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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?
What is primarily used to establish the relationship between vapor pressures and temperature for pure species in vapor/liquid equilibrium calculations?
In vapor/liquid equilibrium, what condition must be fulfilled for phases at the same temperature and pressure?
In vapor/liquid equilibrium, what condition must be fulfilled for phases at the same temperature and pressure?
Which equation of state is specifically developed for vapor/liquid equilibrium calculations?
Which equation of state is specifically developed for vapor/liquid equilibrium calculations?
Raoult's law is understood to be valid under what conditions?
Raoult's law is understood to be valid under what conditions?
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What is the primary role of thermodynamics in the context of vapor/liquid equilibrium?
What is the primary role of thermodynamics in the context of vapor/liquid equilibrium?
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What is the number of degrees of freedom in a system with N chemical species distributed among π phases?
What is the number of degrees of freedom in a system with N chemical species distributed among π phases?
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Which of the following statements is true regarding the phase rule and Duhem's theorem?
Which of the following statements is true regarding the phase rule and Duhem's theorem?
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What must be specified to fix the intensive state of a system at equilibrium?
What must be specified to fix the intensive state of a system at equilibrium?
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In the context of phase equilibria, which property is considered an extensive property?
In the context of phase equilibria, which property is considered an extensive property?
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Which scenario exemplifies the violation of the assumption of ideality in mixtures?
Which scenario exemplifies the violation of the assumption of ideality in mixtures?
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How many equations can be written connecting the variables needed to characterize a phase equilibrium system?
How many equations can be written connecting the variables needed to characterize a phase equilibrium system?
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What happens to the equilibrium state of a closed system when two independently variable properties are specified?
What happens to the equilibrium state of a closed system when two independently variable properties are specified?
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What occurs at temperatures below the lower critical solution temperature (LCST)?
What occurs at temperatures below the lower critical solution temperature (LCST)?
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What defines the consolute points in a two-phase system?
What defines the consolute points in a two-phase system?
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What is the outcome when LLE binodal curves intersect the freezing curve?
What is the outcome when LLE binodal curves intersect the freezing curve?
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In vapor/liquid/liquid equilibrium (VLLE), how many phases are present?
In vapor/liquid/liquid equilibrium (VLLE), how many phases are present?
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What determines the temperature and composition of the three phases in VLLE at a constant pressure?
What determines the temperature and composition of the three phases in VLLE at a constant pressure?
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What is a potential behavior when both LCST and UCST exist in a system?
What is a potential behavior when both LCST and UCST exist in a system?
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In the context of phase diagrams, what do points C and D represent in VLLE?
In the context of phase diagrams, what do points C and D represent in VLLE?
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What indicates a state where no consolute point exists in a system?
What indicates a state where no consolute point exists in a system?
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What is the significance of temperature Tc in the context of liquid-liquid equilibrium?
What is the significance of temperature Tc in the context of liquid-liquid equilibrium?
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What occurs to the equilibrium phase compositions of a system when the pressure is increased?
What occurs to the equilibrium phase compositions of a system when the pressure is increased?
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What happens to the lines 𝐶𝐺 and 𝐷𝐻 as the pressure increases?
What happens to the lines 𝐶𝐺 and 𝐷𝐻 as the pressure increases?
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At high pressures above the critical-solution temperature, the system exhibits which of the following?
At high pressures above the critical-solution temperature, the system exhibits which of the following?
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What is true regarding the vapor phase equilibrium composition for intermediate pressure ranges?
What is true regarding the vapor phase equilibrium composition for intermediate pressure ranges?
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What is the characteristic shape of the diagram at very high pressures?
What is the characteristic shape of the diagram at very high pressures?
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Which point on the diagrams indicates the presence of an azeotrope?
Which point on the diagrams indicates the presence of an azeotrope?
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What represents the critical-solution temperature in this context?
What represents the critical-solution temperature in this context?
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As line 𝐶𝐷 shortens with increasing pressure, what does it indicate about the states of matter?
As line 𝐶𝐷 shortens with increasing pressure, what does it indicate about the states of matter?
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What happens to the vapor phase at point 𝐹 in the context of the system's pressures?
What happens to the vapor phase at point 𝐹 in the context of the system's pressures?
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What happens to the composition of the species in general as temperature increases?
What happens to the composition of the species in general as temperature increases?
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What does the activity coefficient 𝛾𝑖 represent in the context of liquid phase species?
What does the activity coefficient 𝛾𝑖 represent in the context of liquid phase species?
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When considering the equation $y_i \phi_i P = x_i \gamma_i P_{isat}$, what does $y_i$ represent?
When considering the equation $y_i \phi_i P = x_i \gamma_i P_{isat}$, what does $y_i$ represent?
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What simplification can be made when dealing with the Poynting factor at low to moderate pressures?
What simplification can be made when dealing with the Poynting factor at low to moderate pressures?
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In the Antoine equation, what does the term $\ln P_{isat} = A_i - \frac{B}{T + C_i}$ calculate?
In the Antoine equation, what does the term $\ln P_{isat} = A_i - \frac{B}{T + C_i}$ calculate?
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What does the variable $\phi_i$ represent in the equations discussed?
What does the variable $\phi_i$ represent in the equations discussed?
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What is the primary goal of applying thermodynamics to vapor/liquid equilibrium calculations?
What is the primary goal of applying thermodynamics to vapor/liquid equilibrium calculations?
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Which of the following is true regarding $\phi_i = \frac{\phi_{isat}}{\phi_{iv}}$?
Which of the following is true regarding $\phi_i = \frac{\phi_{isat}}{\phi_{iv}}$?
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What implication does the term $x_i \gamma_i$ have in phase equilibrium calculations?
What implication does the term $x_i \gamma_i$ have in phase equilibrium calculations?
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When calculating the fugacity $f_{il}$ for species i, what factors are considered?
When calculating the fugacity $f_{il}$ for species i, what factors are considered?
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Which physical property does $V(P - P_{isat})$ in the equations primarily relate to?
Which physical property does $V(P - P_{isat})$ in the equations primarily relate to?
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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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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.
