DOCSLIB.ORG

Topic790 Compressions: Isentropic: Solutions: Partial and Apparent

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Topic790 Compressions: Isentropic: Solutions: Partial and Apparent Topic790 Compressions: Isentropic: Solutions: Partial and Apparent Molar Isentropic properties of aqueous solutions are defined in a manner analogous to that used to define isothermal compressions and isothermal compressibilities. The assertion is made that a system (e.g. an aqueous solution) can be perturbed along a pathway where the affinity for spontaneous change is zero by a small change in pressure δp, to a neighbouring state having the same entropy. The (equilibrium) isentropic compression is defined by equation (a). = − ∂ ∂ K S (aq) [ V(aq) / p]S(aq);A=0 (a) The constraint on this partial differential refers to 'at constant S(aq)'. The definition of KS (aq) uses non-Gibbsian independent variables. In other words, isentropic parameters do not arise naturally from the formalism which expresses the Gibbs energy in terms of independent variables in the case of, for example, a simple solution, [T,p,n1,nj] [1]. The isothermal compression of a solution KT(aq) and partial molar isothermal compressions of both solvent KT1(aq) and solute KTj (aq) are defined using Gibbsian independent variables. Unfortunately the corresponding equations cannot be simply carried over to the isentropic property KS(aq). The volume of a solution is expressed in terms of the amounts of solvent n1 and solute nj. =⋅ +⋅ V() aq n11 V () aq njj V () aq (b) The latter equation is differentiated with respect to pressure at constant entropy of the solution S(aq). The latter condition includes the condition that the system remains at equilibrium where the affinity for spontaneous change is zero. We emphasise a point. The entropy which remains constant is that of the solution. =− ⋅∂∂ − ⋅ ∂∂ KSSaqAjjSaqA() aq n11 [ V ()/] aq p();== 0 n [ V ()/] aq p (); 0 (c) KS (aq) is an extensive property of the aqueous solution. KS(aq) may also be re-expressed using Euler’s theorem as a function of the composition of the solution. =⋅∂∂ +⋅ ∂∂ KSSTpnjjSjTpn() aq n11 [ K ()/] aq n,,() n [ K ()/] aq n ,,() 1 (d) Because KS(aq) is defined using non-Gibbsian independent variables, two important inequalities follow. −≠∂∂ ∂ ∂ [()/]Vaqp11Saq() [ Kaqn S ()/] Tpnj ,,() (e) − ∂ ∂ ≠ ∂ ∂ [ Vj (aq) / p]S(aq) [ KS (aq) / n j ]T,p,n(1) (f) ∂∂ ∂∂ [KaqnSTpnj ( ) /1 ] ,,() and [KaqnSjTpn ( ) / ] ,,(1) are respectively the partial molar properties of the solvent and solute. Because partial molar properties should describe the effects of a change in composition on the properties of a solution, we write equation (d) for an aqueous solution in the following form. = ⋅ + ⋅ K S (aq) n1 K S1 (aq;def ) n j K Sj (aq;def ) (g) ≠ − ∂ ∂ Hence, K Sj (aq;def ) [ Vj (aq) / p]S(aq) (h) In view of the latter inequality KSj(aq;def) is a non-Lewisian partial molar property [2]. We could define a molar isentropic compression of solute j as (minus) the isentropic differential dependence of partial molar volume on pressure. This alternative definition is consistent with equation (g) expressing a summation rule analogous to that used for partial molar properties. However some other thermodynamic relationships