Thermodynamics: Ideal Gas Mixture Quiz
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Questions and Answers

What is the general guideline for determining the fugacity coefficient in a multicomponent gas mixture?

  • Use the ideal gas law as a basis for calculations.
  • Assume all components behave independently.
  • Apply the general equation along with virial coefficients. (correct)
  • Evaluate only at standard temperature and pressure.

When using the Virial Equation of State for fugacity coefficients, what is the primary variable differentiated with respect to in the case of a gas mixture?

  • Number of moles of a specific gas component (correct)
  • Number of moles of the solvent
  • Number of total moles in the mixture
  • Number of moles of the solute

What is a key assumption made when using the Ideal Solution Model?

  • The volume of the solution changes significantly upon mixing.
  • All solutions are viscous and non-volatile.
  • No interactions occur between solute and solvent. (correct)
  • The enthalpy changes during mixing are significant.

To calculate ln ϕˆi values for pure species, which method is utilized according to the provided content?

<p>Substitution based on compressibility factor data (A)</p> Signup and view all the answers

Which resource is recommended for obtaining virial coefficients for a variety of gases?

<p>Perry's Chemical Engineers' Handbook (D)</p> Signup and view all the answers

What characterizes the behavior of gases in an ideal-gas mixture?

<p>Each gas in the mixture behaves independently. (A)</p> Signup and view all the answers

What is the expression for the partial pressure of species i in an ideal-gas mixture?

<p>The pressure that species i would exert if it alone occupied the molar volume of the mixture. (D)</p> Signup and view all the answers

Why is the ideal-gas mixture model significant in thermodynamics?

<p>It simplifies calculations involving gas mixtures by allowing for independent behavior of each gas. (C)</p> Signup and view all the answers

What happens to the total pressure in an ideal-gas mixture when the partial pressures of each individual gas are summed?

<p>It equals the total pressure of the mixture. (D)</p> Signup and view all the answers

Which of the following is NOT a characteristic of gases in an ideal-gas mixture?

<p>Presence of significant intermolecular forces. (B)</p> Signup and view all the answers

What is the relationship between the partial molar volume and the mixture molar volume in an ideal-gas state?

<p>They are identical at given temperature and pressure. (C)</p> Signup and view all the answers

What role do mole fractions play in determining partial pressures in an ideal-gas mixture?

<p>They are used to determine the individual contributions to total pressure. (B)</p> Signup and view all the answers

What does Gibbs' theorem help engineers optimize?

<p>Design of chemical reactors and separation processes (C)</p> Signup and view all the answers

What is true about the enthalpy change of mixing for ideal gases?

<p>It is zero (B)</p> Signup and view all the answers

How is fugacity best described in relation to real gases?

<p>It often represents a lower value than pressure (D)</p> Signup and view all the answers

What property does the fugacity coefficient represent?

<p>The ratio of fugacity to pressure (B)</p> Signup and view all the answers

What happens to the entropy change of mixing for ideal gases?

<p>It is zero (B)</p> Signup and view all the answers

What does a partial molar property refer to in an ideal-gas-state mixture?

<p>The molar property at its partial pressure in the mixture (B)</p> Signup and view all the answers

Why is fugacity a useful concept in thermodynamics?

<p>It quantifies non-ideal behavior of real gases and mixtures (B)</p> Signup and view all the answers

What characterizes real gases compared to ideal gases?

<p>They show deviations from ideal behavior, especially under high pressure and low temperature (B)</p> Signup and view all the answers

What can be inferred about the behavior of substances with high fugacity coefficients?

<p>They have strong attractive forces with neighboring molecules (A)</p> Signup and view all the answers

What does the fugacity of species i in an ideal-gas-state mixture equal?

<p>Its partial pressure (B)</p> Signup and view all the answers

Which of the following represents the fundamental residual-property relation?

<p>G = H - TS (C)</p> Signup and view all the answers

What is the relationship expressed by the logarithm of the fugacity coefficient of a species in solution?

