a for save as PDF Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities

Size: px
Start display at page:

Download "a for save as PDF Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities"

Transcription

1 a for save as PDF Chemstry 163B Introducton to Multcomponent Systems and Partal Molar Quanttes 1

2 the problem of partal mmolar quanttes mx: 10 moles ethanol C 2 H 5 OH (580 ml) wth 1 mole water H 2 O (18 ml) get (580+18)=598 ml of soluton? no only 594 ml for pure H 2 O V n HO 2 T 298, P 1 bar, n 0 V HO 2 18 ml but n 10 mol V n HO 2 T 298, P 1 bar, n ml 2

3 partal molar quanttes (systems of varable composton) system of n 1 moles substance 1, n 2 moles substance 2, Ω some extensve property of system (volume, free energy, etc) total n T, P, n jn partal molar Ω for component contrbuton of substance to property Ω at T, P when other components present at concentratons n j molar Ω n presence of other speces 3

4 sldes 4-7 are taken from: apparently no longer avalable ste from: Stephen. Cooke, Ph.D. Department of Chemstry Unversty of orth Texas 4 4

5 PRTIL MOLR QUTITIES In a system that contans at least two substances, the total value of any extensve property of the system s the sum of the contrbuton of each substance to that property. The contrbuton of one mole of a substance to the volume of a mxture s called the partal molar volume of that component. V f t constant T and p V dv n p, T, n, n B... dn V n B dn B... V V n p, T, n 5 5

6 PRTIL MOLR VOLUME dd n of to mxture Very Large Mxture of and B V Composton remans essentally unchanged. In ths case: V n p, T, n can be consdered constant and the volume change of the mxture s n V. Lkewse for addton of B. The total change n volume s n V + n B V B. (Composton s essentally unchanged). Scoop out of the reservor a sample contanng n of and n B of B ts volume s n V + n B V B. Because V s a state functon: V V n V B n B

7 PRTIL MOLR VOLUME Illustraton: What s the change n volume of addng 1 mol of water to a large volume of water? The change n volume s 18cm 3 V V H O 2 nh 2O p, T 18cm 3 dfferent answer s obtaned f we add 1 mol of water to a large volume of ethanol. The change n volume s 14cm 3 V V H O 2 nh 2O p, T, n(ch CH OH) cm 3 7 7

8 PRTIL MOLR QUTITIES V s not generally a constant; t s a functon of composton: 8 8

9 Gbbs-Duhem (later) X V V HO 2 XH2O n n T, P, n T, P, n H2O H2O 9

10 partal molar quanttes n bology 10

11 partal molar factods #1 total dfferentals 1. state functon dfferentals for systems of varable composton (stll d wother =0) U U( S, V, n1,..., n) du TdS PdV dn n 1 1 S, V, n n H H( S, P, n1,..., n) dh TdS VdP dn n 1 S, P, n n ( T, V, n1,..., n) d SdT PdV dn n G( T, P, n,..., n ) dg SdT VdP 1 T, V, n n G n 1 T, P, n jn j j j dn 11

12 partal molar factods #2 the chemcal potental 2. The partal molar Gbbs free energy, the chemcal potental, plays a central role G G n T, P, n jn thus dg SdT VdP dn 1 and a very cute dervaton gve ( see handout) : G H U n n n n T, P, n n T, V, n n S, P, n n S, V, n n j j j j note: for,h,u these are OT partal molar quanttes, H, and U 12

13 factod #3: propertes of a system are sum of partal molar propertes 3. n extensve property of a mult-component system s the sum of partal molar contrbutons from each of the components V nv nv n V total G H H H n H note : H etc. n G n n T, P, n n S, P, n n j j 13

14 factod #4: relatonshps among partal molar quanttes 4. Relatonshps among thermodynamc quanttes derved for one-component systems often hold for partal molar quanttes examples : G H TS G H TS or H U PV H U PV [proof n class for G; students do smlar proof for H] 14

15 factod #5: Gbbs Duhem 5. The Gbbs-Duhem relatonshp shows that partal molar quanttes for substances n a mxture can not vary ndependently X H O 2 X V V X B B nb n T, P, n B T, P, n VHO V 2 X n n T, P, n T, P, n H2O [note : the varaton s wth respect to one of the components ( n n both denomnators)] H2O [dervaton done n class] 15

16 Gbbs-Duhem (slope of partal molar volume vs mole fracton) V X H2O VH 2O n X n T, P, n T, P, n H2O H2O VHO X 2 V n X n T P n H O T, P, n,, 2 H H 2O 2O + X 0 X 2 - HO

17 End of Lecture 17 17

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities Chemstry 163 Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto?

