More Phase Equilibrium and Diagrams

Overview of Performance

  • The overall performance was deemed "alright," though possibly lower than the average.

Thermodynamic Equilibrium

  • Discussion of the state of equilibrium concerning temperature, pressure, and chemical potential:

    • Temperature in balance

    • Pressure in balance

    • Chemical potential also balanced, related to components in different phases.

Duhem's Theorem

  • To discuss Duhem's theorem, which can be understood starting from Gibbs Phase Rule for multi-component systems:

    • Gibbs Phase Rule: The rule assists in determining the number of degrees of freedom in phase equilibrium systems by relating independent variables and equations.

    • Formula: 2+C−1−extnumberofequations=extnumberofindependentvariables2 + C - 1 - ext{number of equations} = ext{number of independent variables}

    • Breakdown of terms:

      • 2 refers to temperature and pressure.

      • (C−1)(C - 1) represents the independent compositions of species in each phase, as one composition is dependent due to the relation: the sum of all compositions equals one.

  • Phase equilibria can be described using several conditions for each component, leading to the conclusion that:

    • At equilibrium, only two independent variables are needed (e.g., temperature and pressure, or pressure and composition).

    • Extensive and intensive variables impact the overall system calculations.

VLE Diagrams (Vapor Liquid Equilibrium)

  • VLE diagrams depicted either as intimidating three-dimensional plots or simplified two-dimensional diagrams:

    • Phase Envelope: Represents phases coexisting in equilibrium.

      • Y-axis represents pressure and Z-axis usually indicates vapor and liquid phases.

    • Within the phase envelope, only two parameters (e.g., temperature and pressure) are necessary to determine the composition, aligned with Duhem's theorem.

  • Visualizing VLE:

    • Taking vertical or horizontal slices of a 3D plot can yield 2D P versus XY or T versus XY diagrams.

    • Bubble Line: represents the onset of vapor formation (first bubbles).

    • Dew Line: signifies the last bits of liquid before reaching all vapor states.

  • Practical Example:

    • Example of a PXY Diagram at 120°C:

      • Lower pressures yield vapor phases, while higher pressures yield liquid phases.

      • Can read compositions directly from the diagram by observing the positions on the bubble line and dew line.

  • Calculating Compositions:

    • Using data points on vapor and liquid: e.g., for a 50% N-Heptane, 50% N-Decane mixture under specific pressures.

Tie Lines and Composition Calculation

  • Once within the phase envelope,

    • Tie lines can be drawn to determine vapor and liquid phase compositions. Example:

    • At 135°C, find concentrations of N-Heptane in vapor (0.76) and liquid (0.27).

Analysis of Behavior and Azeotropes

  • Discussion of ideal and non-ideal mixtures, plus azeotropic behavior:

    • Azeotropes: special mixtures exhibiting unique boiling point behaviors at certain compositions, thereby complicating separation.

    • High Boiling Point Azeotrope: e.g., Chloroform and Tetrahydrofuran with boiling points higher than ideal expectations.

    • Low Boiling Point Azeotrope: e.g., Ethanol and Toluene with boiling point lower than those of pure components.

Critical Points and Limits

  • Understanding critical points in phase diagrams, where the critical locus indicates maximum pressure and equal composition for vapor and liquid states.

Liquid-Liquid Equilibrium (LLE)

  • Types of Phase Equilibria:

    • Binodal mixture, UCST, and LCST phenomena-characterize behaviors within phase diagrams.

    • Comprised of phases where upper and lower critical solution temperature lines may meet or be truncated.

Thermodynamic Potentials

  • Introduction of key thermodynamic concepts:

    • Enthalpy, Helmholtz Free Energy, and Gibbs Free Energy.

    • Gibbs Free Energy is crucial for analysis of phase equilibria since it incorporates mechanical and chemical potentials along with temperature dependencies.

Chemical Potential and Fugacity

  • Relationships of chemical potentials are to be expressed to model phase change:

    • G=G(T,P)+extchemicalpotentialsG = G(T, P) + ext{chemical potentials}

  • Fugacity is to be used for simplified equilibration criteria, where:

    • Fugacity of components must match in liquid and vapor phases for equilibrium.

    • Simplified expressions from constants and known equations of state yield critical relationships, including Raoult’s Law for ideal mixtures.

Raoult's Law and Ideal Behavior

  • Definition and conditions of applicability for Raoult's Law:

    • States that the contribution of a component's vapor pressure in a mixture can be expressed as:

    • Pi=xiPi0P_i = x_i P_{i}^0 (where $P_i$ is the partial pressure and $P_{i}^0$ is the saturation pressure).

    • Applicability to low/moderate pressures and chemically similar components for defining phase behavior expected from ideal mixtures.

Next Class Agenda

  • Applications in Excel for constructing phase diagrams

  • Anticipated review of Raoult's Law and precedent material from previous examinations.