Understanding how to solve word problems involving dilutions and concentrations is essential for students studying chemistry, pharmacy, and related fields. These problems often involve calculating the amount of a substance needed to prepare a solution of a desired concentration or determining the concentration of a solution after dilution.

Key Concepts in Dilutions and Concentrations

Before tackling practice problems, it is important to understand some fundamental concepts:

  • Concentration: The amount of solute in a given volume of solution, often expressed as molarity (M), percentage, or parts per million (ppm).
  • Dilution: The process of reducing the concentration of a solute in a solution, usually by adding solvent.
  • Dilution formula: C₁V₁ = C₂V₂, where C and V represent concentration and volume, respectively.

Sample Word Problem 1: Diluting a Solution

Problem: A scientist has 100 mL of a 2 M solution of sodium chloride (NaCl). How much water should be added to dilute the solution to a concentration of 0.5 M?

Solution: Using the dilution formula C₁V₁ = C₂V₂:

Initial concentration (C₁) = 2 M

Initial volume (V₁) = 100 mL

Final concentration (C₂) = 0.5 M

Final volume (V₂) = ?

Applying the formula:

2 M × 100 mL = 0.5 M × V₂

V₂ = (2 M × 100 mL) / 0.5 M = 400 mL

Since the initial solution was 100 mL, the amount of water to add is:

400 mL - 100 mL = 300 mL

Practice Problem 2: Preparing a Diluted Solution

Problem: How much of a 5 M stock solution of potassium permanganate (KMnO₄) is needed to prepare 250 mL of a 1 M solution?

Solution: Using C₁V₁ = C₂V₂:

Initial concentration (C₁) = 5 M

Final concentration (C₂) = 1 M

Final volume (V₂) = 250 mL

Calculating V₁:

V₁ = (C₂ × V₂) / C₁ = (1 M × 250 mL) / 5 M = 50 mL

Therefore, 50 mL of the 5 M stock solution is needed, and the remaining volume (200 mL) should be made up with water.

Additional Practice Tips

When solving dilution problems:

  • Identify the known quantities: initial concentration and volume, and the desired concentration or volume.
  • Use the dilution formula carefully, ensuring units are consistent.
  • Double-check your calculations to avoid common mistakes like incorrect unit conversions.

Practice with various problems to become comfortable with different scenarios involving dilutions and concentrations. This will improve your problem-solving skills and deepen your understanding of solution chemistry.