DOCSLIB.ORG

The Relationship Between Chemical Potentials, Fugacities, Activities

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Relationship Between Chemical Potentials, Fugacities, Activities D. Keffer, Dept. of Chemical Engineering, University of Tennessee The Relationship Between Chemical Potentials, Fugacities, Activities, and Gibbs Free Energies (with specific application to partial derivatives required in mass transport) I. The Chemical Potential φ The chemical potential of component α in phase φ, µα , is defined as φ φ ∂N G µφ ≡ (1) α φ ∂Nα T,P,Nβ≠α where Gφ is the molar Gibbs free energy of the mixture of phase φ, Nφ is the total number of φ moles in phase φ, and Nα is the number of moles of component α in phase φ. As a result of this definition, the molar Gibbs free energy of the mixture is given by Nc φ φ φ G = ∑ xαµα (2) α=1 One typically proceeds by writing the molar Gibbs free energy of the mixture as a sum of an ideal mixture (IM) component and an excess (XS) component, Gφ = Gφ,IM + Gφ,XS , (3) where the excess term, by definition, includes everything that isn’t included in the ideal mixture. The molar Gibbs free energy of an ideal mixture is defined as Nc φ,IM φ φ G ≡ RT ∑ xα ln()xα . (4) α=1 As a consequence of this definition, the excess molar Gibbs free energy of a mixture must be Nc φ,XS φ φ,IM φ φ φ G = G − G = G − RT ∑ xα ln()xα . (5) α=1 The definitions of the mixture properties also defined the partial molar Gibbs free energy of an ideal mixture as 1 D. Keffer, Dept. of Chemical Engineering, University of Tennessee φ,IM φ φ Gα ≡ Gα + RT ln(xα ), (6) φ where Gα is the molar Gibbs free energy of component α in the pure state. The partial molar excess Gibbs free energy of a mixture is φ,XS φ φ φ Gα ≡ µα − Gα − RTln()xα . (7) As a result of equations (6) and (7), we see that we have an expression for the chemical potential in terms of ideal mixture and excess terms, which is analogous to the expression for the molar Gibbs free energy of the mixture in equation (3), namely φ φ,IM φ,XS φ φ φ,XS µα = Gα + Gα = Gα + RTln(xα )+ Gα . (8) II. Fugacities II.A. Fugacities of Pure Components φ In phase φ of the pure component α, we define a fugacity, fα , as Gφ − GIG f φ ≡ Pexp α α , (9) α RT IG where Gα is the molar Gibbs free energy of pure alpha as an ideal gas, where the pressure is equal to zero. When we have an equation of state, the evaluation of the pure component fugacity involves evaluating the following integral P 1 RT f φ ≡ Pexp Vφ (P) − dP . (10) α RT ∫ α P 0 We can also define a fugacity coefficient as f φ ϕφ ≡ α , (11) α P II.B. Fugacities of Mixtures We are interested in multi-component vapor-liquid equilibrium. In the multi-component φ case, the fugacity of component α in a mixture in phase φ, f α , is defined as 2 D. Keffer, Dept. of Chemical Engineering, University of Tennessee φ φ,IGM φ,XS φ φ µα − Gα φ Gα f α ≡ xαPexp = xαPexp . (12) RT RT where IGM indicates an ideal gas mixture. When we have an equation of state, the evaluation of the pure component fugacity involves evaluating the following integral P φ 1 φ φ,IGM f α ≡ Pexp Vα (P) − Vα (P)dP . (13) RT ∫ 0 We can also define a fugacity coefficient in a mixture as φ φ f ϕ ≡ α , (14) α φ xαP Using equation (6), we have a definition for the partial molar Gibbs free energy of component α in an ideal gas mixture φ,IGM φ,IG φ Gα ≡ Gα + RTln()xα (15) III. Activities φ The activity of component α in a mixture in phase φ, aα , is defined as the ratio of the fugacity of component a in a mixture to that in the pure component, at the same T and P. φ f aφ ≡ α (16) α φ fα φ We also can define an activity coefficient, γα , φ φ φ aα ≡ xαγα (17) The activity is related to the chemical potential through the fugacities. 3 D. Keffer, Dept. of Chemical Engineering, University of Tennessee φ φ,IGM φ µα − Gα xαPexp φ RT f aφ ≡ α = α φ φ φ,IG fα G − G Pexp α α RT φ φ,IG φ φ φ,IG µα − G − RTln()xα − G + G = xφ exp α α α (18) α RT µφ − Gφ = exp α α RT Or, alternatively, φ φ φ µα − Gα ln()aα = (19) RT IV. Application in mass transport In mass transport problems, one is concerned about gradients. From a fundamental non- equilibrium thermodynamics point of view, one is truly concerned with chemical potential gradients (as opposed to concentration or mole fraction gradients. The gradient of the chemical potential is related to the gradient of the activity in an isothermal system as follows: φ 1 φ ∇ln()aα = ∇µα (20) RT The gradient of any pure component term is zero. 4.
