Equilibrium concentration varies with temperature where, n is the total number of atomic sites, q v is the energy required for the formation of a vacancy, t is the absolute temperature in kelvins, and k is the gas or boltzmanns constant. And so if multiple phases are present, mu has to be the same in all the phases. Phase equilibrium introduction part 1 chemistry notes. 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.
Interpretation of phase diagrams for a given temperature and composition we can use phase diagramtodetermine. Phase diagram pressuretemperature phase diagram for h2o. Equilibrium class 11 notes chemistry mycbseguide cbse. Lecture notes on phase transformations ju li, university of pennsylvania, 20082010 equilibrium. For onecomponent system, existing in two phases, the chemical potentials of each of these phases is the same at equilibrium. Derivation of phase rule, brief concept on one and two. Besides the methods based on equations of state and liquid activity models, new. Chemical equilibrium gibbs free energy and chemical equilibrium temperature dependence of the equilibrium constant, kp temperature dependence of the equilibrium constant, kp, and entropy.
In the analysis phase, external inputs are also often neglected, leaving system. Phase equilibria, phase diagrams and phase transformations. They provide us with the knowledge of phase composition and phase stability as a function of temperature t, pressure p and composition c. Phase diagrams binary system type i, ii and iii phase. Phase rule and equilibrium the phase rule, also known as the gibbs phase rule, relates the number. Phase equilibria and phase diagrams phase diagrams are one of the most important sources of information concerning the behavior of elements, compounds and solutions.
This means that at equilibrium, the various phases. Just as oil and water represent two distinct liquid phases, two regions of a solid with distinctly. Chapter 10 properties of gases chapter 11 liquids, solids and phase changes chapter 12 solutions and their properties chapter chemical kinetics chapter 14 chemical equilibrium chapter 15 aqueous equilibria. Phase rule and equilibrium the phase rule, also known as. Phase equilibrium and solutions lecture notes docsity.
In homogeneous equilibrium, the reactants and products arc present in the same phase or physical suite gaseous or liquid. Phase equilibrium and solutions introduction to chemical engineering lecture notes, study notes for engineering chemistry. Summary for chapter 8 phase equilibrium in flemings physical chemistry textmap. They provide us with the knowledge of phase composition and phase stability as a function of. 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. Physical chemistry lecture notes thermodynamics, electrochemistry, and 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. Phase equilibrium of a pure substance on tv diagram. Phase equilibria clausiusclapeyron equation ehrenfest criteria, second order phase transitions. Phase equilibrium between a dissolving gas, a, and its dissolved concentration, ah. Phase transformation lecture equilibrium, phase diagram.
Phase equilibrium is the study of the equilibrium which exists between or within different states of matter namely solid, liquid and gas. The best app for cbse students now provides equilibrium class 11 notes chemistry latest chapter wise notes for quick preparation of cbse exams and school based annual examinations. Tempp, gyerature, internal energy and heat most phase changes, or changes of a substance from one phase of matter to another, require large amounts of energy. While this is a complex and challenging area, the use of computational tools has. If they all intersect, called triple point, three phases in equilibrium. If the equilibrium constant for binding a single oxygen is k1. Thisclassisusuallyreferredtoasstatics,butwellbecoveringsomeextra. Solutions 4 with ionic compounds, it is not so easy to predict if they will dissolve in water. And if it isnt, then the molecules will go into the phase with the lower chemical potential. Equilibrium is defined as a stage when chemical potential of any component present in the system stays steady with time.
The piston and weights maintain a constant pressure in the cylinder. So the main point here is that at equilibrium, mu is identical everywhere. For one component systems, the equilibrium state of the system is defined by two independent parameters p and t, t and v, or p and v. Mar 28, 2020 phase equilibrium introduction part 1 chemistry notes edurev is made by best teachers of chemistry. By everywhere, i mean in all phases that are at equilibrium. Consider 1 kg of water ice at 40c 40f contained in pistoncylinder arrangement as shown in figure. 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. Chemical reaction engineering lecture notes januaryapril 2010 department of chemical engineering.
A mixture of oil and water would also be a twophase system. Equilibrium statistical physics physics course materials. Phase equilibria and their applications 821 it has been my pleasure to be the guest editor of this special issue on phase equi libria that really demonstrates how rich the researc h area of phase. Thus, the maximum concentration of a species in an aqueous stream in contact with an organic stream can be estimated by these calculations. Given a chemical equation, write the law of mass action. Approach to equilibrium in evaporation and condensation. Individual chapters and problem sets can also be found below.
Equilibrium phase diagrams represent the relationships between temperature and the compositions. Pay special attention to the introductory treatment of phases. Lecture 12 free download as powerpoint presentation. This is an introductory course on statistical mechanics and thermodynamics given to final year undergraduates. Cbse chemistry chapter 7 equilibrium class 11 notes chemistry in pdf are available for free download in mycbseguide mobile app. Chem 340 lecture notes 9 fall 20 phase equilibria chap. A phase diagrams is a type of graph used to show the equilibrium conditions between the thermodynamicallydistinct. If we heat the system from outside, change of state of water that take place inside the. Lecture notes on nonlinear systems and control spring semester 2018 eth zurich.
