final concentration (C2) and the final volume (V2).
- Solve for V1 = (C2 × V2) ÷ C1.
- The diluent needed is V2 − V1.
Worked examples
Example 1
How many mL of a 50% stock solution are needed to prepare 200 mL of a 10% solution? Round to one decimal place.
Show solution
- C1 × V1 = C2 × V2
- 50% × V1 = 10% × 200 mL
- V1 = (10 × 200) ÷ 50 = 40 mL
Answer: 40 mL
Example 2
How many mL of a 20% stock solution are needed to prepare 200 mL of a 5% solution? Round to one decimal place.
Show solution
- C1 × V1 = C2 × V2
- 20% × V1 = 5% × 200 mL
- V1 = (5 × 200) ÷ 20 = 50 mL
Answer: 50 mL
Example 3
How many mL of a 95% stock solution are needed to prepare 200 mL of a 20% solution? Round to one decimal place.
Show solution
- C1 × V1 = C2 × V2
- 95% × V1 = 20% × 200 mL
- V1 = (20 × 200) ÷ 95 = 42.1053 mL, which rounds to 42.1 mL
Answer: 42.1 mL
Tips
- Keep units consistent: percent with percent, mL with mL.
- The final concentration must be lower than the stock.
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