Chemical Equilibrium and Phase Equilibria
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Questions and Answers

What is a characteristic of a physical equilibrium system?

  • All microscopic processes have stopped.
  • There is significant net change in the system's properties.
  • The forces acting on the system are unbalanced.
  • Macroscopic properties remain constant over time. (correct)

Which of the following statements about vapor/liquid equilibria (VLE) is true?

  • VLE can predict how a system behaves under changes. (correct)
  • VLE implies that all entities in a system are static.
  • VLE is irrelevant in industrial processes.
  • VLE occurs only at high pressure systems.

Which concept is essential for understanding the stability of equilibrium systems?

  • Increased molecular mobility.
  • Entropy increase in systems.
  • Phase rule according to Duhem’s theorem. (correct)
  • Complete absence of forces.

Which process heavily relies on phase equilibria for optimization?

<p>Distillation and crystallization. (A)</p> Signup and view all the answers

In the context of equilibrium systems, what does 'no net change' imply?

<p>There is a dynamic balance with balanced forces. (C)</p> Signup and view all the answers

What is the objective of conducting flash calculations in VLE?

<p>To determine the phase compositions at equilibrium. (D)</p> Signup and view all the answers

One of the benefits of understanding phase equilibria is the ability to optimize which aspect of industrial processes?

<p>Material yield and separation efficiency. (B)</p> Signup and view all the answers

Under what condition can Raoult's Law be approximately valid?

<p>When only chemically similar molecular species are present (B)</p> Signup and view all the answers

Which of the following mixtures would Raoult's Law apply to?

<p>n-hexane and n-heptane in a typical experimental setup (C)</p> Signup and view all the answers

What is a necessary condition for the application of Raoult's Law regarding vapor pressure?

<p>All components must have a known vapor pressure (A)</p> Signup and view all the answers

What is a limitation of Raoult's Law concerning temperature?

<p>It cannot be applied if the temperature exceeds the critical temperature of any species (B)</p> Signup and view all the answers

Which of the following combinations would likely violate the applicability of Raoult's Law?

<p>Ortho-xylene and para-xylene at temperatures well over their critical points (A)</p> Signup and view all the answers

What defines the system's equilibrium state with respect to temperature and pressure?

<p>The fixed values of temperature and pressure. (B)</p> Signup and view all the answers

In the context of vapor-liquid equilibrium, which statement is true regarding the rates of molecular transitions?

<p>The rate of evaporation equals the rate of condensation at equilibrium. (A)</p> Signup and view all the answers

Which of the following is NOT a key concept related to vapor-liquid equilibrium?

<p>Dew point (C)</p> Signup and view all the answers

When pressure and temperature are fixed, what happens to the compositions of the liquid and vapor phases?

<p>They are automatically determined. (B)</p> Signup and view all the answers

At equilibrium, what relationship exists between the liquid and vapor phases?

<p>They have the same temperature and pressure. (A)</p> Signup and view all the answers

Which of the following statements about the preparation of liquid mixtures is incorrect?

<p>Liquid mixtures should be prepared at equal compositions. (C)</p> Signup and view all the answers

What role do phase diagrams play in vapor-liquid equilibrium analysis?

<p>They visualize the relationship between temperature and composition. (A)</p> Signup and view all the answers

Which law pertains to the calculation of vapor pressures in liquid mixtures?

<p>Raoult's Law (A)</p> Signup and view all the answers

What is indicated by a stable composition in the liquid and vapor phases at equilibrium?

<p>The composition will remain unchanged over time. (B)</p> Signup and view all the answers

What does the bubble point curve indicate in a P-x-y diagram?

<p>The temperature at which the first bubble of vapor forms. (C)</p> Signup and view all the answers

In a T-x-y diagram, what does the dew point curve represent?

<p>The temperature at which the first drop of liquid condenses. (D)</p> Signup and view all the answers

Tie lines in a P-x-y diagram are used for what purpose?

<p>To connect points on the bubble point and dew point curves. (B)</p> Signup and view all the answers

At what condition is the bubble point of a liquid mixture defined?