<p>It is a partial property with respect to GR/RT (B)</p> Signup and view all the answers

The mixture second virial coefficient, B, is primarily a function of which factors?

<p>Temperature and composition (D)</p> Signup and view all the answers

When differentiating with respect to ni at constant T, P, and nj, what does this process relate to?

<p>Determining fugacity of species in solution (A)</p> Signup and view all the answers

Which term is NOT a canonical variable in the context of the fundamental residual-property relation?

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

What does the fugacity coefficient measure in solutions?

<p>The potential of a species to escape the solution (D)</p> Signup and view all the answers

In the equation $G = H - TS$, which term represents free energy?

<p>G (D)</p> Signup and view all the answers

What role does temperature play in the second virial coefficient?

<p>It influences molecular interactions (C)</p> Signup and view all the answers

What does the partial residual Gibbs energy relate to?

<p>Partial pressures of species in the mixture (D)</p> Signup and view all the answers

What condition must be true for pure species in a vapor and liquid phase to be in equilibrium?

<p>They must have the same temperature, pressure, and fugacity. (C)</p> Signup and view all the answers

What does the fugacity coefficient ($ _i$) of an ideal gas equal?

<p>1 (C)</p> Signup and view all the answers

In a mixture of real gases, when are multiple phases considered to be at equilibrium?

<p>When the fugacity of each phase constituent species is the same. (C)</p> Signup and view all the answers

What does $G_iR$ represent in terms of fugacity?

<p>The residual Gibbs energy of a real gas compared to an ideal gas. (B)</p> Signup and view all the answers

What is the purpose of the Poynting factor in calculating $ _{i,sat}$?

<p>To adjust pressure effects on fugacity in a liquid phase. (D)</p> Signup and view all the answers

When can the residual Gibbs energy ($G_iR$) be considered zero?

<p>For ideal gases across all conditions. (A)</p> Signup and view all the answers

What determines the fugacity of a pure liquid phase?

<p>The fugacity coefficient and pressure. (A)</p> Signup and view all the answers

Which of the following is a key application of fugacity concepts?

<p>Designing and optimizing chemical processes. (D)</p> Signup and view all the answers

Which statement is true regarding the fugacity in different phases at equilibrium?

<p>Fugacity must be equal for each phase for equilibrium. (A)</p> Signup and view all the answers

Which variable is NOT directly related to fugacity calculations?

<p>Density of the liquid (D)</p> Signup and view all the answers

Flashcards

Ideal-Gas Mixture Model

A thermodynamic model used to analyze mixtures of ideal gases, where each individual gas acts independently within a shared volume.

Partial Pressure in Ideal Gas Mixture

The pressure a component of an ideal gas mixture would exert if it alone occupied the entire volume of the mixture.

Partial Pressure (more specific)

The pressure a component of an ideal gas mixture would exert if it alone occupied the entire volume of the mixture. It is calculated as the product of the mole fraction of that component and the total pressure of the mixture.

Ideal Gas Behavior

A model that assumes no interactions between molecules in a mixture, allowing for easy calculations of thermodynamic properties.

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Equal Molar Volumes for Ideal Gases

This condition holds for all ideal gases at a given temperature and pressure, where the volume occupied by one mole of the gas is the same, regardless of whether it is in a pure state or a mixture.

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Dalton's Law of Partial Pressures

The sum of the partial pressures of each component gas in an ideal-gas mixture equals the total pressure of the mixture.

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Relationship between Partial Pressure and Mole Fraction

The partial pressures of the components in an ideal-gas mixture are directly proportional to their mole fractions.

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Partial Molar Property

A thermodynamic property of a constituent species in an ideal gas mixture that is equal to the corresponding molar property of the species in the pure ideal gas state at the same temperature but at a pressure equal to its partial pressure in the mixture.

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Enthalpy Change of Mixing for Ideal Gases

The change in enthalpy when mixing ideal gases is zero. This means that the total enthalpy of the mixture is equal to the sum of the enthalpies of the individual components.