More information

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities Chemstry 163B Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto?

More information

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,

More information

Lecture. Polymer Thermodynamics 0331 L Chemical Potential

Lecture. Polymer Thermodynamics 0331 L Chemical Potential Prof. Dr. rer. nat. habl. S. Enders Faculty III for Process Scence Insttute of Chemcal Engneerng Department of Thermodynamcs Lecture Polymer Thermodynamcs 033 L 337 3. Chemcal Potental Polymer Thermodynamcs

More information

...Thermodynamics. If Clausius Clapeyron fails. l T (v 2 v 1 ) = 0/0 Second order phase transition ( S, v = 0)

...Thermodynamics. If Clausius Clapeyron fails. l T (v 2 v 1 ) = 0/0 Second order phase transition ( S, v = 0) If Clausus Clapeyron fals ( ) dp dt pb =...Thermodynamcs l T (v 2 v 1 ) = 0/0 Second order phase transton ( S, v = 0) ( ) dp = c P,1 c P,2 dt Tv(β 1 β 2 ) Two phases ntermngled Ferromagnet (Excess spn-up

More information

Chemistry 163B Free Energy and Equilibrium E&R ( ch 6)

Chemistry 163B Free Energy and Equilibrium E&R ( ch 6) Chemstry 163B Free Energy and Equlbrum E&R ( ch 6) 1 ΔG reacton and equlbrum (frst pass) 1. ΔG < spontaneous ( natural, rreversble) ΔG = equlbrum (reversble) ΔG > spontaneous n reverse drecton. ΔG = ΔHΔS

More information

NAME and Section No. it is found that 0.6 mol of O

NAME and Section No. it is found that 0.6 mol of O NAME and Secton No. Chemstry 391 Fall 7 Exam III KEY 1. (3 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). In the reacton 3O O3 t s found that.6 mol of O are consumed. Fnd

More information

Solution Thermodynamics

Solution Thermodynamics CH2351 Chemcal Engneerng Thermodynamcs II Unt I, II www.msubbu.n Soluton Thermodynamcs www.msubbu.n Dr. M. Subramanan Assocate Professor Department of Chemcal Engneerng Sr Svasubramanya Nadar College of

More information

Thermodynamics II. Department of Chemical Engineering. Prof. Kim, Jong Hak

Thermodynamics II. Department of Chemical Engineering. Prof. Kim, Jong Hak Thermodynamcs II Department of Chemcal Engneerng Prof. Km, Jong Hak Soluton Thermodynamcs : theory Obectve : lay the theoretcal foundaton for applcatons of thermodynamcs to gas mxture and lqud soluton

More information

Appendix II Summary of Important Equations

Appendix II Summary of Important Equations W. M. Whte Geochemstry Equatons of State: Ideal GasLaw: Coeffcent of Thermal Expanson: Compressblty: Van der Waals Equaton: The Laws of Thermdynamcs: Frst Law: Appendx II Summary of Important Equatons

More information

CHEMICAL REACTIONS AND DIFFUSION

CHEMICAL REACTIONS AND DIFFUSION CHEMICAL REACTIONS AND DIFFUSION A.K.A. NETWORK THERMODYNAMICS BACKGROUND Classcal thermodynamcs descrbes equlbrum states. Non-equlbrum thermodynamcs descrbes steady states. Network thermodynamcs descrbes

More information

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9.