involving partial molar properties would not be valid in this − ∂ ∂ case. Therefore, [ Vj (aq) / p]S(aq) is a semi-partial molar property. A similar problem is encountered in defining an apparent molar compression for solute j, φ(KSj ) in a solution where the solute has apparent molar volume φ(Vj); cf. equation (h) [3,4]. We might assert that φ(KSj) is related to the isentropic differential dependence of φ(Vj ) on − φ ∂ pressure, [(VpjSaq )/ ](). Alternatively, using as a guide the apparent molar properties φ(Epj ) and φ(KTj ), we could define φ(KSj;def) using equation (i). * K (aq) = n ⋅ K (l) + n ⋅ φ(K ;def ) S 1 S1 j Sj (i) KSj (aq;def) as given by equation (d) and φ(KSj;def) are linked; equation (j). K (aq;def ) = φ(K ;def ) + n ⋅[∂φ(K ;def ) / ∂n ] Sj Sj j Sj j T,p,n(1) (j) Equation (j) is of the general form encountered for other apparent and partial molar properties. This form is also valid in the case of partial and apparent molar isobaric expansions, isothermal compressions and isobaric heat capacities. On the other hand, the semi-partial molar − ∂∂ isentropic compression defined by [()/]VaqjSaq p() and the semi- − ∂φ ∂ apparent molar isentropic compression defined by [()/]VpjSaq() are related. The isentropic pressure dependence of Vj(aq) is given by equation (k). − ∂ ∂ = [ Vj (aq) / p]S(aq) (k) − ∂φ ∂ − ⋅ ∂ ∂φ ∂ ∂ [ (Vj ) / p]S(aq) n j { [ (Vj ) / n j ]T,p,n(1) / p}S(aq) However, ∂∂φ ∂∂∂∂≠ φ ∂∂ { [ (Vnj ) / j ] T,,() p n11 / p } S () aq { [ ( Vp j ) / ] S () aq / n j } T ,,() p n (l) Hence, the analogue of equation (j) does not hold for these 'semi' properties. The inequalities (e) and (f) highlight the essence of non- Lewisian properties. Their origin is a combination of properties defined in terms of Gibbsian and non-Gibbsian independent variables as in equations (e) and (f). This combination is also the reason for the inequality (l). We stress that the isentropic condition in equations (e) and (f) refers to the entropy S(aq) of the solution defined as is the volume V(aq) by the Gibbsian independent variables [T, p , n1 , n j ]. But this is not * * the entropy S1 ()l of the pure solvent having volume V1 ()l . S(aq) at * fixed composition is not simply related to S1 ()l as, for example, linear functions of temperature and pressure. The isentropic condition is involved in the definitions of isentropic * κ * compression, KS1 ()l and isentropic compressibility S1 ()l of the solvent. **=−∂ ∂ * KS1()ll [ V 1 ()/ p ] at constant S1 ()l (m) κ* ( ) = K * ( ) / V* ( ) S1 l S1 l 1 l at constant S* () (n) = − ∂ * ∂ * 1 l [ V1 (l) / p]/ V1 (l) The different isentropic conditions in equation (a) and in equations (m) and (n) signal a complexity in the isentropic differentiation of equation (o) with respect to pressure [5,6]. = = −1 ⋅ * + ⋅ φ V(aq; w 1 1 kg) M1 V1 (l) m j (Vj ) (o) Footnotes [1] J. C. R. Reis, M. J. Blandamer, M. I. Davis and G. Douheret, Chem. Phys. Phys. Chem., 2001, 3,1465. [2] J. C. R. Reis, J. Chem. Soc. Faraday Trans.,2,1982, 78,1565. [3] M. J. Blandamer, M. I. Davis, G. Douheret and J. C. R. Reis, Chem. Soc. Rev.,2001,30,8. [4] J. C. R. Reis, J. Chem. Soc. Faraday Trans.,1998,94,2385. [5] M. J. Blandamer, J. Chem. Soc. Faraday Trans.,1998,94,1057. [6] M. J. Blandamer, Chem. Soc. Rev.,1998,27,73. .
