Chemical Engineering Thermodynamics Module
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Questions and Answers

What is primarily used to establish the relationship between vapor pressures and temperature for pure species in vapor/liquid equilibrium calculations?

  • Raoult's law
  • Vapor pressure constants
  • Cubic equations of state (correct)
  • Ideal-gas model

In vapor/liquid equilibrium, what condition must be fulfilled for phases at the same temperature and pressure?

  • The chemical potentials must be equal.
  • The fugacity of each species must be the same in all phases. (correct)
  • The enthalpy changes for both phases must be equivalent.
  • The density of liquid must equal that of vapor.

Which equation of state is specifically developed for vapor/liquid equilibrium calculations?

  • Boyle's law
  • Carnahan-Starling equation
  • Soave/Redlich/Kwong equation (correct)
  • Clausius-Clapeyron equation

Raoult's law is understood to be valid under what conditions?

<p>In a rational limit. (C)</p> Signup and view all the answers

What is the primary role of thermodynamics in the context of vapor/liquid equilibrium?

<p>It provides the models to interpret molecular behavior. (D)</p> Signup and view all the answers

What is the number of degrees of freedom in a system with N chemical species distributed among π phases?

<p>2 + (N - 1)π (D)</p> Signup and view all the answers

Which of the following statements is true regarding the phase rule and Duhem's theorem?

<p>Duhem's theorem applies to closed systems only. (C)</p> Signup and view all the answers

What must be specified to fix the intensive state of a system at equilibrium?

<p>A limited number of independent variables (A)</p> Signup and view all the answers

In the context of phase equilibria, which property is considered an extensive property?

<p>Mass of the phases (D)</p> Signup and view all the answers

Which scenario exemplifies the violation of the assumption of ideality in mixtures?

<p>Oil-and-vinegar salad dressing (C)</p> Signup and view all the answers

How many equations can be written connecting the variables needed to characterize a phase equilibrium system?

<p>Two fewer than the number of independent variables (A)</p> Signup and view all the answers

What happens to the equilibrium state of a closed system when two independently variable properties are specified?

<p>Both intensive and extensive properties are completely determined (C)</p> Signup and view all the answers

What occurs at temperatures below the lower critical solution temperature (LCST)?

<p>A single liquid phase is obtained (C)</p> Signup and view all the answers

What defines the consolute points in a two-phase system?

<p>They represent the states where the properties of both phases are identical (D)</p> Signup and view all the answers

What is the outcome when LLE binodal curves intersect the freezing curve?

<p>Only UCST exists (B)</p> Signup and view all the answers

In vapor/liquid/liquid equilibrium (VLLE), how many phases are present?

<p>Two liquid phases and one vapor phase (A)</p> Signup and view all the answers

What determines the temperature and composition of the three phases in VLLE at a constant pressure?

<p>The phase rule (A)</p> Signup and view all the answers

What is a potential behavior when both LCST and UCST exist in a system?

<p>A critical point can be established (C)</p> Signup and view all the answers

In the context of phase diagrams, what do points C and D represent in VLLE?

<p>The two liquid phases (A)</p> Signup and view all the answers

What indicates a state where no consolute point exists in a system?

<p>When binodal curves intersect both the freezing and bubblepoint curves (A)</p> Signup and view all the answers

What is the significance of temperature Tc in the context of liquid-liquid equilibrium?

<p>It signifies the exact temperature at which one phase dissolves into another (C)</p> Signup and view all the answers

What occurs to the equilibrium phase compositions of a system when the pressure is increased?

<p>Equilibrium phase compositions change but the overall diagram shape remains similar. (C)</p> Signup and view all the answers

What happens to the lines 𝐶𝐺 and 𝐷𝐻 as the pressure increases?

<p>They extend until they meet at the liquid/liquid consolute point 𝑀. (A)</p> Signup and view all the answers

At high pressures above the critical-solution temperature, the system exhibits which of the following?

<p>Only one liquid phase. (B)</p> Signup and view all the answers

What is true regarding the vapor phase equilibrium composition for intermediate pressure ranges?

<p>It does not lie between the two liquid phase compositions. (D)</p> Signup and view all the answers

What is the characteristic shape of the diagram at very high pressures?

<p>It exhibits a minimum-boiling azeotrope, resembling a valley. (A)</p> Signup and view all the answers

Which point on the diagrams indicates the presence of an azeotrope?

<p>Point 𝐽 (A)</p> Signup and view all the answers

What represents the critical-solution temperature in this context?

<p>The highest temperature at which two liquids can coexist. (C)</p> Signup and view all the answers

As line 𝐶𝐷 shortens with increasing pressure, what does it indicate about the states of matter?

<p>The liquid phases become indistinguishable. (B)</p> Signup and view all the answers

What happens to the vapor phase at point 𝐹 in the context of the system's pressures?

<p>It is in equilibrium with both liquid phases and does not lie between them. (D)</p> Signup and view all the answers

What happens to the composition of the species in general as temperature increases?

