Practice Examples: Calculating Final Concentration After Multiple Dilutions

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Understanding how to calculate the final concentration after multiple dilutions is essential in many scientific and laboratory settings. This article provides practical examples to help students and teachers grasp the process.

Basics of Dilution

A dilution involves reducing the concentration of a solute in a solution, usually by adding more solvent. The key formula used is:

C1V1 = C2V2

Where:

  • C1 = initial concentration
  • V1 = initial volume
  • C2 = final concentration
  • V2 = final volume

Example 1: Single Dilution

Suppose you have 10 mL of a solution with a concentration of 100 mg/mL. You dilute it to a final volume of 50 mL. What is the final concentration?

Using the formula:

C1V1 = C2V2

Plugging in the values:

100 mg/mL × 10 mL = C2 × 50 mL

C2 = (100 mg/mL × 10 mL) / 50 mL = 20 mg/mL

Example 2: Multiple Dilutions

Now, consider a scenario where a solution is diluted twice, sequentially. First, 5 mL of a 200 mg/mL solution is diluted to 25 mL. Then, 10 mL of this new solution is diluted to 50 mL. What is the final concentration?

First Dilution

Using the formula:

200 mg/mL × 5 mL = C1 × 25 mL

C1 = (200 mg/mL × 5 mL) / 25 mL = 40 mg/mL

Second Dilution

Now, 10 mL of the 40 mg/mL solution is diluted to 50 mL:

40 mg/mL × 10 mL = C2 × 50 mL

C2 = (40 mg/mL × 10 mL) / 50 mL = 8 mg/mL

Conclusion

Calculating the final concentration after multiple dilutions involves applying the dilution formula step-by-step. Always keep track of each step to ensure accuracy. Practice with different scenarios to strengthen understanding.