Load more

Recommended publications
  • Chapter 4 Calculation of Standard Thermodynamic Properties of Aqueous Electrolytes and Non-Electrolytes
    Chapter 4 Calculation of Standard Thermodynamic Properties of Aqueous Electrolytes and Non-Electrolytes Vladimir Majer Laboratoire de Thermodynamique des Solutions et des Polymères Université Blaise Pascal Clermont II / CNRS 63177 Aubière, France Josef Sedlbauer Department of Chemistry Technical University Liberec 46117 Liberec, Czech Republic Robert H. Wood Department of Chemistry and Biochemistry University of Delaware Newark, DE 19716, USA 4.1 Introduction Thermodynamic modeling is important for understanding and predicting phase and chemical equilibria in industrial and natural aqueous systems at elevated temperatures and pressures. Such systems contain a variety of organic and inorganic solutes ranging from apolar nonelectrolytes to strong electrolytes; temperature and pressure strongly affect speciation of solutes that are encountered in molecular or ionic forms, or as ion pairs or complexes. Properties related to the Gibbs energy, such as thermodynamic equilibrium constants of hydrothermal reactions and activity coefficients of aqueous species, are required for practical use by geologists, power-cycle chemists and process engineers. Derivative properties (enthalpy, heat capacity and volume), which can be obtained from calorimetric and volumetric experiments, are useful in extrapolations when calculating the Gibbs energy at conditions remote from ambient. They also sensitively indicate evolution in molecular interactions with changing temperature and pressure. In this context, models with a sound theoretical basis are indispensable, describing with a limited number of adjustable parameters all thermodynamic functions of an aqueous system over a wide range of temperature and pressure. In thermodynamics of hydrothermal solutions, the unsymmetric standard-state convention is generally used; in this case, the standard thermodynamic properties (STP) of a solute reflect its interaction with the solvent (water), and the excess properties, related to activity coefficients, correspond to solute-solute interactions.
    [Show full text]
  • Chapter 8 Thermodynamic Properties of Mixtures
    Chapter 8 Thermodynamic Properties of Mixtures 2012/3/29 1 Abstract The thermodynamic description of mixtures, extended from pure fluids. The equations of change, i.e., energy and entropy balance, for mixtures are developed. The criteria for phase and chemical equilibrium in mixtures 2012/3/29 2 8.1 THE THERMODYNAMIC DESCRIPTION OF MIXTURES Thermodynamic property for pure fluids, θθ=()TPN , , where N is the number of moles. θθ=()TP , where the number of mole equals to 1. Thermodynamic property for mixtures, θθ=()TPN , ,12 , N ,L , Nc where Ni is the number of moles of the ith component. θθ=()TPx , ,12 , x ,L , xci where x is the mole fraction of the ith component. For example UUTPNN=() , ,12 , ,LL , Ncc or UUTPxx=() , , 12 , , , x VVTPNN=() , ,12 , ,L , Nc or VVTPxx=() , ,12 , ,L , xc 2012/3/29 3 Summation of the properties of pure fluids (before mixing at TP and ) C UTPxx(), ,12 , ,L , xci− 1= ∑ xUTPi () , (8.1-1) i=1 where UU is the molar internal energy, i is the internal energy of the pure i-th component at TP and . C ˆˆ UTPww()(), ,12 , ,L , wcii− 1= ∑ wUTP , (8.1-2) i=1 where wi is the mass fraction of component i. 2012/3/29 4 At the same T and P 50 cc 25 cc + 25 cc H2O H2O or 52 cc 25 cc + 25 cc 48 cc + 2 cc A B -2 cc Attractive Repulsive 2012/3/29 5 Property change upon mixing (at constantTP and ) C Δ=mixθθ()TPx,,ii −∑ x θi () TP , i=1 Volume change upon mixing C Δ=mixVTP(),,,, VTPx()ii −∑ xVTPi () i=1 Enthalpy change upon mixing C Δ=mix HTP(),,,, HTPx()ii −∑ xHTPi () i=1 2012/3/29 6 Experimental data : properties changes upon mixing (H and V) Figure 8.1-1 Enthalpy-concentration diagram for aqueous sulfuric acid at 0.1 MPa.