<p>At constant pressure as the temperature increases. (A)</p> Signup and view all the answers

Which statement is true regarding the behavior of the vapor phase on a P-x-y diagram?

<p>The vapor phase equilibrates with the liquid phase at specific pressures. (B)</p> Signup and view all the answers

What is the significance of the first vapor bubble forming in relation to the bubble point?

<p>It signifies the onset of vaporization from the liquid phase. (A)</p> Signup and view all the answers

When interpreting a T-x-y diagram, what does the area above the dew point curve represent?

<p>The vapor phase only. (C)</p> Signup and view all the answers

Which characteristic uniquely defines the dew point curve in both P-x-y and T-x-y diagrams?

<p>It indicates the point of liquid condensation. (C)</p> Signup and view all the answers

What happens at the equilibrium point represented by a tie line in phase diagrams?

<p>The chemical potential of phases is equal. (D)</p> Signup and view all the answers

What does Raoult's Law primarily describe in the context of vapor-liquid equilibrium?

<p>The vapor pressure of pure species and their mole fraction in the liquid phase (C)</p> Signup and view all the answers

Which equation of state is not mentioned as suitable for high pressure calculations?

<p>Clausius-Clapeyron (B)</p> Signup and view all the answers

What are fugacity coefficients used for in the context of vapor-liquid equilibrium?

<p>To correct for non-ideal behavior in the vapor phase (B)</p> Signup and view all the answers

In which pressure range does Henry's Law typically apply?

<p>Low pressure (&lt;1 atm) (D)</p> Signup and view all the answers

When introducing activity coefficients in modified Raoult's Law, what is being accounted for?

<p>Non-ideal behavior of mixtures at moderate pressures (A)</p> Signup and view all the answers

What property of gases does Henry's Law highlight in its application?

<p>Their solubility in liquids under varying conditions (B)</p> Signup and view all the answers

At which condition would one primarily utilize modified Raoult's Law?

<p>When dealing with non-ideal mixtures at moderate pressure (A)</p> Signup and view all the answers

What can be inferred about the phase behavior at pressures greater than 10 atm?

<p>Supercritical fluid behavior can occur (D)</p> Signup and view all the answers

What does the concept of fugacity essentially represent in physical chemistry?

<p>A corrected pressure regarding ideal gas deviations (B)</p> Signup and view all the answers

What type of mixtures does Raoult's Law apply to?

<p>Ideal mixtures at moderate pressures (A)</p> Signup and view all the answers

Flashcards

Physical Equilibria

A state where a system's physical properties remain constant over time. It occurs when all forces that could potentially cause a change in the system are perfectly balanced.

Equilibrium System

The state where a system at rest experiences no net change in its macroscopic properties, despite constant microscopic activity. This means the system is in equilibrium.

Equilibrium Criteria

The criteria define the necessary conditions for a system to reach equilibrium, ensuring stability and predictability in its behavior.

Phase Rule

This principle explains how many phases can coexist in a system at equilibrium. It considers the number of components, phases, and degrees of freedom.

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Duhem's Theorem

This rule, also known as Gibbs' Phase Rule, is a powerful tool for understanding and predicting the behavior of multiphase systems at equilibrium.

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Vapor/Liquid Equilibria (VLE)

The study of how vapor and liquid phases interact at equilibrium, crucial for processes like distillation and separation.

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VLE Models

Models used to describe and predict the behavior of vapor/liquid systems at equilibrium, considering factors like pressure and temperature.

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Vapor-Liquid Equilibrium (VLE)

The state where a liquid and its vapor (gas phase) coexist at a specific temperature and pressure, with no net change in their compositions.

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Equilibrium in VLE

The condition where the liquid and vapor phases have the same temperature and pressure, and their compositions remain stable over time.

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T-x-y and P-x-y Diagrams

A graphical representation of the relationship between temperature or pressure and the composition of the liquid and vapor phases in a VLE system.

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Raoult's Law

A simplified model that predicts the vapor pressure of a liquid solution based on the vapor pressures of individual components and their mole fractions in the solution.

