Overview
This lecture covers how to solve dilution problems in chemistry, focusing on changing solution concentrations by adding/removing solvent or mixing solutions, and introduces key equations for these processes.
The Dilution Equation
- Use the equation M₁V₁ = M₂V₂ for dilution calculations, where M = molarity and V = volume (units must match).
- To decrease concentration, add solvent (e.g., water); the concentration decreases proportionally to volume increase.
- To increase concentration, either add more solute or remove solvent (e.g., by evaporation).
Example Problems and Solutions
- Problem 1: Given a 0.8M HCl solution diluted to 0.2M at a final volume of 500 mL, the original volume is 125 mL.
- The amount of water added is the difference in volume: 500 mL - 125 mL = 375 mL.
- Problem 2: A 300 mL KCl solution's concentration increased from 0.25M to 0.75M by evaporation; new volume is 100 mL.
- Water removed is 300 mL - 100 mL = 200 mL.
- Problem 3: Adding 350 mL water to 225 mL of 4.5M NaOH gives a new volume of 575 mL and a new concentration of 1.761M for NaOH.
- Problem 4: Mixing 60 mL of 0.8M NaCl with 80 mL of 0.5M KBr yields a final volume of 140 mL; new NaCl concentration is 0.343M, KBr is 0.286M.
- Problem 5: Mixing 150 mL of 0.6M CaCl₂ with 300 mL of 0.9M CaCl₂ gives a final concentration of 0.8M; use the weighted average formula for mixtures of the same substance.
Equations for Mixing Solutions
- For mixing different solutions of the same substance:
M₁V₁ + M₂V₂ = M₃V₃, where M₃ is the final concentration, and V₃ is total volume.
- For more than two solutions, add more MV terms.
Key Terms & Definitions
- Molarity (M) — the concentration of a solution in moles of solute per liter of solution.
- Dilution — decreasing the concentration of a solution by adding solvent.
- Evaporation — removing solvent (usually water) to increase concentration.
- Weighted Average — an average that takes into account differing quantities of components.
Action Items / Next Steps
- Practice additional dilution and mixing problems.
- Review the use of M₁V₁ = M₂V₂ for single-solute dilutions.
- Memorize the weighted average formula for mixing solutions containing the same solute.