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Entropy Change of Mixing for Ideal Gases

The change in entropy when mixing ideal gases is always positive. It is a measure of the increase in disorder or randomness when different gases are mixed.

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Fugacity

A thermodynamic property that quantifies the tendency of a substance to move from one phase or mixture to another.

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Fugacity Coefficient

A measure of how much the fugacity of a real gas deviates from its ideal gas behavior. It is the ratio of fugacity to pressure.

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Fugacity for an Ideal Gas

For an ideal gas, fugacity is equal to the pressure, indicating that the gas behaves ideally.

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Fugacity for Real Gases

For real gases, fugacity is generally lower than pressure, especially at high pressures and low temperatures.

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Partial Pressure in an Ideal Gas Mixture

The partial pressure of a component in an ideal gas mixture.

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Partial Molar Gibbs Free Energy

The partial molar Gibbs free energy of a component in a solution, a measure of the change in Gibbs free energy when one mole of that component is added to the mixture.

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Partial Residual Gibbs Energy

The partial derivative of the residual Gibbs energy with respect to the number of moles of a specific component, keeping temperature, pressure, and other component mole numbers constant.

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Fugacity in Ideal Gas State

The fugacity of a species in an ideal-gas state mixture is equal to its partial pressure.

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Fundamental Residual-Property Relation

The logarithm of the fugacity coefficient of a species in solution is equal to the partial molar Gibbs free energy divided by RT.

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Virial Equation of State

The second virial coefficient describes the interactions between molecules in a mixture, and can be used to calculate the fugacity coefficients.

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Fugacity Deviation

A measure of how much the fugacity of a species in a solution differs from its value in an ideal gas state.

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Pressure Deviation

A measure of how much the total pressure of a mixture differs from the sum of the partial pressures of its components.

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Multicomponent Vapor-Liquid Equilibrium

The process of determining the equilibrium conditions for a multicomponent vapor/liquid system, where both phases are present.

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Vapor-Liquid Equilibrium Constant

The ratio of the mole fraction of a species in the vapor phase to its mole fraction in the liquid phase at equilibrium.

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Fugacity at Equilibrium

At equilibrium, the tendency of a substance to escape from one phase to another is the same in all phases.

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Residual Gibbs Energy (GiR)

The difference between the actual Gibbs energy of a real gas and that of an ideal gas at the same temperature and pressure.

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Fugacity Coefficient (Ï•i)

A measure of the tendency of a species to escape from a solution compared to an ideal gas at the same conditions. It's like a 'correction factor' for real solutions.

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Vapor-Liquid Equilibrium (VLE) for Pure Species

For a pure species, vapor and liquid phases are in equilibrium when their temperature, pressure, and fugacity are all the same.

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Poynting Factor

The fugacity of a pure liquid can be calculated using this factor and represents the effect of pressure on the fugacity of the liquid.

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Fugacity of Species in Solution

The fugacity of a species in a mixture of real gases, or in a solution of liquids, is the partial pressure that the species would exert if it behaved ideally.

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Equilibrium Conditions for Mixtures

This describes the equilibrium state of a mixture where multiple phases coexist. It states that for every species in the mixture, its fugacity is the same in all phases.

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Compressibility Factor (Zi)

A parameter that describes the compressibility of a real gas.

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Fugacity of a Pure Liquid

The fugacity of a pure liquid is calculated using the liquid molar volume (Vil), the saturated liquid pressure (P), and the fugacity coefficient (Ï•i). It tells us the escaping tendency of a species from a liquid.

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Applications of Fugacity

The process of designing and optimizing chemical processes often involves understanding and utilizing the principles of fugacity and equilibrium. For example, it's used to design separation processes like distillation.

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Fugacity coefficient calculation

The fugacity coefficient is determined by integrating the compressibility factor (Z) with respect to pressure from zero pressure to the system pressure, at a constant temperature. The integration is performed using data from compressibility-factor tables or graphs.