Thermodynamic principles are central to understanding material behaviour, particularly as the application of these concepts underpins phase equilibrium. The rate of cooling will change as the sample or some portion of it begins to undergo a phase change. Whether it is an accurate description of, say, a series of snapshots of a real system which we observe to be an an equilibrium macrostate is not something we are prepared to address. This document is highly rated by chemistry students and has been viewed 1517 times.
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. Jun 23, 2019 summary for chapter 8 phase equilibrium in flemings physical chemistry textmap. Mar 16, 2018 cbse chemistry chapter 7 equilibrium class 11 notes chemistry in pdf are available for free download in mycbseguide mobile app. Phase equilibria phase equilibria phase equilibrium describes the way phases such as solid, liquid andor gas coexist at some temperatures. Its phase portrait is a representative set of its solutions, plotted as parametric curves. Given the equilibrium constant k eq for a reaction, predict whether the reactants or products are predominant.
Equilibrium phase diagrams represent the relationships between temperature and the compositions and the quantities of phases at equilibrium. T, p, and composition of a phase, which can be changed independently without altering the number and kinds of phases which coexist at equilibrium. 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. Phase rule and equilibrium the phase rule, also known as the gibbs phase. Math 312 lecture notes linearization warren weckesser department of mathematics colgate university 23 march 2005 these notes discuss linearization, in which a linear system is used to approximate the behavior of a nonlinear system. A system consisting of more than one phase is said to be heterogeneous. View notes notes on phase equilibria 2016 from cem 2005w at university of cape town.
An equilibrium point is said to behyperbolic if all the eigenvalues of its linear variational equations have nonzero real parts. The established pressure in the gas phase is referred to as the equilibrium vapor pressure, which is normally. Many chemical reactions do not go to completion but instead attain a state of chemical equilibrium. In general practice it is sufficient to consider only solid and liquid phases, thus pressure is assumed to be constant 1 atm. A system may have none, one or any number of equilibrium points in virtually a spatial pattern in state space. Saturated solution at some point, even with highly soluble compounds, a solution will reach its capacity to dissolve. An equilibrium point in a nonlinear system is lyapunov unstable if there exists at least one eigenvalue of the linear variational equations which has a positive real part. In fact, we will spend much of the rest of the course discussing aspects of this concept. Stable compounds often form between the two extremes of pure component a and pure component b in binary systems these are referred to as intermediate compounds. Feb, 2019 this is first part of phase equilibrium topic see second part of this topic for complete information.
Notes on phase equilibria 2016 cem2005w phase equilibria. Lecture notes on nonlinear vibrations cornell university. Lecture 1 introduction, units, linear algebra 0introduction welcometoengineeringmechanicsi. Chapter 14 equilibrium notes page 1 of 6 chapter 14. Typically, when we are talking about a triple point it is the solid, liquid, gas triple point. Cooling curves the method that is used to map the phase boundaries on a phase diagram is to measure the rate of cooling for a sample of known composition. Phase diagramis a graphical representation of all the equilibrium phases as a function of temperature, pressure, and composition. Equilibrium refers to a state wherein there is a balance of forces as we. Phase is a region where the intermolecular interaction is spatially uniform or in. Introduction to solid state chemistry lecture notes no.
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. A state in which the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products remain constant. This will be our starting point for deriving thermodynamics and other things. Use le chateliers principle to explain how a chemical reaction at equilibrium responds when a. Thus characterization of equilibrium points is not only technically more dicult, it is a much broader question. Let us give another example with the axisymmetric top we studied in lecture 4. When various phases are in equilibrium with one another in a heterogeneous system, there can be no transfer of energy or mass from one phase to another. For h2o, a typical diagram shows the temperature and pressure at which ice solid,water liquid. Solutions concentration measures, molarity, molality, mole fraction thermodynamics of mixing of ideal gases. The second one, unifac, is a group contribution method gcm but. We will focus on twodimensional systems, but the techniques used here also work in n dimensions. In heterogeneous equilibrium the reactants and products are present in two or more physical states or phases.
Gibbs phase rule hammett free energy relationships isonarcotic activity of esters, alcohols, ketones, and ethers formula sheet 2. The equilibrium point distribution is potentially more complex in the nonlinear case than in the linear case. Equilibrium and metastable phases cementite fe 3 c is a metastable phase and after long term treatment decompose to form aferrite and carbon. This is the temperature and pressure at which three phases are in equilibrium. Introduction to solid state chemistry lecture notes. Monday, february 21, 2005 page 1 of 11 lecture notes j.
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