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