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Henry's Law

A model that predicts the partial pressure of a solute in a dilute solution, based on its mole fraction and a constant specific to the solute and solvent.

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Preparing Liquid Mixtures

The process of creating various liquid mixtures with different compositions.

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Equilibrating the System

The process of allowing a liquid mixture to reach equilibrium, so the vapor phase forms above the liquid.

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Measuring Vapor Pressure

The process of measuring the vapor pressure of the system at equilibrium, which provides information about the composition of the vapor phase.

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Analyzing Data and Developing Models

Analyzing the data obtained from the experiment and using it to develop or validate models that describe the behavior of the VLE system.

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T-x-y diagram

A diagram that represents the relationship between temperature, liquid composition, and vapor composition at equilibrium.

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Bubble Point

The point on a T-x-y diagram where the first bubble of vapor forms from the liquid mixture as temperature increases.

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Dew Point

The point on a T-x-y diagram where the first drop of liquid condenses from the vapor mixture as temperature decreases.

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Tie Lines

Horizontal lines on a T-x-y diagram that connect points on the bubble point and dew point curves. They represent the equilibrium between the liquid and vapor phases at a specific temperature.

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Bubble Point (P-x-y diagram)

The pressure at which the first bubble of vapor forms from the liquid mixture as pressure decreases.

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Dew Point (P-x-y diagram)

The pressure at which the first drop of liquid condenses from the vapor mixture as pressure increases.

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Ideal Liquid Solutions

These solutions follow Raoult's law, demonstrating ideal behavior where intermolecular interactions between different components are similar to those between identical molecules. This leads to predictable vapor pressures based on component proportions.

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Non-Ideal Liquid Solutions

These solutions depart from ideal behavior. Interactions between different molecules differ from those between identical molecules. This makes vapor pressure harder to predict.

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Partial Vapor Pressure

The vapor pressure of the pure component of the solution. It applies to the component when it is present alone. Its value is typically determined experimentally.

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Mole Fraction

The ratio of moles of each component to the total moles in the solution.

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P-T Diagram (Phase Diagram)

A graphical representation showing the relationship between pressure and temperature for a substance in different phases (solid, liquid, gas). It helps visualize the conditions under which different phases exist and how transitions occur.

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Supercritical Fluid

A state of matter where a substance exhibits properties of both a liquid and a gas. It exists at high pressure and temperature, above the critical point.

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Modified Raoult's Law

An extension of Raoult's Law that accounts for non-ideal behavior in liquid mixtures. Activity coefficients are introduced to account for deviations from ideality.

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Equations of State (EOS)

Equations of State (EOS) are used to model the behavior of fluids under different conditions. They relate pressure, temperature, and volume to determine the state of a substance.

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Advanced EOS (Peng-Robinson & Soave-Redlich-Kwong)

Advanced equations of state used to model VLE in systems with high pressure. These models account for non-ideal behavior in both the vapor and liquid phases.

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Fugacity

A measure of the tendency of a substance to escape from a liquid phase into a vapor phase. It is a corrected pressure that accounts for deviations from ideal gas behavior.

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Fugacity Coefficients

Coefficients used in VLE models to account for non-ideal behavior in the vapor phase. They adjust for deviations from ideal gas behavior, specifically for fugacity.

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Study Notes

Chemical Engineering Thermodynamics | Physical Equilibria

  •  The ability to develop solutions to equilibrium problems encompassing vapor/liquid phases is key.

Content

  • Introduction to equilibrium systems
  • Equilibrium criteria and stability
  • The phase rule - Duhem's theorem
  • Introduction to vapor/liquid equilibria (VLE)
  • VLE behavior and models
  • VLE for low to moderate pressure systems
  • VLE for high pressure systems
  • Flash calculations
  • The Gamma/Phi formulation of VLE

1. Introduction to equilibrium systems

  • Physical equilibria: A state where a system's physical properties remain constant over time.

  • Occurs when all forces causing change are perfectly balanced.

  • The system is at rest.

  • No net change in macroscopic properties.

