11.4 Liquid-liquid and solid-liquid equilibria

Liquid-liquid and solid-liquid equilibria are crucial concepts in solution thermodynamics. They help us understand how different substances mix and separate, which is key for many industrial processes and everyday phenomena.

These equilibria involve phase diagrams, miscibility gaps, and critical solution temperatures. We'll explore how to determine compositions using the lever rule and tie lines, and dive into solubility curves and colligative properties.

Phase Equilibria Fundamentals

Phase Diagrams and Miscibility Gaps

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• Phase diagrams graphically represent the equilibrium states of a system as a function of temperature, pressure, and composition
  • Provide information about the phases present at different conditions (solid, liquid, gas)
  • Help predict the behavior of mixtures and the conditions at which phase transitions occur
• Miscibility gaps represent regions on a phase diagram where two liquid phases coexist in equilibrium
  • Occur when the components of a mixture have limited solubility in each other
  • The mixture separates into two distinct liquid layers with different compositions (oil and water)

Critical Solution Temperature and Eutectic Points

• Critical solution temperature (CST) is the temperature above or below which a mixture becomes completely miscible
  • Upper critical solution temperature (UCST): the mixture is miscible above this temperature and separates into two phases below it (nitrobenzene and hexane)
  • Lower critical solution temperature (LCST): the mixture is miscible below this temperature and separates into two phases above it (triethylamine and water)
• Eutectic points represent the lowest temperature and composition at which a mixture of solid phases can coexist in equilibrium with a liquid phase
  • At the eutectic point, the solid phases melt simultaneously, forming a liquid with the eutectic composition
  • Eutectic mixtures have a lower melting point than the individual components (lead-tin solder)

Composition Determination

Lever Rule and Tie Lines

• The lever rule is used to determine the relative amounts of phases present in a two-phase region of a phase diagram
  • The ratio of the distances from a point in the two-phase region to the phase boundaries is inversely proportional to the ratio of the amounts of each phase present
  • Allows for the calculation of the mass fractions or mole fractions of each phase at equilibrium
• Tie lines connect the compositions of coexisting phases in a two-phase region
  • Represent the equilibrium compositions of the phases at a given temperature and pressure
  • The endpoints of a tie line lie on the phase boundaries and indicate the compositions of the individual phases (liquid and vapor in a vapor-liquid equilibrium)

Solubility Curves

• Solubility curves represent the maximum amount of a solute that can dissolve in a solvent at a given temperature
  • Show the temperature dependence of solubility for a particular solute-solvent system
  • The area below the solubility curve represents the conditions under which the solution is unsaturated, while the area above the curve represents supersaturation (sugar in water)
• The shape of the solubility curve depends on the nature of the solute and solvent interactions
  • Some solutes exhibit increasing solubility with temperature (most salts in water), while others show decreasing solubility (calcium hydroxide in water)
  • Solubility curves help determine the conditions required for crystallization or precipitation of a solute from a solution

Colligative Properties

Freezing Point Depression and Boiling Point Elevation

• Colligative properties are properties of solutions that depend on the concentration of the solute particles, but not on their identity
  • Include freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure
  • These properties arise from the change in the chemical potential of the solvent due to the presence of the solute
• Freezing point depression is the lowering of the freezing point of a solvent when a non-volatile solute is added
  • The magnitude of the depression is proportional to the molal concentration of the solute (salt in water)
  • Freezing point depression is used in applications such as antifreeze in automotive cooling systems and the production of ice cream
• Boiling point elevation is the increase in the boiling point of a solvent when a non-volatile solute is added
  • The magnitude of the elevation is proportional to the molal concentration of the solute (ethylene glycol in water)
  • Boiling point elevation is used in applications such as the production of concentrated solutions and the purification of solvents through distillation