Solutions & Colligative Properties

Solutions & Colligative Properties

• A solution is a homogeneous mixture of two or more components.

Classification of Solutions

• Binary solutions contain two components.
• Components refer to substances preparing the solution.
• The solvent is the component present in the largest quantity and determines the solution's physical state.
• The solute is the component present in a lesser quantity.
• Components can be solid, liquid, or gas.

Types of Solutions

• Gaseous solutions consist of gas in gas (e.g., oxygen and nitrogen mixture), liquid in gas (e.g., chloroform in nitrogen), or solid in gas (e.g., camphor in nitrogen).
• Liquid solutions consist of gas in liquid (e.g., oxygen in water), liquid in liquid (e.g., ethanol in water), or solid in liquid (e.g., glucose in water).
• Solid solutions consist of gas in solid (e.g., hydrogen in palladium), liquid in solid (e.g., mercury in sodium amalgam), or solid in solid (e.g., copper in gold).

Strength of Solutions

• Strength of a solution refers to the amount of solute dissolved in a unit of solution or solvent
• Several methods to measure the strength of a solution exist
  • Mass percentage (%w/w) represents the mass of a component in 100g of solution.
  • Volume percentage (%v/v) represents the volume of a component in 100 mL of solution.
  • Mass by volume percentage (%w/v) represents the mass of solute in grams per 100 mL of solution.
  • Parts per million (ppm) represents the number of parts of a component per million parts of the solution.
  • Mole fraction (x) represents the moles of a solute in one mole of solution.
    • For a binary mixture, the mole fraction of component A is XA= na / (na + nb)
  • Molarity (M) represents moles of solute per liter of solution, with units of mol/L, 'M', or 'Molar."
    • Density of a solution is the mass of the solution per unit volume, d= m / V
  • Molality (m) represents moles of solute per kilogram of solvent, with units of mol/kg or 'molal'
  • Normality (N) represents the number of equivalents of solute per liter of solution.

Important Relationships

• Dilution Law: M1V1 = M2V2 and N1V1 = N2V2
• Normality = z Molarity

Important information

• Mass %, ppm, mole fraction, and molality are temperature independent, whereas molarity and normality are temperature dependent.
• Volume depends on temperature, while mass does not.

Vapour Pressure

• Vapour pressure of a liquid/solution is the pressure exerted by vapours in equilibrium with the liquid/solution at a specific temperature.
• Vapour pressure indicates escaping tendency.

Vapour Pressure of Solutions and Raoult's Law

• Raoult's law: For volatile liquids, the partial vapor pressure of each component is directly proportional to its mole fraction.
  • p1 = p10 x1 and p2 = p20 x2
  • ptotal = p1 + p2 = x1 p10 + x2 p20 = p10 + (p20 - p10) x2
• Raoult's Law for Non-Volatile Solutes: The partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.
  • p1 = p10 x1 and p1 = x1 p10 = ptotal

Ideal and Non-Ideal Solutions

• Ideal solutions obey Raoult's law under all conditions.
  • ΔHMIXING = 0
  • ΔVMIXING = 0
  • Intermolecular forces between A-A and B-B are nearly equal to A-B.
• Non-ideal solutions do not obey Raoult's law.
  • Solutions showing positive deviation from Raoult's Law: A-B force is weaker than A-A & B-B.
    • Vapour pressure is higher than predicted
    • ΔHMIXING > 0
    • ΔVMIXING > 0
  • Solutions showing negative deviations from Raoult's law: Solvent-Solute (A-B) type of force is stronger than the other two.
    • Vapour pressure is lower than predicted
    • ΔHMIXING < 0
    • ΔVMIXING < 0

Azeotropes

• Azeotropes are binary mixtures with the same composition in liquid and vapour phase, boiling at a constant temperature.
  • Solutions with large positive deviations from Raoult's law form a minimum boiling azeotrope.
  • Solutions with large negative deviations from Raoult's law form a maximum boiling azeotrope.

Solubility of a Solid in Liquid

• Solubility is the maximum dissolvable amount of a substance in a specified amount of solvent.
  • Like dissolves like.
    • NaCl and sugar dissolve in water, naphthalene and anthracene do not.
    • Naphthalene and anthracene dissolve in benzene, but sodium chloride and sugar do not.
• In a nearly saturated solution
  • If (ΔHsol > 0), solubility increases with rising temperature. Also, the solubility decreases with rising temperature if (ΔHsol < 0).
• Pressure: Pressure does not have a significant effect on solids and liquids.

Henry's Law

• At constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas
  • p = KHx, where KH is the Henry's law constant
  • Higher KH, means lower gas solubility in the liquid.
  • KH values increase with temperature, indicating gas solubility decreases.

Applications of Henry's Law

• Production of carbonated beverages
• Deep sea diving
• Climbers or people at high altitudes

Raoult’s Law

• Raoult's law becomes a special case of Henry's law where KH equals p10

Colligative Properties

• Colligative properties depend on the number of solute particles relative to the total particles in a solution
  • Relative Lowering of Vapour Pressure
  • Elevation in Boiling Point
  • Depression in Freezing Point
  • Osmotic Pressure

Relative Lowering of Vapour Pressure

• Adding a non-volatile solute to a solvent lowers the vapour pressure
  • Δp1= ptotal0 - p1 = (w2 M1) / (M2 w1)

Elevation in Boiling Point

• Boiling point increases when a non-volatile solute is added.
• Increase in boiling point is known as the elevation of boiling point
  • ΔTb = Tb - T0b
  • ΔTb = Kb m, where Kb is the boiling point elevation constant

Depression in Freezing Point

• Freezing point decreases when a non-volatile solute is added.
• Decrease in freezing point is known as depression in freezing point
  • ΔTf = Tf0− Tf
  • ΔTf = Kf m, where Kf is the freezing point depression constant

Osmosis

• Osmosis is the phenomenon where solvent particles pass through a semi-permeable membrane from the solvent side to the solution side
• Semipermeable membrane: Allows small molecules to pass through but blocks larger solute molecules.
  • Osmotic pressure is the excess pressure required to halt solvent molecules when crossing a semipermeable membrane into the a solution
  • π = CRT, where π is osmotic pressure
    • Solutions with the same osmotic pressure are isotonic. Lower concentration solutions are "Hypotonic" while higher concentration solutions are “Hypertonic”.

Abnormal Molar Masses

• Show different values than theoretically determined
  • solute undergoes association
  • the solute undergoes dissociation
  • i = (Normal molar mass) / (Abnormal molar mass)
  • i = (Observed colligative property) / (Calculated colligative property)

Vapour Pressure

• In general increase the temperature of the vapor pressure of a liquid increases
  • ln(p2/p1) = (ΔHvap/R) (1/T1 – 1/T2)

Understand solutions as homogeneous mixtures and their classification based on components and physical states. Explore different types of solutions, including gaseous, liquid, and solid solutions, with examples. Learn about the strength of solutions.