    [Show full text]
  • Physical Chemistry
    Subject Chemistry Paper No and Title 10, Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics) Module No and Title 10, Free energy functions and Partial molar properties Module Tag CHE_P10_M10 CHEMISTRY Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics) Module No. 10: Free energy functions and Partial molar properties TABLE OF CONTENTS 1. Learning outcomes 2. Introduction 3. Free energy functions 4. The effect of temperature and pressure on free energy 5. Maxwell’s Relations 6. Gibbs-Helmholtz equation 7. Partial molar properties 7.1 Partial molar volume 7.2 Partial molar Gibb’s free energy 8. Question 9. Summary CHEMISTRY Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics) Module No. 10: Free energy functions and Partial molar properties 1. Learning outcomes After studying this module you shall be able to: Know about free energy functions i.e. Gibb’s free energy and work function Know the dependence of Gibbs free energy on temperature and pressure Learn about Gibb’s Helmholtz equation Learn different Maxwell relations Derive Gibb’s Duhem equation Determine partial molar volume through intercept method 2. Introduction Thermodynamics is used to determine the feasibility of the reaction, that is , whether the process is spontaneous or not. It is used to predict the direction in which the process will be spontaneous. Sign of internal energy alone cannot determine the spontaneity of a reaction. The concept of entropy was introduced in second law of thermodynamics. Whenever a process occurs spontaneously, then it is considered as an irreversible process.
    [Show full text]
  • Lecture Outline
    LECTURE OUTLINE 1. Equilibrium of heterogeneous system 2. Phase transformations R&Y, Chapter 2 Salby, Chapter 4 C&W, Chapter 4 A Short Course in Cloud Physics, R.R. Rogers and M.K. Yau; R&Y Thermodynamics of Atmospheres Fundamentals of Atmospheric Physics, and Oceanes, M.L. Salby; Salby J.A. Curry and P.J. Webster; C&W 2 /25 LECTURE OUTLINE 1. Equilibrium of heterogeneous system 2. Phase transformations Equilibrium conditions for a homogeneous system: • thermal equilibrium • mechanical equilibrium (at most an infinitesimal pressure difference exists between the system and its environment). A heterogeneous system must also be in: • chemical equilibrium. No conversion of mass occurs from one phase to the other. Chemical equilibrium requires a certain state variables to have no difference between the phases present. 4 /30 For a homogeneous system, two intensive properties describe the thermodynamic state. Only two state variables may be varied independently, so a homogeneous system has two thermodynamic degrees of freedom. For a heterogeneous system, each phase may be regarded as a homogeneous sub-system, one that is ‚open’ due to exchanges with the other phases present. The number of intensive properties that describes the thermodynamic state is proportional to the number of phases present. However, thermodynamic equilibrium between phases introduces additional constraints that actually reduce the degrees of freedom of a heterogeneous system below those of a homogeneous system. The system we consider is a two-component mixture of: • dry
    [Show full text]
  • Thermodynamics, Experimental, and Modelling of Aqueous Electrolyte and Amino Acid Solutions
    Downloaded from orbit.dtu.dk on: Sep 26, 2021 Thermodynamics, Experimental, and Modelling of Aqueous Electrolyte and Amino Acid Solutions Breil, Martin Peter Publication date: 2001 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Breil, M. P. (2001). Thermodynamics, Experimental, and Modelling of Aqueous Electrolyte and Amino Acid Solutions. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Thermodynamics, Experimental, and Modelling of Aqueous Electrolyte and Amino Acid Solutions Martin P. Breil 2001 IVC-SEP Department of Chemical Engineering Technical University of Denmark DK-2800 Kongens Lyngby, Denmark Preface iii Preface This thesis is submitted as a partial fulfilment of the Ph.D. degree at the Technical University of Denmark. The project, granted by the IVC-SEP, has been carried out from October 1998 to September 2001 at the Department of Chemical Engineering, Technical University of Denmark under the supervision of Jørgen Mollerup.
