Understanding the Dilution Equation (C1V1 = C2V2)

The dilution equation, represented as C1V1 = C2V2, is a fundamental formula in chemistry that allows us to calculate the concentration and volume of solutions. Here, C1 is the concentration of the stock solution, V1 is the volume of the stock solution required, C2 is the concentration of the diluted solution, and V2 is the final volume of the diluted solution. By mastering this equation, you can efficiently prepare solutions for various applications, from laboratory experiments to industrial processes. Below are three practical examples that illustrate its use in real-world scenarios.

Example 1: Preparing a Sodium Chloride Solution

In a laboratory setting, a researcher needs to prepare a 0.5 M sodium chloride (NaCl) solution for an experiment. They have a stock solution of 2 M NaCl available. To determine the volume of stock solution needed, they can apply the dilution equation:

• Given:
  • C1 (stock concentration) = 2 M
  • C2 (desired concentration) = 0.5 M
  • V2 (final volume) = 500 mL (0.5 L)

Using the equation:

C1V1 = C2V2
2 M × V1 = 0.5 M × 0.5 L
2V1 = 0.25
V1 = 0.25 / 2
V1 = 0.125 L or 125 mL

The researcher needs to take 125 mL of the 2 M NaCl stock solution and dilute it with distilled water until the total volume reaches 500 mL to achieve the desired concentration.

Notes:

• Always ensure to mix the solution thoroughly after dilution.
• If you need a different final volume, adjust V2 accordingly and recalculate V1.

Example 2: Diluting Acetic Acid for a Titration Experiment

During a titration experiment, a chemistry student needs to prepare a diluted acetic acid solution with a concentration of 0.1 M. The stock solution of acetic acid they have is 1 M. They need to know how much of the stock solution to use:

• Given:
  • C1 (stock concentration) = 1 M
  • C2 (desired concentration) = 0.1 M
  • V2 (final volume) = 250 mL (0.25 L)

Applying the dilution equation:

C1V1 = C2V2
1 M × V1 = 0.1 M × 0.25 L
V1 = (0.1 × 0.25) / 1
V1 = 0.025 L or 25 mL

The student should measure out 25 mL of the 1 M acetic acid and dilute it with water to a final volume of 250 mL. This will provide the correct concentration for the titration.

Notes:

• It’s important to add acid to water, not the other way around, to prevent exothermic reactions.
• Always label your solutions with concentration and date for safe use.

Example 3: Creating a Diluted Food Coloring Solution

In food preparation, a chef may want to create a specific shade of a colored frosting using food coloring. They have a highly concentrated food coloring solution (C1) at 5 M and need to make a lighter solution of 0.2 M for decorating cakes:

• Given:
  • C1 (stock concentration) = 5 M
  • C2 (desired concentration) = 0.2 M
  • V2 (final volume) = 200 mL (0.2 L)

Using the dilution equation:

C1V1 = C2V2
5 M × V1 = 0.2 M × 0.2 L
5V1 = 0.04
V1 = 0.04 / 5
V1 = 0.008 L or 8 mL

The chef will mix 8 mL of the 5 M food coloring with enough water to reach a total volume of 200 mL for the desired color intensity.

Notes:

• Food coloring can vary in concentration; ensure to check the label before diluting.
• Experiment with small batches to achieve the exact color desired before scaling up.