🧤Physical Chemistry I Unit 9 – Mixtures and Solutions

Key Concepts and Definitions

• Mixtures combine two or more substances without chemical bonding or changes to individual components
• Solutions are homogeneous mixtures with solute(s) dissolved in a solvent, forming a single phase
• Solubility measures the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature
  • Factors affecting solubility include temperature, pressure, and the nature of the solute and solvent (polarity, intermolecular forces)
• Concentration quantifies the amount of solute present in a solution, expressed as molarity (moles of solute per liter of solution), molality (moles of solute per kilogram of solvent), or mass percent (mass of solute divided by total mass of solution)
• Intermolecular forces, such as dipole-dipole interactions, hydrogen bonding, and London dispersion forces, play a crucial role in the formation and stability of mixtures and solutions
• Colligative properties depend on the number of solute particles in a solution, not their identity, and include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure
• Phase diagrams represent the equilibrium states of a substance under different conditions of temperature, pressure, and composition, illustrating phase transitions and coexistence regions

Types of Mixtures and Solutions

• Homogeneous mixtures have a uniform composition throughout, with no visible boundaries between components (salt water, air)
• Heterogeneous mixtures have a non-uniform composition, with distinct phases or regions of different compositions (oil and water, sand and gravel)
• Suspensions are heterogeneous mixtures containing large particles that settle over time and can be separated by filtration (muddy water, paint)
• Colloids are heterogeneous mixtures with particles larger than those in solutions but smaller than those in suspensions, exhibiting unique properties like the Tyndall effect (milk, fog, gelatin)
  • Types of colloids include aerosols (liquid droplets or solid particles in gas), foams (gas bubbles in liquid or solid), emulsions (liquid droplets in another liquid), and sols (solid particles in liquid)
• Saturated solutions contain the maximum amount of solute that can dissolve at a given temperature, while unsaturated solutions can dissolve more solute
• Supersaturated solutions contain more solute than the equilibrium solubility allows, and are typically unstable, prone to crystallization upon perturbation (seeding, agitation)

Thermodynamics of Mixing

• Mixing is a spontaneous process driven by an increase in entropy (disorder) as components intermingle
• Gibbs free energy change ($\Delta G_{\text{mix}}$) determines the spontaneity of mixing, with negative values indicating a spontaneous process
  • $\Delta G_{\text{mix}} = \Delta H_{\text{mix}} - T\Delta S_{\text{mix}}$, where $\Delta H_{\text{mix}}$ is the enthalpy of mixing, $T$ is the absolute temperature, and $\Delta S_{\text{mix}}$ is the entropy of mixing
• Ideal solutions have a zero enthalpy of mixing ($\Delta H_{\text{mix}} = 0$) and a positive entropy of mixing ($\Delta S_{\text{mix}} > 0$), resulting in a negative Gibbs free energy change and spontaneous mixing
• Non-ideal solutions deviate from ideal behavior due to intermolecular interactions between components, leading to non-zero enthalpies of mixing and deviations from Raoult's law
• Raoult's law states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by its pure vapor pressure, assuming ideal behavior
• Azeotropes are non-ideal mixtures with a constant boiling point and composition, where the vapor and liquid phases have the same composition at a specific temperature and pressure (ethanol-water azeotrope)

Colligative Properties

• Vapor pressure lowering occurs when a non-volatile solute is added to a solvent, reducing the solvent's vapor pressure in proportion to the solute concentration (Raoult's law)
• Boiling point elevation is the increase in the boiling point of a solution compared to the pure solvent, caused by the reduced vapor pressure of the solvent in the presence of a solute
  • $\Delta T_b = K_b \cdot m$, where $\Delta T_b$ is the boiling point elevation, $K_b$ is the molal boiling point elevation constant (specific to the solvent), and $m$ is the molality of the solution
• Freezing point depression is the decrease in the freezing point of a solution compared to the pure solvent, caused by the solute particles interfering with the formation of the solid phase
  • $\Delta T_f = K_f \cdot m$, where $\Delta T_f$ is the freezing point depression, $K_f$ is the molal freezing point depression constant (specific to the solvent), and $m$ is the molality of the solution
• Osmotic pressure is the pressure that must be applied to a solution to prevent the net flow of solvent molecules across a semipermeable membrane from a region of high solvent concentration (pure solvent) to a region of low solvent concentration (solution)
  • $\Pi = MRT$, where $\Pi$ is the osmotic pressure, $M$ is the molarity of the solution, $R$ is the gas constant, and $T$ is the absolute temperature
• Colligative properties are important in various applications, such as antifreeze agents (ethylene glycol), osmotic drug delivery systems, and desalination processes (reverse osmosis)

