Summary of Molarity, Molality, Volume & Mass Percent, Mole Fraction & Density - Solution Concentration Problems

Summary of Video:

"Molarity, Molality, Volume & Mass Percent, Mole Fraction & Density - Solution Concentration Problems"

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Main Concepts and Definitions:

1. Solution Components:
   • Solute: Substance being dissolved (e.g., Sodium Chloride).
   • Solvent: Substance doing the dissolving (e.g., water).
   • Solution: Solute + Solvent combined.
2. Concentration Units and Formulas:
   • Mass Percent (%)
     Mass % = (mass of solute / mass of solution) × 100
   • Volume Percent (v/v %)
     Volume % = (volume of solute / volume of solution) × 100
   • Mole Fraction (X):
     For substance A in a mixture:
     XA = moles of A / total moles in solution
   • Molarity (M):
     M = moles of solute / liters of solution
     Volume must be in liters.
   • Molality (m):
     m = moles of solute / kilograms of solvent
     Note: Molality uses mass of solvent, not solution.
   • Density (ρ):
     ρ = mass / volume
     Common units: g/mL or g/cm³ (1 mL = 1 cm³).
     Useful conversions:
     • 1 L = 1000 mL
     • 1 kg = 1000 g

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Important Distinctions:

• Molarity vs Molality:
  Molarity depends on volume of entire solution (solute + solvent).
  Molality depends on mass of solvent only.
• Solute vs Solvent in Mixed Solvent Systems:
  If both substances can act as solvents (e.g., Methanol and water), the solute is usually the component in lesser quantity or as specified by the problem.

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Step-by-Step Problem-Solving Methodology:

1. Identify solute and solvent.
2. Use the correct formula based on the concentration unit asked.
3. Convert units as necessary:
   • Grams to moles (using molar mass).
   • Milliliters to liters (for Molarity).
   • Grams to kilograms (for Molality).
4. Calculate total mass or volume of solution if not given (solute + solvent).
5. Use Density to convert between mass and volume if needed.
6. Plug values into formulas and solve.

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Example Problems and Solutions:

1. Mass Percent of NaCl:
   Given 15 g NaCl + 225 g water → total solution = 240 g.
   Mass % NaCl = (15/240) × 100 = 6.25%.
2. Volume Percent of Methanol and Mass Percent of Water:
   Methanol volume = 25 mL, Water volume = 150 mL → solution volume = 175 mL.
   Volume % Methanol = (25/175) × 100 = 14%.
   Use Density to find mass:
     - Methanol mass = 25 mL × 0.792 g/mL = 19.8 g
     - Water mass = 150 mL × 1 g/mL = 150 g
   Total mass = 169.8 g
   Mass % water = (150/169.8) × 100 = 88.3%.
3. Mole Fraction of KCl:
   2 moles KCl + 8 moles water → total moles = 10.
   Mole Fraction KCl = 2/10 = 0.2.
4. Mole Fraction of NaF:
   Convert 25 g NaF to moles:
     - Molar mass NaF ≈ 42 g/mol → 25/42 = 0.595 moles.
   Convert 200 g water to moles:
     - Molar mass H₂O ≈ 18 g/mol → 200/18 = 11.1 moles.
   Mole Fraction NaF = 0.595 / (0.595 + 11.1) ≈ 0.

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