    [Show full text]
  • Proquest Disserststions
    THERMODYNAMIC PROPERTIES OF NUCLEIC ACID BASES AND NUCLEOSIDES UNDER HYDROTHERMAL CONDITIONS A Thesis Presented to The Faculty of Graduate Studies of The University of Guelph by VANESSA MANN In partial fulfilment of requirements for the degree of Master of Applied Science August, 2009 © Vanessa Mann, 2009 Library and Archives Bibliothèque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de l'édition 395 Wellington Street 395, rue Wellington OttawaONK1A0N4 OttawaONK1A0N4 Canada Canada Your file Votre référence ISBN: 978-0-494-68602-7 Our file Notre référence ISBN: 978-0-494-68602-7 NOTICE: AVIS: The author has granted a non- L'auteur a accordé une licence non exclusive exclusive license allowing Library and permettant à la Bibliothèque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par télécommunication ou par l'Internet, prêter, telecommunication or on the Internet, distribuer et vendre des thèses partout dans le loan, distribute and sell theses monde, à des fins commerciales ou autres, sur worldwide, for commercial or non- support microforme, papier, électronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriété du droit d'auteur ownership and moral rights in this et des droits moraux qui protège cette thèse. Ni thesis. Neither the thesis nor la thèse ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent être imprimés ou autrement printed or otherwise reproduced reproduits sans son autorisation.
    [Show full text]
  • Thermodynamic Study of Aqueous Rare Earth
    THERMODYNAMICS OF AQUEOUS SOLUTIONS KRISTY M. ERICKSON B.Sc., University of Lethbridge, 2005 A Thesis Submitted to the School of Graduate Studies of the University of Lethbridge in Partial Fulfillment of the Requirements for the Degree [MASTER OF SCIENCE] Department of Chemistry and Biochemistry University of Lethbridge LETHBRIDGE, ALBERTA, CANADA © Kristy M. Erickson, 2007 A STUDY OF THE THERMODYNAMICS OF AQUEOUS RARE EARTH ELEMENT CONTAINING TRIFLATE SALT SYSTEMS KRISTY M. ERICKSON Approved: (Print Name) (Signature) (Rank) (Highest Date Degree) _________________ _______________________ ___________ ___________ _____ Supervisor _________________ _______________________ ___________ ___________ _____ Thesis Examination Committee Member _________________ _______________________ ___________ ___________ _____ Thesis Examination Committee Member _________________ _______________________ ___________ ___________ _____ External Examiner _________________ _______________________ ___________ ___________ _____ Chair, Thesis Examination Committee ii “Thermodynamics is not difficult if you can just keep track of what it is you are talking about.” -William F. Giauque, Nobel Laureate 1949 (as cited in Bent, 1972) iii ABSTRACT Relative densities and relative massic heat capacities have been measured for aqueous solutions of triflic acid (CF3SO3H), sodium triflate (NaCF3SO3), gadolinium triflate (Gd(CF3SO3)3), dysprosium triflate (Dy(CF3SO3)3), neodymium triflate (Nd(CF3SO3)3), erbium triflate (Er(CF3SO3)3), ytterbium triflate (Yb(CF3SO3)3), and yttrium triflate (Y(CF3SO3)3) at T = (288.15, 298.15, 313.15, and 328.15) K and p = 0.1 MPa. The resulting densities and massic heat capacities have been used to calculate out apparent molar volume and apparent molar heat capacity data for each of the investigated aqueous systems. The concentration dependencies of the apparent molar volumes and apparent molar heat capacities have been modeled using Pitzer-ion interaction equations.