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9. 9.9 Real Solutons Exhbt Devatons from Raoult s Law If two volatle and mscble lquds are combned to form a soluton, Raoult s law s not obeyed. Use the expermental data n Table 9.3: Physcal Chemstry 00 Pearson

More information

Chemical Equilibrium. Chapter 6 Spontaneity of Reactive Mixtures (gases) Taking into account there are many types of work that a sysem can perform

Chemical Equilibrium. Chapter 6 Spontaneity of Reactive Mixtures (gases) Taking into account there are many types of work that a sysem can perform Ths chapter deals wth chemcal reactons (system) wth lttle or no consderaton on the surroundngs. Chemcal Equlbrum Chapter 6 Spontanety of eactve Mxtures (gases) eactants generatng products would proceed

More information

3. Be able to derive the chemical equilibrium constants from statistical mechanics.

3. Be able to derive the chemical equilibrium constants from statistical mechanics. Lecture #17 1 Lecture 17 Objectves: 1. Notaton of chemcal reactons 2. General equlbrum 3. Be able to derve the chemcal equlbrum constants from statstcal mechancs. 4. Identfy how nondeal behavor can be

More information

Energy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model

Energy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model Lecture 4. Thermodynamcs [Ch. 2] Energy, Entropy, and Avalablty Balances Phase Equlbra - Fugactes and actvty coeffcents -K-values Nondeal Thermodynamc Property Models - P-v-T equaton-of-state models -

More information

Solution Thermodynamics

Solution Thermodynamics Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs

More information

Introduction to Statistical Methods

Introduction to Statistical Methods Introducton to Statstcal Methods Physcs 4362, Lecture #3 hermodynamcs Classcal Statstcal Knetc heory Classcal hermodynamcs Macroscopc approach General propertes of the system Macroscopc varables 1 hermodynamc

More information

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law: CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and

More information

Effect of adding an ideal inert gas, M

Effect of adding an ideal inert gas, M Effect of adding an ideal inert gas, M Add gas M If there is no change in volume, then the partial pressures of each of the ideal gas components remains unchanged by the addition of M. If the reaction

More information

Supplementary Notes for Chapter 9 Mixture Thermodynamics

Supplementary Notes for Chapter 9 Mixture Thermodynamics Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects

More information

Chapter 5. Simple Mixtures Fall Semester Physical Chemistry 1 (CHM2201)

Chapter 5. Simple Mixtures Fall Semester Physical Chemistry 1 (CHM2201) Chapter 5. Simple Mixtures 2011 Fall Semester Physical Chemistry 1 (CHM2201) Contents The thermodynamic description of mixtures 5.1 Partial molar quantities 5.2 The thermodynamic of Mixing 5.3 The chemical

More information

Review of Classical Thermodynamics

Review of Classical Thermodynamics Revew of Classcal hermodynamcs Physcs 4362, Lecture #1, 2 Syllabus What s hermodynamcs? 1 [A law] s more mpressve the greater the smplcty of ts premses, the more dfferent are the knds of thngs t relates,

More information

Chapter 18, Part 1. Fundamentals of Atmospheric Modeling

Chapter 18, Part 1. Fundamentals of Atmospheric Modeling Overhead Sldes for Chapter 18, Part 1 of Fundamentals of Atmospherc Modelng by Mark Z. Jacobson Department of Cvl & Envronmental Engneerng Stanford Unversty Stanford, CA 94305-4020 January 30, 2002 Types

More information

The Euler Equation. Using the additive property of the internal energy U, we can derive a useful thermodynamic relation the Euler equation.

The Euler Equation. Using the additive property of the internal energy U, we can derive a useful thermodynamic relation the Euler equation. The Euler Equation Using the additive property of the internal energy U, we can derive a useful thermodynamic relation the Euler equation. Let us differentiate this extensivity condition with respect to

More information

Lecture 2 Grand Canonical Ensemble GCE

Lecture 2 Grand Canonical Ensemble GCE Lecture 2 Grand Canoncal Ensemble GCE 2.1 hermodynamc Functons Contnung on from last day we also note that thus, dω = df dµ µd = Sd P dv dµ (2.1) P = V = S = From the expresson for the entropy, we therefore

More information

Osmotic pressure and protein binding

Osmotic pressure and protein binding Osmotc pressure and proten bndng Igor R. Kuznetsov, KochLab Symposum talk 5/15/09 Today we take a closer look at one of the soluton thermodynamcs key ponts from Steve s presentaton. Here t s: d[ln(k off

More information

4.2 Chemical Driving Force

4.2 Chemical Driving Force 4.2. CHEMICL DRIVING FORCE 103 4.2 Chemcal Drvng Force second effect of a chemcal concentraton gradent on dffuson s to change the nature of the drvng force. Ths s because dffuson changes the bondng n a

More information

Introduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015

Introduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015 Introducton to Interfacal Segregaton Xaozhe Zhang 10/02/2015 Interfacal egregaton Segregaton n materal refer to the enrchment of a materal conttuent at a free urface or an nternal nterface of a materal.