Load more

Recommended publications
  • FUGACITY It Is Simply a Measure of Molar Gibbs Energy of a Real Gas
    FUGACITY It is simply a measure of molar Gibbs energy of a real gas . Modifying the simple equation for the chemical potential of an ideal gas by introducing the concept of a fugacity (f). The fugacity is an “ effective pressure” which forces the equation below to be true for real gases: θθθ f µµµ ,p( T) === µµµ (T) +++ RT ln where pθ = 1 atm pθθθ A plot of the chemical potential for an ideal and real gas is shown as a function of the pressure at constant temperature. The fugacity has the units of pressure. As the pressure approaches zero, the real gas approach the ideal gas behavior and f approaches the pressure. 1 If fugacity is an “effective pressure” i.e, the pressure that gives the right value for the chemical potential of a real gas. So, the only way we can get a value for it and hence for µµµ is from the gas pressure. Thus we must find the relation between the effective pressure f and the measured pressure p. let f = φ p φ is defined as the fugacity coefficient. φφφ is the “fudge factor” that modifies the actual measured pressure to give the true chemical potential of the real gas. By introducing φ we have just put off finding f directly. Thus, now we have to find φ. Substituting for φφφ in the above equation gives: p µ=µ+(p,T)θ (T) RT ln + RT ln φ=µ (ideal gas) + RT ln φ pθ µµµ(p,T) −−− µµµ(ideal gas ) === RT ln φφφ This equation shows that the difference in chemical potential between the real and ideal gas lies in the term RT ln φφφ.φ This is the term due to molecular interaction effects.
    [Show full text]
  • Selection of Thermodynamic Methods
    P & I Design Ltd Process Instrumentation Consultancy & Design 2 Reed Street, Gladstone Industrial Estate, Thornaby, TS17 7AF, United Kingdom. Tel. +44 (0) 1642 617444 Fax. +44 (0) 1642 616447 Web Site: www.pidesign.co.uk PROCESS MODELLING SELECTION OF THERMODYNAMIC METHODS by John E. Edwards [email protected] MNL031B 10/08 PAGE 1 OF 38 Process Modelling Selection of Thermodynamic Methods Contents 1.0 Introduction 2.0 Thermodynamic Fundamentals 2.1 Thermodynamic Energies 2.2 Gibbs Phase Rule 2.3 Enthalpy 2.4 Thermodynamics of Real Processes 3.0 System Phases 3.1 Single Phase Gas 3.2 Liquid Phase 3.3 Vapour liquid equilibrium 4.0 Chemical Reactions 4.1 Reaction Chemistry 4.2 Reaction Chemistry Applied 5.0 Summary Appendices I Enthalpy Calculations in CHEMCAD II Thermodynamic Model Synopsis – Vapor Liquid Equilibrium III Thermodynamic Model Selection – Application Tables IV K Model – Henry’s Law Review V Inert Gases and Infinitely Dilute Solutions VI Post Combustion Carbon Capture Thermodynamics VII Thermodynamic Guidance Note VIII Prediction of Physical Properties Figures 1 Ideal Solution Txy Diagram 2 Enthalpy Isobar 3 Thermodynamic Phases 4 van der Waals Equation of State 5 Relative Volatility in VLE Diagram 6 Azeotrope γ Value in VLE Diagram 7 VLE Diagram and Convergence Effects 8 CHEMCAD K and H Values Wizard 9 Thermodynamic Model Decision Tree 10 K Value and Enthalpy Models Selection Basis PAGE 2 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Design Ltd, Teesside, UK www.pidesign.co.uk Process Modelling Selection of Thermodynamic Methods References 1.
