For a phase transition, the two phases are in equilibrium. Phase equilibrium lecture diffusion chemical equilibrium. Properties of chemical equilibria the equilibrium constant and units reaction quotient and predicting the direction of a reaction revisiting a kinetics problem manipulating equilibrium constants special cases reactions involving h 2 ol reactions involving phase changes equilibrium constants in. Given the equilibrium constant k eq for a reaction, predict whether the reactants or products are predominant. Typically, when we are talking about a triple point it is the solid, liquid, gas triple point. Introduction to chemical equilibrium this lecture is outside the confines of the textbook development of chemical equilibrium and is intended as a sweeping introduction to chemical equilibrium a topic that will engage us for much the rest of the semester. It is a part of a system, uniform through out in chemical composition and physical properties, that is separated a uniform component part of the system that is separated from the other homogeneous parts e. Lectures on mathematical modelling of biological systems. In general practice it is sufficient to consider only solid and liquid phases, thus pressure is assumed to be constant 1 atm.
Drude theory of metals university of california, irvine. Equilibrium statistical physics physics course materials. For onecomponent system, existing in two phases, the chemical potentials of each of these phases is the same at equilibrium. Obviously, the endemic equilibrium exists only if s 0 which means that, as in the previous cases, the basic reproduction ratio r. Phase equilibria, phase diagrams and phase transformations. Phase equilibria the equilibrium phase is always the one with the lowest free energy g h t s the driving force for a phase change is the minimization of free energy equilibrium state with minimum free energy under some specified combination of temperature, pressure, and composition e.
S this means that at the phase transition temperature. By doing this, weve developed this great concept of dynamic equilibrium, that tells us that equilibrium occurs when there are competing processes occurring at the same rates. Notes for chemical equilibrium thermodynamics chemical equilibrium understanding how to work problems for chemical equilibrium is one of the most important concepts in secondsemester chemistry. In the previous lectures, weve been studying phase equilibrium of pure solutions, pure liquids and pure gasses, corresponding to the same material. Phase equilibrium lecture free download as powerpoint presentation. Phase transformation lecture equilibrium, phase diagram. By everywhere, i mean in all phases that are at equilibrium. Chapter 6 phase and phase equilibrium prepared by prof. When a gas and a liquid phase which are not thermodynamically in equilibrium are brought into close contact, transfer of one or more components may occur from the gas phase to the liquid or, vice versa, by the mechanism of molecular diffusion. Lecture description determine the equilibrium conversion of a gas phase reaction with and without the presence of an inert. Mass transfer by molecular diffusion is the basic physical mechanism underlying many important areas of soil science, petroleum.
Oct 03, 2016 lecture on the thermodynamics of phase equilibrium, with an introduction to chemical potential as a thermodynamic parameter. In the alcu system, the stable precipitate is cual2 but because it is di. Lecture 2 masc 504 diffusion and phase equilibria recap. Criterion for phase equilibrium the thermodynamic criterion for phase equilibrium is simple.
Phase rule and equilibrium the phase rule, also known as the gibbs phase rule, relates the number of. State p kpa t k phase 1 2000 475 liquid 2 500 vapor. Use le chateliers principle to explain how a chemical reaction at equilibrium responds when a. The first module deals with phase diagrams charts that tell us how a material will behave given a certain set of variables such as temperature, pressure, and composition. Just as oil and water represent two distinct liquid phases, two regions of a solid with distinctly. They refer to the independent chemical species that comprise the system. Lecture on the thermodynamics of phase equilibrium, with an introduction to chemical potential as a thermodynamic parameter. At equilibrium, the two phases will have the same free energy. Introduction to solid state chemistry lecture notes. This means something from the thermodynamics standpoint. When c l c e, eutectic solidification occurs, and the liquid solidifies like a pure metal.
Examples are tcomposition phase diagrams for binary. Phase diagrams of onecomponent systems are also discussed with a. Feb, 2019 this is first part of phase equilibrium topic see second part of this topic for complete information. Purchase phase equilibrium engineering, volume 3 1st edition. Phase diagrams can equilibrium exist over a range of conditions or whether a system must be bought to a definite pressure, temperature and composition before equilibrium is established. Materials scientists are most familiar with phase diagrams which involve temperature, and t composition as variables. Equilibrium phase diagrams represent the relationships between temperature and the compositions. Learn definitions and basic concepts of phase equilibria and phase diagrams. Phase equilibrium is the study of the equilibrium which exists between or within different states of matter namely solid, liquid and gas. Investigate if the phase equilibrium can be correlated by an eos model by identifying the interaction parameters by regression. The thermodynamics of phase equilibrium laszlo tisza departiment of physics, research laboratory of electronics, massachusetts institute of technology, cambridge, massachusetts thermodynamics is usually subdivided into a theory dealing with equilibrium and into one concerned with irreversible processes. The rst equilibrium is the disease free equilibrium. Onecomponent systems enthalpy and entropy dependence on p and t gibbs free energy dependence on p and t effect of pressure on the equilibrium phase diagram for pure iron 3. N 2o 4g 2no 2g the equilibrium constant with the concentrations of reactants and products expressed in terms of molarity, k c, is.
