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?

Substitution based on compressibility factor data Signup and view all the answers

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

Perry's Chemical Engineers' Handbook Signup and view all the answers

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

Each gas in the mixture behaves independently. Signup and view all the answers

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

The pressure that species i would exert if it alone occupied the molar volume of the mixture. Signup and view all the answers

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

It simplifies calculations involving gas mixtures by allowing for independent behavior of each gas. 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?

It equals the total pressure of the mixture. Signup and view all the answers

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

Presence of significant intermolecular forces. 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?

They are identical at given temperature and pressure. Signup and view all the answers

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

They are used to determine the individual contributions to total pressure. Signup and view all the answers

What does Gibbs' theorem help engineers optimize?

Design of chemical reactors and separation processes Signup and view all the answers

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

It is zero Signup and view all the answers

How is fugacity best described in relation to real gases?

It often represents a lower value than pressure Signup and view all the answers

What property does the fugacity coefficient represent?

The ratio of fugacity to pressure Signup and view all the answers

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

It is zero Signup and view all the answers

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

The molar property at its partial pressure in the mixture Signup and view all the answers

Why is fugacity a useful concept in thermodynamics?

It quantifies non-ideal behavior of real gases and mixtures Signup and view all the answers

What characterizes real gases compared to ideal gases?

They show deviations from ideal behavior, especially under high pressure and low temperature Signup and view all the answers

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

They have strong attractive forces with neighboring molecules Signup and view all the answers

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

Its partial pressure Signup and view all the answers

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

G = H - TS Signup and view all the answers

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

It is a partial property with respect to GR/RT Signup and view all the answers

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

Temperature and composition Signup and view all the answers

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

Determining fugacity of species in solution Signup and view all the answers

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

Density Signup and view all the answers

What does the fugacity coefficient measure in solutions?

The potential of a species to escape the solution Signup and view all the answers

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

G Signup and view all the answers

What role does temperature play in the second virial coefficient?

It influences molecular interactions Signup and view all the answers

What does the partial residual Gibbs energy relate to?

Partial pressures of species in the mixture Signup and view all the answers

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

They must have the same temperature, pressure, and fugacity. Signup and view all the answers

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

1 Signup and view all the answers

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

When the fugacity of each phase constituent species is the same. Signup and view all the answers

What does $G_iR$ represent in terms of fugacity?

The residual Gibbs energy of a real gas compared to an ideal gas. Signup and view all the answers

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

To adjust pressure effects on fugacity in a liquid phase. Signup and view all the answers

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

For ideal gases across all conditions. Signup and view all the answers

What determines the fugacity of a pure liquid phase?

The fugacity coefficient and pressure. Signup and view all the answers

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

Designing and optimizing chemical processes. Signup and view all the answers

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

Fugacity must be equal for each phase for equilibrium. Signup and view all the answers

Which variable is NOT directly related to fugacity calculations?

Density of the liquid Signup and view all the answers

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 (xᵢ)
Key equations describe properties like partial molar volumes, entropies, and enthalpies in terms of ideal solution properties (e.g. Vᵢ, Sᵢ, Hᵢ) and mole fractions (xᵢ).

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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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.