    [Show full text]
  • Molecular Thermodynamics
    Chapter 1. The Phase-Equilibrium Problem Homogeneous phase: a region where the intensive properties are everywhere the same. Intensive property: a property that is independent of the size temperature, pressure, and composition, density(?) Gibbs phase rule ( no reaction) Number of independent intensive properties = Number of components – Number of phases + 2 e.g. for a two-component, two-phase system No. of intensive properties = 2 1.2 Application of Thermodynamics to Phase-Equilibrium Problem Chemical potential : Gibbs (1875) At equilibrium the chemical potential of each component must be the same in every phase. i i ? Fugacity, Activity: more convenient auxiliary functions 0 i yi P i xi fi fugacity coefficient activity coefficient fugacity at the standard state For ideal gas mixture, i 1 0 For ideal liquid mixture at low pressures, i 1, fi Psat In the general case Chapter 2. Classical Thermodynamics of Phase Equilibria For simplicity, we exclude surface effect, acceleration, gravitational or electromagnetic field, and chemical and nuclear reactions. 2.1 Homogeneous Closed Systems A closed system is one that does not exchange matter, but it may exchange energy. A combined statement of the first and second laws of thermodynamics dU TBdS – PEdV (2-2) U, S, V are state functions (whose value is independent of the previous history of the system). TB temperature of thermal bath, PE external pressure Equality holds for reversible process with TB = T, PE =P dU = TdS –PdV (2-3) and TdS = Qrev, PdV = Wrev U(S,V) is state function. The group of U, S, V is a fundamental group. Integrating over a reversible path, U is independent of the path of integration, and also independent of whether the system is maintained in a state of internal equilibrium or not during the actual process.
    [Show full text]
  • Equation of State. Fugacities of Gaseous Solutions
    ON THE THERMODYNAMICS OF SOLUTIONS. V k~ EQUATIONOF STATE. FUGACITIESOF GASEOUSSOLUTIONS' OTTO REDLICH AND J. N. S. KWONG Shell Development Company, Emeryville, California Received October 15, 1948 The calculation of fugacities from P-V-T data necessarily involves a differentia- tion with respect to the mole fraction. The fugacity rule of Lewis, which in effect would eliminate this differentiation, does not furnish a sufficient approximation. Algebraic representation of P-V-T data is desirable in view of the difficulty of nu- merical or graphical differentiation. An equation of state containing two individ- ual coefficients is proposed which furnishes satisfactory results above the critical temperature for any pressure. The dependence of the coefficients on the composi- tion of the gas is discussed. Relations and methods for the calculation of fugacities are derived which make full use of whatever data may be available. Abbreviated methods for moderate pressure are discussed. The old problem of the equation of state has a practical aspect which has become increasingly important in recent times. The systematic description of gas reactions under high pressure requires information about the fugacities, derived sometimes from extensive data but frequently from nothing more than t,he critical pressure and temperature. For practical purposes a representation of the relation between pressure, vol- ume, and temperature based on two or three individual coefficients is desirable, although a representation of this type satisfies the theorem of corresponding states and therefore cannot be accurate. Since the calculation of fugacities involves a differentiation with respect to the mole fraction, an algebraic repre- sentation by means of an equation of state appears to be desirable.