<p>Species become more soluble in each other. (D)</p> Signup and view all the answers

What does the activity coefficient 𝛾𝑖 represent in the context of liquid phase species?

<p>The deviation of the species' behavior from an ideal solution (D)</p> Signup and view all the answers

When considering the equation $y_i \phi_i P = x_i \gamma_i P_{isat}$, what does $y_i$ represent?

<p>Mole fraction of the vapor phase (D)</p> Signup and view all the answers

What simplification can be made when dealing with the Poynting factor at low to moderate pressures?

<p>It can be omitted without significant error (A)</p> Signup and view all the answers

In the Antoine equation, what does the term $\ln P_{isat} = A_i - \frac{B}{T + C_i}$ calculate?

<p>The vapor pressure of pure species i at temperature T (B)</p> Signup and view all the answers

What does the variable $\phi_i$ represent in the equations discussed?

<p>The fugacity coefficient in the vapor phase (D)</p> Signup and view all the answers

What is the primary goal of applying thermodynamics to vapor/liquid equilibrium calculations?

<p>To determine the temperatures, pressures, and compositions in equilibrium (B)</p> Signup and view all the answers

Which of the following is true regarding $\phi_i = \frac{\phi_{isat}}{\phi_{iv}}$?

<p>It illustrates the relationship between fugacity coefficients (C)</p> Signup and view all the answers

What implication does the term $x_i \gamma_i$ have in phase equilibrium calculations?

<p>It represents the contribution of species i to the liquid phase (B)</p> Signup and view all the answers

When calculating the fugacity $f_{il}$ for species i, what factors are considered?

<p>The activity coefficient and the mole fraction in the liquid (B)</p> Signup and view all the answers

Which physical property does $V(P - P_{isat})$ in the equations primarily relate to?

<p>The difference in pressure due to the phase change (C)</p> Signup and view all the answers

Flashcards

Phase Rule

The phase rule determines the number of independent variables (degrees of freedom) in a system at equilibrium.

Degrees of Freedom

The number of intensive variables (like temperature, pressure, and composition) that can be varied independently in a multi-phase system at equilibrium.

Phase Rule for Equilibrium

For a system with N chemical species in π phases, the degrees of freedom depend on the number of species and phases.

Duhem's Theorem

For a closed system, the equilibrium state is determined by any two independently variable properties.

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Intensive Variable

A physical property that does not depend on the size or amount of the system.

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Extensive Variable

A physical property that depends on the size or amount of the system.

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Phase Stability

The tendency of a specific phase to exist in a system under given conditions without transforming into another phase.

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Lower Consolute Temperature (LCST)

The temperature below which two liquid phases are in equilibrium, and above which only one liquid phase exists.

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Upper Consolute Temperature (UCST)

The temperature above which two liquid phases are in equilibrium, and below which only one liquid phase exists.

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Liquid-Liquid Equilibrium (LLE)

The condition where two liquid phases coexist in equilibrium at a given temperature and pressure.

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VLLE

A system containing two liquid phases and one vapor phase at equilibrium; compositions and temperature established at a given pressure.

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Consolute Points

The limiting temperatures (LCST and UCST) where the two liquid phases become identical.

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Binary System

A system containing two components.

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VLE Bubble Point Curve

The curve marking the boundaries of single liquid phase and starting of the vapor phase.

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Freezing Curve

The curve on a phase diagram that shows the temperatures at which a substance changes from a liquid to a solid.

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Constant Pressure Txy Diagram

A diagram showing the equilibrium between vapor and liquid phases at a specific pressure.

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Equilibrium Phase Compositions

Composition of the liquid and vapor phases that are in equilibrium, dependent on temperature and pressure.

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Solubility (and Temperature)

Two substances dissolving better in each other at higher temperatures.

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Three-Phase Equilibrium

Describes the conditions where vapor, liquid 1, and liquid 2 are present together in equilibrium.

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Critical Solution Temperature

The temperature at which two liquids become completely miscible(can't be separated).

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Minimum-Boiling Azeotrope

A mixture of liquids whose boiling point is lower than that of the individual components.

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Two-Phase VLE

Vapor-Liquid Equilibrium; a state where vapor and liquid phases coexist in equilibrium.

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Consolute Point (Liquid-Liquid)

The point on a T-x diagram where two liquid phases become miscible and are no longer distinct phases.

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Vapor composition

The composition of the vapor in equilibrium with the liquids

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Activity Coefficient (Liquid Phase)

A measure of the deviation of a species' behavior in a liquid mixture from ideal behavior. Represents how much the activity of a species differs from its mole fraction.

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Fugacity Coefficient

Represents the deviation of a species' fugacity (a measure of escaping tendency) from its partial pressure. This measure applies to vapor phase.

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Poynting Factor

A correction factor that accounts for the effect of pressure on the fugacity of a liquid species.

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Equation 4.0

This equation establishes a relationship between the vapor-phase and liquid-phase compositions, fugacity coefficients, activity coefficients, and vapor pressure of a component. It's the core of our understanding of VLE calculations.