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Fugacity coefficient for a gas

The fugacity coefficient is a measure of the deviation of a real gas's behavior from ideal gas behavior. It is a ratio of fugacity to pressure, quantifying how much a real gas's tendency to move from one phase to another differs from the ideal-gas scenario.

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Importance of Fugacity Coefficient

The fugacity coefficient is a crucial parameter in thermodynamics, representing the deviation of a real gas's fugacity from its ideal gas behavior. It is essential for accurate calculation of thermodynamic properties in real systems and has broad applications in various fields, including chemical engineering, process design, and equilibrium calculations.

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Study Notes

Chemical Engineering Thermodynamics (II)

  • Course code: KMJ22003/3
  • Instructor: Dr. Norzilah binti Abdul Halif
  • Course semester: 2024/2025

Content

  • Ideal-Gas Mixture Model
  • Fugacity & Fugacity Coefficient
  • The Fundamental Residual-Property Relation
  • Fugacity Coefficients from the Virial Equation of State
  • Generalized Correlations for the Fugacity Coefficient
  • The Ideal Solution Model
  • Excess Properties

1. Ideal-Gas Mixture Model

  • A mathematical model for evaluating/describing ideal gas mixtures thermodynamically
  • An ideal gas mixture comprises multiple ideal gases occupying the same volume and maintaining uniform temperature and pressure
  • Each gas in the mixture behaves independently
  • Overall mixture properties are determined by considering individual gas properties
  • Ideal gas behavior assumes no intermolecular forces and negligible molecular volume.
  • Objective: To design and analyze processes involving gas mixtures

2. Fugacity, f, & Fugacity Coefficient, Ø

  • A method to quantify how much a substance "wants" to move between phases or mixtures, correcting for non-ideal gas behavior
  • Often thought of as a corrected pressure
  • Key points about fugacity:
    • For ideal gases: fugacity equals pressure
    • For real gases: fugacity is often lower than pressure, especially at high pressures and low temperatures
    • Fugacity coefficient: ratio of fugacity to pressure; quantifies the deviation from ideal behavior
    • At equilibrium, the fugacity of a substance is the same in all phases

3. The Fundamental Residual-Property Relation

  • General relation expressing nG/RT as a function of T, P, and mole numbers
  • Special case of the ideal gas state: nG/RT = 0

4. Fugacity Coefficients from the Virial Equation of State

  • The mixture second virial coefficient, B, is a function of temperature and composition
  • For a binary mixture, B calculations use mixing rules and cross coefficients
  • References to thermodynamics handbooks, online databases, and earlier editions for specific values or calculations

5. Generalized Correlations for the Fugacity Coefficient: Pure Species

  • Fugacity coefficients of pure species using generalized correlations.
  • Equations and tables for determining values based on compressibility factor data (e.g. Lee/Kesler correlations).

5. Generalized Correlations for the Fugacity Coefficient: Gas Mixtures

  • Generalized correlations for calculating fugacity coefficients in gas mixtures.
  • Equations relate fugacity coefficient to mixture composition and other variables (e.g. using Zcij and kij)

6. The Ideal Solution Model

  • Focuses on liquid solutions where solute and solvent mix without enthalpy or volume change.
  • Ideal model properties are related to mole fractions (xáµ¢)
  • Key equations describe properties like partial molar volumes, entropies, and enthalpies in terms of ideal solution properties (e.g. Váµ¢, Sáµ¢, Háµ¢) and mole fractions (xáµ¢).

7. Excess Properties

  • Thermodynamic quantities that show deviation from ideal behavior
  • The difference between actual mixture property and property of a hypothetical ideal solution under same conditions (T, P, composition)
  • Excess properties are key to accurately modelling and understanding the behavior of real mixtures (important for scientific research and practical applications in industry).

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W10 Solution Thermodynamics (II) v2 PDF

Description

Test your knowledge on the principles of thermodynamics concerning ideal gas mixtures. This quiz covers fugacity coefficients, the Virial Equation of State, and key characteristics of gases in mixtures. Challenge yourself with questions related to ideal solutions and gas behavior in thermodynamic contexts.

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