    [Show full text]
  • Fugacity of Condensed Media
    Fugacity of condensed media Leonid Makarov and Peter Komarov St. Petersburg State University of Telecommunications, Bolshevikov 22, 193382, St. Petersburg, Russia ABSTRACT Appearance of physical properties of objects is a basis for their detection in a media. Fugacity is a physical property of objects. Definition of estimations fugacity for different objects can be executed on model which principle of construction is considered in this paper. The model developed by us well-formed with classical definition fugacity and open up possibilities for calculation of physical parameter «fugacity» for elementary and compound substances. Keywords: fugacity, phase changes, thermodynamic model, stability, entropy. 1. INTRODUCTION The reality of world around is constructed of a plenty of the objects possessing physical properties. Du- ration of objects existence – their life time, is defined by individual physical and chemical parameters, and also states of a medium. In the most general case any object, under certain states, can be in one of three ag- gregative states - solid, liquid or gaseous. Conversion of object substance from one state in another refers to as phase change. Evaporation and sublimation of substance are examples of phase changes. Studying of aggregative states of substance can be carried out from a position of physics or on the basis of mathematical models. The physics of the condensed mediums has many practical problems which deci- sion helps to study complex processes of formation and destruction of medium objects. Natural process of object destruction can be characterized in parameter volatility – fugacity. For the first time fugacity as the settlement size used for an estimation of real gas properties, by means of the thermodynamic parities de- duced for ideal gases, was offered by Lewis in 1901.
    [Show full text]
  • Lecture 4. Thermodynamics [Ch. 2]
    Lecture 4. Thermodynamics [Ch. 2] • Energy, Entropy, and Availability Balances • Phase Equilibria - Fugacities and activity coefficients -K-values • Nonideal Thermodynamic Property Models - P-v-T equation-of-state models - Activity coefficient models • Selecting an Appropriate Model Thermodynamic Properties • Importance of thermodyyppnamic properties and equations in separation operations – Energy requirements (heat and work) – Phase equilibria : Separation limit – Equipment sizing • Property estimation – Specific volume, enthalpy, entropy, availability, fugacity, activity, etc. – Used for design calculations . Separator size and layout . AiliAuxiliary components : PiPipi ing, pumps, va lves, etc. EnergyEnergy,, Entropy and Availability Balances Heat transfer in and out Q ,T Q ,T in s out s OfdOne or more feed streams flowing into the system are … … separated into two or more prodttduct streams thtflthat flow Streams in out of the system. n,zi ,T,P,h,s,b,v : Separation : : : process n Molar flow rate : (system) : z Mole fraction Sirr , LW Streams out T Temperature n,zi ,T,P,h,s,b,v P Pressure h Molar enthalpy … … (Surroundings) s Molar entropy T b Molar availability 0 (W ) (W ) s in s out v Specific volume Shaft work in and out Energy Balance • Continuous and steady-state flow system • Kinetic, potential, and surface energy changes are neglected • First law of thermodynamics (conservation of energy) (stream enthalpy flows + heat transfer + shaft work)leaving system - (t(stream en thlthalpy flows +h+ hea ttt trans fer + s hfthaft wor k)entering
    [Show full text]
  • Activity and Fugacity Ray Fu
    Activity and Fugacity Ray Fu Notation symbol description m, M intensive (molar) and extensive property of pure species mi, Mi as above, but specifically for species i m◦, mig, mid reference state, ideal gas, and ideal solution conditions msat saturation (liquid-vapor equilibrium) conditions mα, mβ, ml, mv α, β arbitrary and l, v liquid and vapor phases ^ f, ', fi,' ^i fugacity (coeffcient) of pure species and of species i in mixture xi, yi liquid and gas phase mole fraction of species i PT total pressure of mixture * a harder exercise Fugacity in the gas phase For an ideal gas, and assuming constant T and N, we have P dµ = dg = v dP () µ − µ◦ = g − g◦ = RT ln : (1) P ◦ Exercise 1 Prove the above identity. For non-ideal gases and fluids, we can extend this identity by defining an effective pressure f such that f f µ − µig =: RT ln = RT ln : (2) P ig f ig We call f the fugacity; it is the pressure that an ideal gas with the same chemical potential would have. By construction, f ig = P ig, and the second equality follows. The pressure P ig is the pressure of the (real) gas; the superscript ig reminds us that we are considering an ideal gas reference state. It is also convenient to define the fugacity coefficient ', satisfying 'P ig f =: 'P ig () µ − µig = RT ln = RT ln ': (3) P ig The fugacity coefficient ' contains no new thermodynamics. It simply hides all the complicated intermolec- ular interactions that real gases possess, and we can interpret it as a measure of a gas's deviation from ideality: the further the fugacity coefficient of a gas diverges from one, the less ideal is the gas.