Phase Diagrams and Equilibria

• Phase diagrams represent the equilibrium states of a substance as a function of temperature, pressure, and composition
• Triple point is the unique temperature and pressure at which all three phases (solid, liquid, and gas) coexist in equilibrium
• Critical point is the highest temperature and pressure at which the liquid and gas phases can coexist, beyond which the substance exists as a supercritical fluid
• Phase boundaries (solid-liquid, liquid-gas, and solid-gas) represent the conditions at which two phases are in equilibrium
  • Solid-liquid boundary is the melting/freezing curve, liquid-gas boundary is the vaporization/condensation curve, and solid-gas boundary is the sublimation/deposition curve
• Lever rule is used to determine the relative amounts of phases present in a two-phase region of a phase diagram, based on the distances from the overall composition to the phase boundaries
• Eutectic point is the lowest temperature and composition at which a mixture of two or more components can exist as a liquid, characterized by the simultaneous crystallization of the components upon cooling
• Tie lines connect the compositions of coexisting phases in a two-phase region, with the overall composition lying on the tie line

Separation Techniques

• Distillation separates components of a liquid mixture based on differences in their boiling points, by vaporizing the mixture and condensing the vapor at different temperatures (fractional distillation of crude oil)
• Crystallization separates a solid solute from a solution by cooling or evaporation, causing the solute to precipitate as crystals (purification of pharmaceuticals, production of salt)
• Extraction separates components of a mixture based on their relative solubilities in two immiscible liquids, typically an aqueous phase and an organic phase (caffeine extraction from coffee beans using dichloromethane)
• Chromatography separates components of a mixture based on their differential interactions with a stationary phase and a mobile phase, resulting in different migration rates (gas chromatography, high-performance liquid chromatography)
  • Types of chromatography include adsorption (interactions with solid surface), partition (distribution between two liquid phases), ion-exchange (electrostatic interactions with charged resin), and size-exclusion (separation by molecular size)
• Filtration separates solid particles from a liquid or gas by passing the mixture through a porous medium that retains the solids and allows the fluid to pass through (water treatment, air purification)
• Centrifugation separates components of a mixture based on differences in their densities, by applying a centrifugal force to the mixture in a rotating container (separation of blood cells from plasma)
• Electrophoresis separates charged particles in a mixture based on their migration in an electric field, with different particles moving at different rates depending on their charge and size (DNA sequencing, protein analysis)

Applications in Industry and Research

• Pharmaceuticals rely on separation techniques like crystallization and chromatography to purify active ingredients and remove impurities
• Petrochemicals use distillation to separate crude oil into various fractions (gasoline, diesel, kerosene) based on their boiling points
• Environmental monitoring employs chromatography and mass spectrometry to detect and quantify pollutants in air, water, and soil samples
• Food and beverage industry uses extraction, distillation, and filtration to isolate desired components (essential oils, alcohol, sugar) and remove unwanted ones (impurities, microorganisms)
• Materials science utilizes phase diagrams to design alloys with specific properties, such as strength, durability, and corrosion resistance (steel, aluminum alloys)
• Biomedical research employs electrophoresis and chromatography to separate and analyze biomolecules like proteins, nucleic acids, and metabolites
• Chemical synthesis often involves the use of solvents to dissolve reactants, control reaction rates, and facilitate product separation and purification
• Nanotechnology relies on the principles of colloidal science to create and manipulate nanoscale structures with unique properties (drug delivery systems, quantum dots)

Problem-Solving Strategies

• Identify the key components of the mixture or solution and their relevant properties (molecular structure, polarity, solubility, boiling point)
• Determine the type of mixture or solution (homogeneous, heterogeneous, ideal, non-ideal) and the appropriate mathematical relationships (Raoult's law, colligative property equations)
• Use dimensional analysis to convert between different units and ensure consistency in calculations
• Apply the concept of equilibrium to determine the conditions under which phases coexist and interconvert (phase diagrams, solubility curves)
• Consider the thermodynamic factors that drive mixing and separation processes (entropy, enthalpy, Gibbs free energy) and how they can be manipulated (temperature, pressure, composition)
• Break down complex problems into smaller, manageable steps and solve them systematically, checking units and reasonableness of results at each stage
• Utilize graphical methods (phase diagrams, solubility curves, chromatograms) to visualize and interpret data, and to predict the behavior of mixtures and solutions under different conditions
• Consult reference materials (solubility tables, phase diagrams, handbooks) to obtain necessary data and constants for calculations and problem-solving