6: Multiple Component Phase Equilibrium
- Page ID
- 453684
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- 6.1: Thermodynamics of Mixing
- When solids, liquids or gases are combined, the thermodynamic quantities of the system experience a change as a result of the mixing. This module will discuss the effect that mixing has on a solution’s Gibbs energy, enthalpy, and entropy, with a specific focus on the mixing of two gases.
- 6.2: Partial Molar Volume
- he partial molar volume of compound A in a mixture of A and B can be defined using the total differential of V.
- 6.3: Chemical Potential
- The chemical potential tells how the Gibbs function will change as the composition of the mixture changes. And since systems tend to seek a minimum aggregate Gibbs function, the chemical potential will point to the direction the system can move in order to reduce the total Gibbs function.
- 6.4: Non-ideality in Gases - Fugacity
- The relationship for chemical potential was derived assuming ideal gas behavior. But for real gases that deviate widely from ideal behavior, the expression has only limited applicability. In order to use the simple expression on real gases, a “fudge” factor is introduced called fugacity. Fugacity is used instead of pressure.
- 6.5: A Mixture is a Combination of Two or More Substances
- Since mixtures are comprised of two or more substances, we often use partial molar quantities, such as the partial molar volume, molality, or mole fractions, to describe their behavior and properties (e.g. composition, \(T\), and \(P\)). Mixtures can consist of multiple gases, multiple liquids, multiple solids, or even liquids and gases mixed together.
- 6.6: The Gibbs-Duhem Equation Relates Chemical Potential and Composition at Equilibrium
- The Gibbs-Duhem equation relates how the chemical potential can change for a given composition while the system maintains equilibrium. So for a binary system, consisting of components A and B (the two most often studied compounds in all of chemistry)
- 6.7: Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears
- Chemical potential tells how energy, such as the Gibbs function, changes as the composition of the mixture changes. As systems seek to minimize Gibbs energy, we can use the chemical potential of a mixture to determine the direction of equilibrium.
- 6.8: Colligative Properties
- Colligative properties are properties of solutions that depend on the number of particles in the solution and not on the nature of the chemical species. More specifically, a colligative property depends on the ratio between the number of particles of the solute and the number of particles of the solvent. This ratio can be measured using any unit of concentration, such as mole fraction, molarity, and normality.
- 6.9: Osmotic Pressure can Determine Molecular Masses
- Osmometry is still of some practical usefulness in polymer science as it is able to measure large molecules up to about 8000 daltons. Many polymers, however, are bigger than that and their mass distribution is usually determined by different means.
- 6.10: Raoult’s Law and Phase Diagrams of Ideal Solutions
- The behavior of the vapor pressure of an ideal solution can be mathematically described by a simple law established by François-Marie Raoult (1830–1901). Raoult’s law states that the partial pressure of each component, i, of an ideal mixture of liquids, Pi, is equal to the vapor pressure of the pure component P∗i multiplied by its mole fraction in the mixture xi.
- 6.11: Fractional Distillation of Ideal Mixtures
- This page explains how the fractional distillation (both in the lab and industrially) of an ideal mixture of liquids relates to their phase diagram.
- 6.12: Most Solutions are Not Ideal
- The Gibbs-Duhem equation relates how the chemical potential can change for a given composition while the system maintains equilibrium. So for a binary system, consisting of components A and B (the two most often studied compounds in all of chemistry)
- 6.13: Phase Diagrams of Non-Ideal Solutions
- Non-ideal solutions follow Raoult’s law for only a small amount of concentrations. The typical behavior of a non-ideal solution with a single volatile component is reported in the PxB plot in Figure 13.2.1.
- 6.14: Fractional Distillation of Non-ideal Mixtures (Azeotropes)
- Remember that a large positive deviation from Raoult's Law produces a vapor pressure curve with a maximum value at some composition other than pure A or B. If a mixture has a high vapor pressure it means that it will have a low boiling point. The molecules are escaping easily and you won't have to heat the mixture much to overcome the intermolecular attractions completely.
- 6.15: Activity
- For non-ideal gases, we introduced in chapter 11 the concept of fugacity as an effective pressure that accounts for non-ideal behavior.