    [Show full text]
  • THE PENG-ROBINSON EQUATION of STATE Using Mathematica
    $5::j class and home problems ) The object of this column is to enhance our readers' collections of interesting and novel prob­ lems in chemical engineering. Problems of the type that can be used to motivate the student by presenting a particular principle in class, or in a new light, or that can be assigned as a novel home problem, are requested, as well as those that are more traditional in nature and that elucidate dif­ ficult concepts. Manuscripts should not exceed 14 double-spaced pages and should be accompanied by the originals of any figures or photographs. Please submit them to Professor James 0. Wilkes (e-mail: [email protected]), Chemical Engineering Department, University of Michigan, Ann Arbor, Ml 48109-2136. Applications of THE PENG-ROBINSON EQUATION OF STATE Using Mathematica HousAM Brnous National Institute ofApplied Sciences and Technology • Tunis, Tunisia onsider a single component characterized by its critical where pressure, temperature, acentric factor, Pc Tc, and w. The CPeng-Robinson equation of state[24J is given by: (7) P=~- a (1) (V-b) [v(v+b)+b(V-b)] (8) where (9) i=l i=l b = 0.07780 R Tc (2) P, p pc Ai= 0.45724ai T; and B = 0 07780_l.. (10) I • T (RT )2 2 ri ri (3) a= 0.45724----t"-[ 1 +m( I-Jr:)] For each component, we define the reduced pressure and C temperature using P,, = P / Pc, and T,, = T / Tc, , and ai is (4) identified by an equation similar to Eq. (3) - given for the pure component case. The binary interaction parameter, kii , and 2 m = 0.37464 + 1.54226w-0.26992w .
    [Show full text]
  • Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium
    Subject Chemistry Paper No and Title 10, Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics) Module No and 11, Fugacity and Third law of thermodynamics Title Module Tag CHE_P10_M11 CHEMISTRY Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics) Module No. 11: Fugacity and Third law of thermodynamics TABLE OF CONTENTS 1. Learning Outcomes 2. Fugacity 3. Fugacity coefficient 4. Determination of fugacity of gas 5. Physical significance of fugacity 6. Third law of thermodynamics 7. Determination of entropy for solids, liquids and gases 8. Residual entropy 9. 9.Summary CHEMISTRY Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics) Module No. 11: Fugacity and Third law of thermodynamics 1. Learning Outcomes After studying this module you shall be able to: Know the concept of fugacity Determine the coefficient of fugacity Learn about the third law of thermodynamics Know the concept of residual entropy 2. Fugacity The concept of fugacity was introduced by an American chemist, G.N Lewis. It is used for representing the real behavior of Vander Waal’s gases which is different from behavior of ideal gases. At constant temperature, the variation of free energy with pressure is given by: (/)GPV …(1) T For one mole of an ideal gas, V stands for the molar volume and thus we can write it as: ()/dG RT dP P …(2) T Similarly for n number of moles of gas, the equation turns into: (dG ) nRT dP / P nRT ln P …(3) T Integrating the equation (3) G G* nRT ln P …(4) in which G* (the integration constant) is the free energy of n moles of the gas when pressure P is unity.
    [Show full text]
  • Standard State Fugacity Coefficient~ for the Hypothetical Vapor
    STANDARD STATE FUGACITY COEFFICIENT~ FOR THE HYPOTHETICAL VAPOR BY BRIDGING FROM THE REAL GAS FUGACITY COEFFICIENTS THROUGH THE GIBBS-DUHEM EQUATION By Arthur Dale Godfrey // Bachelor of Science The University of Nebraska Lincoln, Nebraska 1943 Submitted to the Faculty of the Graduate School of the Oklahoma. State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE August, 1964 OKLAHOMA ITATE UNIVERSIT( LIBRARY JAN 5 1965 . ' ~~~ STANuARD STAT!!.: FUGACITY COEFFICIENTS Fo:a. THE HYPOTHETICAL -----·- VAPO.R BY BRIDGING FROM 'I'HE HEAL GAS FUGACITY COEFFICIENTS Tl1ROUGH THE GIBBS-DUHEM EQUATION Thesis Approved: ~c!··~~ ~is Lctviser . Dean of the Graduate School 561!564 PREFACE A generalized method for determining the standard state fugacity coefficients for hypothetical vapors was developed by bridging from ·the fugacity coefficient of the real gaseous component to that of the hypothetical gaseous component through the Gibbs-Duhem equation. Binary systems of hydrogen sulfide with methane, ethane, propane and n-pentane selected from the literature formed the basis for the correlation. The application of this method for the development of a similar correlation for the standard state fugacity coefficients of hypo­ thetical liquids is outlined. I sincerely appreciate the aid of Professor W. C. Edmister in suggesting the topic of this thesis and in guiding it to its com­ pletion. I am also grateful to Professor.Edmister for arranging his schedule to the convenience of the author as a "drive in11 student. I am greatly indebted to Mr. A. N. Stuckey, Jr. for his suggestions and aid toward the completion of this work, particularly his work in calculating the fugacity coefficients on the IIM-650 digital computer.