    [Show full text]
  • Computation of Partial Molar Properties Using Continuous Fractional Component Monte Carlo
    Delft University of Technology Computation of partial molar properties using continuous fractional component Monte Carlo Rahbari, A.; Hens, R.; Nikolaidis, I.K.; Poursaeidesfahani, A.; Ramdin, M.; Economou, I. G.; Moultos, O. A.; Dubbeldam, D.; Vlugt, T. J.H. DOI 10.1080/00268976.2018.1451663 Publication date 2018 Document Version Final published version Published in Molecular Physics: an international journal at the interface between chemistry and physics Citation (APA) Rahbari, A., Hens, R., Nikolaidis, I. K., Poursaeidesfahani, A., Ramdin, M., Economou, I. G., Moultos, O. A., Dubbeldam, D., & Vlugt, T. J. H. (2018). Computation of partial molar properties using continuous fractional component Monte Carlo. Molecular Physics: an international journal at the interface between chemistry and physics, 116(21-22), 3331-3344. https://doi.org/10.1080/00268976.2018.1451663 Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10. Molecular Physics An International Journal at the Interface Between Chemistry and Physics ISSN: 0026-8976 (Print) 1362-3028 (Online) Journal homepage: http://www.tandfonline.com/loi/tmph20 Computation of partial molar properties using continuous fractional component Monte Carlo A.
    [Show full text]
  • Analysis of the Partial Molar Excess Entropy of Dilute Hydrogen in Liquid Metals and Its Change at the Solid-Liquid Transition
    Analysis of the Partial Molar Excess Entropy of Dilute Hydrogen in Liquid Metals and Its Change at the Solid-Liquid Transition Andrew H. Caldwella, Antoine Allanorea,∗ aDepartment of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139 Abstract mix A systematic change in the partial molar enthalpy of mixing (∆hH ) and partial ex molar excess entropy (∆sH ) for dilute hydrogen-metal systems at the solid- mix ex liquid transition is reported. Expressions for ∆hH and ∆sH are derived from ex the Fowler model of hydrogen solubility, and the change in ∆sH at melting is bounded. The theoretical bound is in agreement with measured data. A ex connection is made between the change in ∆sH and short range order in the metal-hydrogen system. Keywords: Liquids, Hydrogen, Solubility, Statistical mechanics, Thermodynamics 1 1. Introduction 2 Metals processing invariably requires the handling of metals in the liquid 3 state. Such operations rarely occur in inert atmospheres. The mole fraction 4 of dissolved gases, in particular hydrogen (H), are typically in the range of −6 −2 5 10 to 10 for liquid metals, and therefore degassing procedures are routinely 6 employed in process metallurgy. This is done to prevent degradation of the 7 mechanical properties of the solidified product, and such effects are well-studied 8 [1, 2]. The severity of these effects depends on the concentration of H in the 9 metal M, which can be determined from the solution thermodynamics of the M- 10 H system. Calculating and predicting H solubility, defined here as its equilibrium ∗Corresponding author Email address: [email protected] (Antoine Allanore) Preprint submitted to Elsevier January 25, 2019 11 concentration in the metal, is therefore of considerable importance for metals 12 processing.
    [Show full text]
  • Thermodynamics of 3+ Metal Cation Containing Systems
    THERMODYNAMICS OF 3+ METAL CATION CONTAINING SYSTEMS Michael James Lukacs B.Sc, University of Lethbridge, 2001 A Thesis Submitted to the School of Graduate Studies of the University of Lethbridge in Partial Fulfilment of the Requirements for the Degree MASTER OF SCIENCE Department of Chemistry and Biochemistry University of Lethbridge LETHBRIDGE, ALBERTA, CANADA June, 2003 ''Michael James Lukacs, 2003 ABSTRACT Measurements of relative densities and relative massic heat capacities have been made for several aqueous rare earth chloride and perchlorate systems. Densities and relative massic heat capacities of acidified aqueous perchlorates of yttrium, ytterbium, dysprosium, and samarium as well as the chlorides of yttrium, ytterbium, dysprosium, samarium and gadolinium have been measured at the temperatures 288.15, 298.15, 313.15 and 328.15 K. Using the density and massic heat capacity data, apparent molar volumes and apparent molar heat capacities have been calculated. These data have been modeled using the Pitzer ion interaction approach as well as the Helgeson, Kirkham and Flowers equations of state. Apparent molar volumes and apparent molar heat capacities previously presented in the literature have been compared to the data presented here. Single ion apparent molar volume and apparent molar heat capacity contributions were calculated. Infinite dilution properties have been compared to existing models used to predict infinite dilution properties. Densities of aqueous perchloric acid and ytterbium perchlorate at the temperatures from 348.15 to 423.15 K and at pressures from 10.00 to 30.00 MPa were measured. Apparent molar volumes were calculated from the density measurements. The apparent molar volume data were modeled using Pitzer ion interaction theory as well as HKF equations of state.