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Antoine Equation

Describes the relationship between the vapor pressure of a pure component and its temperature.

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Gamma/Phi Formulation

A method to represent the vapor-liquid equilibrium using activity coefficients (gamma) and fugacity coefficients (phi). Different variations exist based on how these coefficients are calculated.

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Vapor-Liquid Equilibrium (VLE)

The state where the vapor phase and liquid phase of a mixture are in equilibrium. The composition and pressure of the phases stay constant.

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Intensive Property

A property that does not depend on the size or amount of the system, like temperature or pressure.

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Extensive Property

A property that depends on the size or amount of the system, like volume or mass.

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Study Notes

Module Introduction

  • This module covers phase equilibria of solution thermodynamics, including gamma/phi formulation, VLE from Cubic EOS, equilibrium and stability, liquid/liquid equilibrium, and vapor/liquid/liquid equilibrium.
  • Discussions are largely based on "Introduction to Chemical Engineering Thermodynamics" by J.M. Smith, H. Van Ness, et.al.
  • Additional resources, including YouTube videos, are available in the Google Classroom.
  • Exams are available in both online and hard copy formats, assessments are conducted after each module.

Intended Learning Outcomes

  • Students will apply physical chemistry concepts and calculus techniques to derive thermodynamic property relations, calculate changes in thermodynamic properties of mixtures, and derive phase and chemical equilibrium relations.
  • Students will be able to identify and solve vapor-liquid equilibrium problems for ideal and non-ideal solutions.
  • They will apply vapor-liquid equilibrium relations based on cubic equations of state and other EOS models.
  • Students will derive solution properties from vapor-liquid equilibrium experimental data.
  • Interpret phase equilibrium diagrams.
  • Solve for the equilibrium conversion of single reaction systems and analyze the effect of operating variables on reactions.
  • Utilize spreadsheets and numerical software for vapor-liquid equilibrium calculations, phase equilibrium diagram construction, and multi-reaction equilibrium conversion calculations.
  • This learning aligns with CMO No. 19 s.2017 for Chemical Engineering Courses.

Review of Phase Rule

  • The intensive state of a PVT system is characterized by fixed temperature, pressure, and phase compositions.
  • The phase rule determines the number of independent variables (degrees of freedom) needed to fix the intensive state at equilibrium.
  • For a system with N chemical species distributed among π phases, the phase rule variables are temperature (T), pressure (P), and (N-1)π mole fractions.
  • Duhem's Theorem applies to closed systems, stating that the intensive and extensive states of a system are completely determined by two independently variable properties at equilibrium.

Equilibrium and Phase Stability

  • Homogenous mixtures are assumed initially, though in reality, mixtures like oil-and-vinegar can split into phases to reduce Gibbs free energy.
  • The Gibbs free energy is minimized at equilibrium.
  • A closed system with uniform temperature and pressure, but the compositions are not constant; the system transitions from nonequilibrium to equilibrium states through irreversible changes while moving towards equilibrium with the surroundings.
  • The equilibrium state of a closed system at constant temperature and pressure occurs when the Gibbs energy reaches its minimum value.
  • The entropy change of the surroundings is given by dSsurr = dQsurr/Tsurr, where dQsurr is the heat transfer to the surroundings.

Additional Concepts (from subsequent pages)

  • Criteria for phase stability: For a single-phase binary mixture at constant T and P, the second derivative of the Gibbs energy with respect to composition must be positive. This ensures the mix is stable.
  • Liquid-Liquid Equilibrium (LLE): The relationship between temperature and composition is depicted with binodal curves. Temperature values between lower and upper critical solution temperature values allow for a two-phase LLE.
  • Vapor-Liquid-Liquid Equilibrium (VLLE): A condition where the system contains vapor as well as two distinct liquid phases. This occurs when binodal curves intersect VLE bubblepoint curves.
  • The Gamma/Phi Formulation: Calculating vapor-liquid equilibrium involves considering fugacity (f) and activity coefficients (y), along with equations of state for liquid and vapor phases.
  • Cubic Equations of States (VLE Calculations): The Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) equations are used for vapor-liquid equilibrium (VLE) calculations and are presented in the reference; this section provides parameters and equations useful for these calculations using mole fractions (x or y) at equilibrium conditions.
  • Mixture properties: The parameters used in the equations are functions of composition and are presented in the text.

Exercises

  • Several exercises are provided, requiring calculations involving vapor pressures, equilibrium mole fractions, and other concepts covered in the module. Specific numerical data is provided for calculations.

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CHE 408 SEMI-FINALS - Phase Equilibria PDF

Description

This module introduces phase equilibria in solution thermodynamics, focusing on essential concepts like VLE and stability. Based on 'Introduction to Chemical Engineering Thermodynamics' by J.M. Smith, students will learn to derive thermodynamic properties and solve equilibrium problems for various solutions. Additional resources and assessments are provided throughout.

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