    [Show full text]
  • Numerical Modeling of CO2, Water, Sodium Chloride, and Magnesium Carbonates Equilibrium to High Temperature and Pressure
    energies Article Numerical Modeling of CO2, Water, Sodium Chloride, and Magnesium Carbonates Equilibrium to High Temperature and Pressure Jun Li * and Xiaochun Li State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [email protected] * Correspondence: [email protected] Received: 26 September 2019; Accepted: 27 November 2019; Published: 28 November 2019 Abstract: In this work, a thermodynamic model of CO2-H2O-NaCl-MgCO3 systems is developed. The new model is applicable for 0–200 ◦C, 1–1000 bar and halite concentration up to saturation. The Pitzer model is used to calculate aqueous species activity coefficients and the Peng–Robinson model is used to calculate fugacity coefficients of gaseous phase species. Non-linear equations of chemical potentials, mass conservation, and charge conservation are solved by successive substitution method to achieve phase existence, species molality, pH of water, etc., at equilibrium conditions. From the calculated results of CO2-H2O-NaCl-MgCO3 systems with the new model, it can be concluded that (1) temperature effects are different for different MgCO3 minerals; landfordite solubility increases with temperature; with temperature increasing, nesquehonite solubility decreases first and then increases at given pressure; (2) CO2 dissolution in water can significantly enhance the dissolution of MgCO3 minerals, while MgCO3 influences on CO2 solubility can be ignored; (3) MgCO3 dissolution in water will buffer the pH reduction due to CO2 dissolution. Keywords: thermodynamic modeling; CO2 storage; MgCO3 minerals; phase behaviors; mineral solubility; CO2 solubility 1. Introduction CO2 geological storage has been proved as an important option to reduce carbon emission and a clean way of using fossil energy resources [1].
    [Show full text]
  • Chemical Equilibrium
    Chemical Equilibrium • Concepts Activity Fugacity Equilibrium constant Solid vapor equilibrium Ellingham diagrams Sievert’s law Control of oxygen partial pressure WS2002 1 1 Activity/Fugacity • For ideal gases and mixtures of condensed phases, the “activity” of a species is equal to its mole fraction. That means that its influence on the properties of the system is its mole fraction (X) multiplied by the total system property. For a gas mixture, the partial pressure of A is: = PXP AA • In real systems, the influence of one component on the properties of the system may be different than its mole fraction would suggest. Activity is given by the ratio of the fugacity of a substance to its fugacity in a standard state (usually pure substance at 1 atm, same T) = fA aA o fA • You may also see this expressed in terms of an activity coefficient an mole fraction, but the idea is the same. The proportional effect of the amount of substance A on the whole system property in question is not simply given by its mole fraction =γ aX AAA WS2002 2 2 Activity/Fugacity • For real gases, the fugacity is the effective pressure corrected for non-ideality • For solids and liquids, fugacity is equal to the vapor pressure of in equilibrium with the condensed phase since, at equilibrium, the partial molar free energy of the solid and gas must be equal • For gases, the ratio of fugacity to partial pressure must approach one (ideal behavior) as total pressure approaches zero. WS2002 3 3 Activity =− + • For any substance dGAA S dT V A dP At constant temperature = dG AA V dP • The difference between the Gibbs’ free energy of a material under any conditions can be determined by integrating that equation.
    [Show full text]