Unit 5: Solutions

Table of Contents

Ideal and Non-ideal Solutions

Ideal Solutions and Raoult's Law

Raoult's Law: For a solution of volatile liquids, the partial vapour pressure (PA) of each component in the solution is equal to the vapour pressure of the pure component (PA°) multiplied by its mole fraction (XA) in the liquid phase.
Formula: PA = XA PA°

The total pressure (PT) above the solution is the sum of the partial pressures (Dalton's Law):
PT = PA + PB = XA PA° + XB PB°

Ideal Solution: A solution that obeys Raoult's Law at all concentrations and temperatures.

Thermodynamic Conditions for an Ideal Solution:

  1. Δ Hmix = 0: No heat is absorbed or evolved when mixing.
  2. Δ Vmix = 0: The total volume of the solution is the sum of the volumes of the components.
  3. Forces: The intermolecular forces between A-B molecules are identical to the A-A and B-B forces.

Example: Benzene and Toluene.

Non-ideal Solutions and Deviations from Raoult's Law

Solutions that do not obey Raoult's Law. Δ Hmix ≠ 0 and Δ Vmix ≠ 0.

1. Positive Deviation from Raoult's Law

2. Negative Deviation from Raoult's Law

Vapour Pressure Curves and Distillation

Vapour Pressure-Composition and Temperature-Composition Curves

These phase diagrams plot the composition of a binary liquid mixture against its vapour pressure or boiling temperature.

1. Vapour Pressure-Composition Curve

  • Plots P vs. X (mole fraction).
  • Contains two lines:
    • Liquid Line: Shows the total pressure of the liquid solution.
    • Vapour Line: Shows the composition of the vapour in equilibrium with the liquid.
  • The region between the lines is the 2-phase (Liquid + Vapour) region.
  • Key: The vapour is always richer in the more volatile component (the one with the higher P°).

2. Temperature-Composition (Boiling Point) Curve

  • Plots T (Boiling Point) vs. X. This graph is an "inversion" of the V-P curve.
  • The liquid line is now below the vapour line.
  • The vapour is always richer in the more volatile component (the one with the lower Tb).

Distillation of Solutions

  • Simple Distillation: The process of boiling a liquid and condensing the vapour.
  • Fractional Distillation: Used to separate ideal solutions. The boiling-condensation cycle is repeated many times in a fractionating column. At each "plate" or cycle, the vapour becomes progressively more enriched in the more volatile component, leading to separation.

Azeotropes

Definition: A binary liquid mixture (non-ideal) that has a specific composition at which it boils at a constant temperature, and the vapour produced has the same composition as the liquid.

Azeotropes (or "constant-boiling mixtures") cannot be separated by fractional distillation.

  1. Minimum-Boiling Azeotrope:
    • Formed by solutions showing large positive deviation.
    • The boiling point of the azeotrope is lower than either pure component.
    • Example: 95.6% Ethanol + 4.4% Water (boils at 78.1°C).
  2. Maximum-Boiling Azeotrope:
    • Formed by solutions showing large negative deviation.
    • The boiling point of the azeotrope is higher than either pure component.
    • Example: 68% Nitric Acid + 32% Water (boils at 120.5°C).

Partial and Complete Immiscibility

Partial Miscibility of Liquids

This describes two liquids that only dissolve in each other to a limited extent (e.g., phenol and water). They form two conjugate solutions (e.g., a layer of "phenol-in-water" and a layer of "water-in-phenol").

Critical Solution Temperature (CST)

Definition: The specific temperature at which two partially miscible liquids become fully miscible (soluble in all proportions).
  • Upper CST (Tc): The liquids are miscible above this temperature. (e.g., Phenol-Water system, Tc = 65.8° C). Below Tc, they separate into two layers.
  • Lower CST: The liquids are miscible below this temperature. (e.g., Triethylamine-Water system).
  • Some systems have both (e.g., Nicotine-Water).

Effect of Impurity on Partial Miscibility

Rule: An impurity will (raise/lower) the CST depending on its solubility.

  • If the impurity is soluble in only one of the two liquids (e.g., NaCl in water), it raises the Upper CST (or lowers the Lower CST), making the liquids less miscible.
  • If the impurity is soluble in both liquids (e.g., soap), it lowers the Upper CST (or raises the Lower CST), making the liquids more miscible.

Immiscibility of Liquids and Steam Distillation

Immiscible liquids (e.g., CCl4 and water) do not mix at all.

Principle of Steam Distillation

This technique is used to purify organic compounds that are:

  1. Immiscible with water.
  2. Have a high boiling point (and may decompose if heated to it).
  3. Have an appreciable vapour pressure near 100°C.

Principle: An immiscible mixture boils when the sum of the partial vapour pressures equals the atmospheric pressure.

Formula: Patm = PA° + PWater°

Key Consequence: Since the vapour pressure of water (PWater°) contributes to the total, Patm is reached at a temperature below 100°C (the boiling point of water). This allows the high-boiling organic compound to co-distill with steam at a low, safe temperature, preventing its decomposition.

Nernst Distribution Law

The Law (or Partition Law)

Definition: At a constant temperature, when a solute distributes itself between two immiscible solvents (Solvent 1 and Solvent 2) at equilibrium, the ratio of the solute's concentrations in the two solvents is a constant.

This assumes the solute has the same molecular form in both solvents.

Formula: KD = (C1) / (C2)
Where:
  • KD = Distribution Coefficient or Partition Coefficient.
  • C1 = Equilibrium concentration of solute in Solvent 1.
  • C2 = Equilibrium concentration of solute in Solvent 2.
Modification for Association/Dissociation:
  • If the solute associates (e.g., dimerizes) in Solvent 2 (e.g., benzoic acid in benzene), the law becomes KD = (C1) / (√(C2)).
  • If the solute dissociates in Solvent 2 (e.g., HCl in water), the law becomes KD = (C1) / (C2(1-α)), where α is the degree of dissociation.

Applications of Distribution Law

The main application is Solvent Extraction.

  • Solvent Extraction: A technique to separate a solute from one solvent by shaking it with another, immiscible solvent in which it is more soluble.
  • Example: Extracting iodine (I2) from an aqueous solution (where it's slightly soluble) into CCl4 (where it's very soluble, KD ≈ 85).
  • Principle of Efficiency: Extraction is more efficient if a given volume of extracting solvent is used in several small portions (e.g., 4 portions of 25 mL) rather than all at once in a single portion (e.g., 1 portion of 100 mL).