  • Properties like temperature, pressure, and volume stay constant.

  • Predict System Behavior: Predicting how a system behaves under various conditions.

  • Design Processes: Many industrial processes (distillation, crystallization) rely on phase equilibria to separate mixtures.

  • Optimize Efficiency: Optimize the efficiency of these processes.

1. Introduction to equilibrium systems: Criteria & Stability

  • Phase Equilibria: Involves systems with multiple phases (solid, liquid, gas) in contact. At equilibrium, phase transition rates are equal in both directions; no net change in phase amounts.
  • Thermal Equilibrium: Two systems have the same temperature, with no net heat transfer between them.
  • Mechanical Equilibrium: Systems are either at rest or move at constant velocity with no net force acting on them.

1. Introduction to equilibrium systems: Equilibrium Criteria & Stability

  • Equilibrium Criteria: Conditions for a system to be in equilibrium (e.g., uniform temperature, pressure, chemical potential).
  • Stability: A system's ability to return to its equilibrium state after a small disturbance.
    • Stable: Returns to equilibrium after a small disturbance.
    • Unstable: Moves away from equilibrium after a small disturbance.
    • Metastable: Stable to small disturbances, unstable to large disturbances.
    • Minimum in potential function corresponds to stable equilibrium.

3. The phase rule - Duhem's theorem

  • Phase rule (J. Willard Gibbs)
    • For a multiphase system at equilibrium, the number of independent variables that must be arbitrarily fixed to determine its intensive state is called the number of degrees of freedom.
    • Applicable to non-reacting systems.
    • Formula: F = 2 - π + N
      • F = number of degrees of freedom
      • π = number of phases
      • N = number of chemical species/components

3. The phase rule - Duhem's theorem/rule

  • Duhem's theorem (Pierre Duhem): In a closed system at equilibrium, the number of independent intensive variables is reduced by one (F' = F - 1).
  • In a system with fixed number of components and phases, temperature and pressure are fixed, composition is automatically determined.
  • The phase rule gives a general framework for determining degrees of freedom. Duhem's rule refines it by accounting for intensive variable interdependence in a closed system.

4. Introduction to vapor/liquid Equilibria (VLE)

  • Equilibrium condition where a liquid and its vapor are in equilibrium at a given temperature and pressure.
  • Vaporization and condensation rates are equal.
  • Key Concepts of VLE: Liquid and vapor phases have the same T and P, composition is stable over time.
  • Phase Diagrams and Models: T-x-y and P-x-y diagrams (temperature-composition, pressure-composition), Raoult's Law, Henry's Law.

5. VLE Behaviour & Models: Data Representation

  • Data and models for representing vapor-liquid equilibrium (VLE) behavior. Includes relevant charts and graphs (e.g., T-xy and P-xy).

5. VLE Behaviour & Models

  • Raoult's Law (ideal mixtures): Describes the relationship between the vapor pressure of each component and its mole fraction in the liquid phase, useful for moderate pressures.
  • Modified Raoult's Law (non-ideal mixtures): accounts for deviations from ideal behavior using activity coefficients.
  • Henry's Law (dilute solutions): relationship between the solubility of a gas in a liquid and the partial pressure of the gas over the liquid.

5. VLE from K-value correlations

  • K-value: A measure of the tendency of a species to partition between liquid and vapor phases; a measure of a species' 'lightness.'
  • K > 1: Species is preferentially in the vapor phase
  • K < 1: Species is preferentially in the liquid phase

Flash Calculation

  • A thermodynamic process to determine the equilibrium state of a mixture when it's partially vaporized at a specific temperature (T) and pressure (P).
  • Phase Equilibrium: Describes the thermodynamic equilibrium reached in the drum.
  • Single-Stage Separation:  A flash drum separates a pressurized liquid feed, producing vapor and separated liquid product streams. A pressure drop induces vaporization.

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Description

This quiz covers the fundamentals of chemical equilibrium systems, focusing on vapor/liquid equilibria (VLE) and their implications in industrial processes. Test your understanding of key concepts such as stability, optimization, and phase equilibria calculations.

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