It consists of atoms of at least two different types where solute atoms. In fact, we will spend much of the rest of the course discussing aspects of this concept. Given a chemical equation, write the law of mass action. Phase diagrams and phase equilibria this course picks up with an overview of basic thermodynamics and kinetics as they pertain to the processing of crystalline materials. Equilibrium is the state that is achieved given sufficient time. A phase diagram is a graphical representation of the values of the thermodynamic variables when equilibrium is established among the phases of a system. Thus, the free energy curve for gp1 zones is located above that for cual2 in fig. This is the temperature and pressure at which three phases are in equilibrium. Phase equilibrium engineering, volume 3 1st edition. Introduction this lecture is concerned with classical stochastic manyparticle systems far away from thermal equilibrium. Phase equilibria phase equilibria phase equilibrium describes the way phases such as solid, liquid andor gas coexist at some temperatures and pressure, but interchange at others. Equilibrium phase diagrams represent the relationships between temperature and the compositions and the quantities of phases at equilibrium. Phase equilibria, phase diagrams and phase transformations second edition thermodynamic principles are central to understanding material behaviour, particularly as the application of these concepts underpins phase equilibrium, transformation and state.
And so if multiple phases are present, mu has to be the same in all the phases. If we have just one phase in equilibrium, or way over in the solid or just gas or just liquid part of the phase diagram. And if it isnt, then the molecules will go into the phase with the lower chemical potential. Introduction to materials science chapter 9, phase diagrams 5 a system is at equilibrium if at constant temperature, pressure and composition the system is stable, not changing with time. K c 2 n o no 2 4 2 gas phase expressions can also be expressed by k p. If f is the number of degrees of freedom, c is the number of components and p is the number of phases, then. Phase is a region where the intermolecular interaction is spatially uniform or in. Please do not blindly follow the presentation files only, refer it just as reference material. A gas phase equilibrium consider a simple gas phase reaction, the conversion of cis. Selected lecture notes and problems from equilibrium statistical physics, taught by gerhard muller at the university of rhode island.
A mixture of oil and water would also be a twophase system. So the main point here is that at equilibrium, mu is identical everywhere. Every point of this diagram is an equilibrium state. But the time to achieve equilibrium may be very long. I hope you will see just how easily equilibrium concepts can be applied to. Phase equilibria and their applications article pdf available in the european physical journal special topics 2265.
Phase equilibria and phase diagrams phase diagrams are one of the most important sources of information concerning the behavior of elements, compounds and solutions. Such systems are used as models of a much more complex physical reality with many degrees of freedom in which chaotic or quantummechanical e. Equilibrium is defined as a stage when chemical potential of any component present in the system stays steady with time. If they all intersect, called triple point, three phases in equilibrium. Phase equilibria and phase diagrams phase diagrams are one of the most important sources of information concerning the. Lecture 8 south dakota school of mines and technology. Epidemic trajectory a typical trajectory of the system solution in the is phase plane is given in fig. Made by faculty at the university of colorado boulder, department of chemical and biological engineering. Derivation of phase rule, brief concept on one and two. The phase rule is a general principle governing systems in thermodynamic equilibrium.
The lines dividing different phases are called the coexistence curves. Thermodynamic principles are central to understanding material behaviour, particularly as the application of these concepts underpins phase equilibrium. Single component phase diagrams the stability of phases can be predicted by the chemical potential, in that the most stable form of the substance will have the minimum chemical potential at the given temperature and pressure. A phase diagrams is a type of graph used to show the equilibrium conditions between the thermodynamicallydistinct phases. While this is a complex and challenging area, the use of computational tools has. Chem 340 lecture notes 9 fall 20 phase equilibria chap. Tie line connects the phases in equilibrium with each. Thus, the maximum concentration of a species in an aqueous stream in contact with an organic stream can be estimated by these calculations. Solidification of single phase alloys when a piece of alloy solid is growing with a plane front from an alloy liquid with an overall alloy composition, c. It consists of atoms of at least two different types where solute atoms occupy either substitutionalor interstitial positions in the. Phase rule and equilibrium the phase rule, also known as the gibbs phase rule, relates the number of components and the number of degrees of freedom in a system at equilibrium by the formula f c. Such systems are used as models of a much more complex physical reality with many degrees of freedom in which chaotic or.
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