Equilíbrio de Fases na Termodinâmica

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UFMG — ESCOLA DE ENGENHARIA | DEPARTAMENTO DE ENGENHARIA QUÍMICA
Estudo Dirigido: O Problema do Equilíbrio de Fases
Baseado no livro: Molecular Thermodynamics of Fluid-Phase Equilibria (Prausnitz et al., 1986)
1. O que ocorre ao colocarmos duas ou mais fases em contato?
When two phases are brought into contact, they are generally not in equilibrium and tend to exchange their
constituents. Matter and energy are transferred across the phase boundaries until the composition of each phase reaches
a constant value, stopping further net transport. 
2. Quando (em que condições) podemos afirmar que as fases estão em equilíbrio?
Phases are in a state of equilibrium when the composition of each phase attains a constant value over time and all
microscopic driving forces or tendencies for further change have completely ceased. 
3. O que a Termodinâmica procura estabelecer ao estudar o equilíbrio entre as fases?
Phase-equilibrium thermodynamics seeks to establish quantitative mathematical relations among the primary state
properties—specifically temperature, pressure, and compositions of all phases—that ultimately prevail once the system
achieves an equilibrium state. 
4. Cite exemplos de operações industriais de processos de separação cujo princípio se
baseia em equilíbrio de fases.
Essential unit operations in the chemical industry based on phase equilibria include: 
Distillation
Liquid-liquid extraction
Gas absorption
Adsorption
Leaching
5. O que permite a estes processos a separação ou purificação de misturas ou soluções?
Separation is enabled because the equilibrium compositions of two contacting phases are often very different from one
another. This difference in equilibrium distribution coefficients causes components to concentrate preferentially in one
phase over the other. 
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6. Descreva a essência do problema de equilíbrio de fases que a Termodinâmica procura
resolver.
The core objective is to relate quantitatively the variables describing two or more homogeneous phases free to
interchange energy and matter. Given a subset of known properties (such as temperature and phase compositions),
thermodynamics aims to predict the remaining unknown equilibrium properties (such as system pressure or the
composition of the coexisting phase). 
7. Defina: fase homogênea.
A homogeneous phase at equilibrium is defined as any continuous region in space where all intensive properties are
uniform and identical throughout. 
8. Defina: propriedades intensivas.
Intensive properties are physical characteristics of a phase that are independent of the total mass, size, or geometric
shape of the phase, such as temperature, pressure, density, and mole fractions. 
9. O que especifica a Regra das Fases de Gibbs?
The Gibbs Phase Rule specifies the exact number of independent intensive properties ($F$) required to fix
unambiguously the state of equilibrium in a system without chemical reactions: 
F = N - π + 2
where N is the number of chemical components and π is the number of coexisting phases. 
10. Como a Termodinâmica provê uma solução para o problema de equilíbrio?
Thermodynamics provides an abstract mathematical framework demonstrating that at equilibrium, the chemical
potential (μi) of each species i must be equal across all coexisting phases (μi
α = μi
β = ...). 
11. Explique os três passos ou etapas usadas em Termodinâmica para se solucionar
problemas de equilíbrio.
Step I: The real, physical phase-equilibrium problem is translated into an abstract mathematical formulation by
defining useful thermodynamic functions.
Step II: A mathematical solution is derived within the realm of pure thermodynamics (yielding the equality of
chemical potentials).
Step III: The abstract result is translated back into physically meaningful terms, relating chemical potentials to
measurable variables like temperature, pressure, and mole fractions.
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12. Para obter resultados numéricos, que dificuldades costumam ser encontradas e que tipos
de conceitos precisam ser aplicados na Etapa III?
Classical thermodynamics alone is insufficient to yield direct numerical results because it provides limited information
on how abstract chemical potentials relate to real, experimentally accessible variables. To resolve Step III, concepts
from statistical thermodynamics, molecular physics, physical chemistry, and models for intermolecular forces must be
applied. 
13. De que forma as funções auxiliares nos ajudam a resolver problemas de equilíbrio?
Auxiliary functions such as fugacity (f) and activity coefficients (γ) translate the abstract, non-measurable concept of
chemical potential into variables that are much closer to physical perception and easier to relate to real system
properties. 
14. Cite alguns motivos pelos quais é preferível trabalhar com a Equação (1-2-2) em
comparação à Equação (1-2-1), ao analisarmos problemas de equilíbrio de fases.
Equation (1-2-2) (φi yi P = γi xi fi
0) explicitly contains three primary variables of interest (xi, yi, and P) and provides a
convenient, practical frame of reference for experimental chemistry and engineering compared to the abstract equality
of chemical potentials (μi
α = μi
β). 
15. Por que é útil definirmos sistemas ou misturas ideais?
Defining ideal mixtures establishes a convenient reference state where auxiliary parameters simplify significantly (e.g.,
φi = 1 and γi = 1). This simplifies the equilibrium equations and allows real mixture behavior to be evaluated as
structured deviations from ideal benchmarks. 
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