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## Vapor-liquid equilibrium
## Additional recommended knowledge
## VLE data introductionThe concentration of a vapor in contact with its liquid, especially at equilibrium, is often given in terms of vapor pressure, which could be a partial pressure (part of the total gas pressure) if any other gas(es) are present with the vapor. The equilibrium vapor pressure of a liquid is usually very dependent on temperature. At vapor-liquid equilibrium, a liquid with individual components (compounds) in certain concentrations will have an equilibrium vapor in which the concentrations or partial pressures of the vapor components will have certain set values depending on all of the liquid component concentrations and the temperature. This fact is true in reverse also; if a vapor with components at certain concentrations or partial pressures is in vapor-liquid equilibrium with its liquid, then the component concentrations in the liquid will be set dependent on the vapor concentrations, again also depending on the temperature. The equilibrium concentration of each component in the liquid phase is often different from its concentration (or vapor pressure) in the vapor phase, but there is a correlation. Such VLE concentration data is often known or can be determined experimentally for vapor-liquid mixtures with various components. In certain cases such VLE data can be determined or approximated with the help of certain theories such as Raoult's Law, Dalton's Law, and/or Henry's Law. Such VLE information is useful in designing columns for distillation, especially fractional distillation, which is a particular specialty of chemical engineers. In mixtures containing two or more components where their concentrations are compared in the vapor and liquid phases, concentrations of each component are often expressed as mole fractions. A mole fraction is number of moles of a given component in an amount of mixture in a phase (either vapor or liquid phase) divided by the total number of moles of all components in that amount of mixture in that phase. Binary mixtures are those having two components. Three-component mixtures could be called ternary mixtures. There can be VLE data for mixtures with even more components, but such data becomes copious and is often hard to show graphically. VLE data is often shown at a certain overall pressure, such as 1 atm or whatever pressure a process of interest is conducted at. When at a certain temperature, the total of partial pressures of all the components becomes equal to the overall pressure of the system such that vapors generated from the liquid displace any air or other gas which maintained the overall pressure, the mixture is said to boil and the corresponding temperature is the boiling point (This assumes excess pressure is relieved by letting out gases to maintain a desired total pressure). A boiling point at an overall pressure of 1 atm is called the ## Thermodynamic description of vapor-liquid equilibriumThe field of thermodynamics describes when vapor-liquid equilibrium is possible, and its properties. Much of the analysis depends on whether the vapor and liquid consist of a single component, of if they are mixtures. ## Pure (single-component) systemsIf the liquid and vapor are pure, in that they consist of only one molecular component and no impurities, then the equilibrium state between the two phases is described by the following equations: - ;
- ; and
where and are the pressures within the liquid and vapor, and are the temperatures within the liquid and vapor, and and are the molar Gibbs free energies (units of energy per amount of substance) within the liquid and vapor, respectively. An equivalent, more common way to express the vapor-liquid equilibrium condition in a pure system is by using the concept of fugacity. Under this view, equilibrium is described by the following equation: where and are the fugacities of the liquid and vapor, respectively, at the system temperature and pressure . ## Multicomponent systemsIn a multicomponent system, where the vapor and liquid consist of more than one type of molecule, describing the equilibrium state is more complicated. For all components in the system, the equilibrium state between the two phases is described by the following equations: - ;
- ; and
where and are the temperature and pressure for each phase, and and are the partial molar Gibbs free energies (units of energy per amount of substance) within the liquid and vapor, respectively, for each phase. The partial molar Gibbs free energy is defined by: where is the (extensive) Gibbs free energy, and is the amount of substance of component . ## Boiling point diagramsBinary mixture VLE data at a certain overall pressure, such as 1 atm, showing mole fraction vapor and liquid concentrations when boiling at various temperatures can be shown as a two-dimensional graph called a _{1} + x_{2} = 1 In multi-component mixtures in general with n components, this becomes: _{1} + x_{2} + ... + x_{n} = 1
The preceding equations are typically applied for each phase (liquid or vapor) individually. In a binary boiling point diagram, temperature ( T ) is graphed vs. x These two lines (or curves) meet where the mixture becomes purely one component, where x If one wants to represent a VLE data for a three-component mixture as a boiling point "diagram", a three-dimensional graph can be used. Two of the dimensions would be used to represent the composition mole fractions, and the third dimension would be the temperature. Using two dimensions, the composition can be represented as an equilateral triangle in which each corner representing one of the pure components. The edges of the triangle represent a mixture of the two components at each end of the edge. Any point inside the triangle represent the composition of a mixture of all three components. The mole fraction of each component would correspond to where a point lies along a line starting at that component's corner and perpendicular to the opposite edge. The bubble point and dew point data would become curved surfaces inside a triangular prism, which connect the three boiling points on the vertical temperature "axes". Each face of this triangular prism would represent a two-dimensional boiling point diagram for the corresponding binary mixture. Due to their three-dimensional complexity, such boiling point diagrams are rarely seen. Alternately, the three-dimensional curved surfaces can be represented on a two-dimensional graph by the use of curved isotherm lines at graduated intervals, similar to iso-altitude lines on a map. Two sets of such isotherm lines are needed on such a two-dimensional graph: one set for the bubble point surface and another set for the dew point surface. ##
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Vapor-liquid_equilibrium". A list of authors is available in Wikipedia. |