    [Show full text]
  • Solution Thermodynamics
    CH2351 Chemical Engineering Thermodynamics II Unit – I, II www.msubbu.in Solution Thermodynamicswww.msubbu.in Dr. M. Subramanian Associate Professor Department of Chemical Engineering Sri Sivasubramaniya Nadar College of Engineering Kalavakkam – 603 110, Kanchipuram (Dist) Tamil Nadu, India msubbu.in[AT]gmail.com Jan-2012 Contents • UNIT I: PROPERTIES OF SOLUTIONS – Partial molar properties, ideal and non-ideal solutions, standard states definition and choice,www.msubbu.in Gibbs-Duhem equation, excess properties of mixtures. • UNIT II: PHASE EQUILIBRIA – Criteria for equilibrium between phases in multi component non- reacting systems in terms of chemical potential and fugacity Jan-2012 M Subramanian www.msubbu.in Typical Chemical Plant Jan-2012 M Subramanian Introduction • Most of the materials of the real world are not pure substances with all atoms or molecules identical but rather are mixtures of one type or another. • The pure substances from www.msubbu.inwhich a solution may be prepared are called components , or constituents, of the solution. • Solutions are not limited to liquids: for example air, a mixture of predominantly N 2 and O 2, forms a vapor solution. Solid solutions such as the solid phase in the Si-Ge system are also common Jan-2012 M Subramanian Multicomponent Systems – Basic Relations • Single component system: – Intensive properties: depends on Pressure, Temperature – Extensive properties: depends on Pressure, Temperature, and amount www.msubbu.in • Multicomponent system: – Intensive properties: depends on Pressure, Temperature, and composition – Extensive properties: depends on Pressure, Temperature, amount of each component Jan-2012 M Subramanian Composition Mole fraction www.msubbu.in For binary solution In dealing with dilute solutions it is convenient to speak of the component present in the largest amount as the solvent , while the diluted component is called the solute .
    [Show full text]
  • Partial Molar Volume of That Component
    Chapter 6 Chemical Potential in Mixtures Partial molar quantities Thermodynamics of mixing The chemical potentials of liquids Chapter 7 : Slide 1 Duesberg, Chemical Thermodynamics Concentration Units • There are three major concentration units in use in thermodynamic descriptions of solutions. • These are – molarity – molality – mole fraction • Letting J stand for one component in a solution (the solute), these are represented by • [J] = nJ/V (V typically in liters) • bJ = nJ/msolvent (msolvent typically in kg) • xJ = nJ/n (n = total number of moles of all species present in sample) PARTIAL MOLAR QUANTITIES Recall our use of partial pressures: p = xA p + xB p + … pA = xA p is the partial pressure For binary mixtures (A+B): xA + xB= 1 We can define other partial quantities… Chapter 7 : Slide 3 Duesberg, Chemical Thermodynamics PARTIAL MOLAR QUANTITIES: Volume In a system that contains at least two substances, the total value of any extensive property of the system is the sum of the contribution of each substance to that property. The contribution of one mole of a substance to the volume of a mixture is called the partial molar volume of that component. V f p,T,nA,nB... V VA At constant T and p nA p,T ,n A V V dV dnA dnB ... nA nB Chapter 7 : Slide 4 Duesberg, Chemical Thermodynamics Partial molar volume Add nA of A to mixture Very Large Mixture of A and B When you add nA of A to a large mixture of A and B, the composition remains essentially unchanged. In this case: VA can be considered constant and the volume change of the mixture is n V .
    [Show full text]