More information

Thermodynamic Variables and Relations

Thermodynamic Variables and Relations MME 231: Lecture 10 Thermodynamic Variables and Relations A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Thermodynamic relations derived from the Laws of Thermodynamics Definitions

More information

Name: SID: Discussion Session:

Name: SID: Discussion Session: Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 141 -- Fall 007 Thursday, November 15, 007 Mdterm II SOLUTIONS - 70 mnutes 110 Ponts Total Closed Book and Notes (0 ponts) 1. Evaluate whether

More information

Gasometric Determination of NaHCO 3 in a Mixture

Gasometric Determination of NaHCO 3 in a Mixture 60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)

More information

Electrochemical Equilibrium Electromotive Force

Electrochemical Equilibrium Electromotive Force CHM465/865, 24-3, Lecture 5-7, 2 th Sep., 24 lectrochemcal qulbrum lectromotve Force Relaton between chemcal and electrc drvng forces lectrochemcal system at constant T and p: consder Gbbs free energy

More information

Thermodynamics General

Thermodynamics General Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,

More information

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014 Lecture 12 7/25/14 ERD: 7.1-7.5 Devoe: 8.1.1-8.1.2, 8.2.1-8.2.3, 8.4.1-8.4.3 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 2014 A. Free Energy and Changes n Composton: The

More information

Thermodynamics and statistical mechanics in materials modelling II

Thermodynamics and statistical mechanics in materials modelling II Course MP3 Lecture 8/11/006 (JAE) Course MP3 Lecture 8/11/006 Thermodynamcs and statstcal mechancs n materals modellng II A bref résumé of the physcal concepts used n materals modellng Dr James Ellott.1

More information

I wish to publish my paper on The International Journal of Thermophysics. A Practical Method to Calculate Partial Properties from Equation of State

I wish to publish my paper on The International Journal of Thermophysics. A Practical Method to Calculate Partial Properties from Equation of State I wsh to publsh my paper on The Internatonal Journal of Thermophyscs. Ttle: A Practcal Method to Calculate Partal Propertes from Equaton of State Authors: Ryo Akasaka (correspondng author) 1 and Takehro

More information

Non-Ideality Through Fugacity and Activity

Non-Ideality Through Fugacity and Activity Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,

More information

modeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products

modeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products modelng of equlbrum and dynamc mult-component adsorpton n a two-layered fxed bed for purfcaton of hydrogen from methane reformng products Mohammad A. Ebrahm, Mahmood R. G. Arsalan, Shohreh Fatem * Laboratory

More information

Some properties of the Helmholtz free energy

Some properties of the Helmholtz free energy Some properties of the Helmholtz free energy Energy slope is T U(S, ) From the properties of U vs S, it is clear that the Helmholtz free energy is always algebraically less than the internal energy U.

More information

Assignment 4. Adsorption Isotherms

Assignment 4. Adsorption Isotherms Insttute of Process Engneerng Assgnment 4. Adsorpton Isotherms Part A: Compettve adsorpton of methane and ethane In large scale adsorpton processes, more than one compound from a mxture of gases get adsorbed,

More information

NUMERICAL DIFFERENTIATION

NUMERICAL DIFFERENTIATION NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the

More information

Be true to your work, your word, and your friend.

Be true to your work, your word, and your friend. Chemstry 13 NT Be true to your work, your word, and your frend. Henry Davd Thoreau 1 Chem 13 NT Chemcal Equlbrum Module Usng the Equlbrum Constant Interpretng the Equlbrum Constant Predctng the Drecton

More information

Envr 210, Chapter 3, Intermolecular forces and partitioning Free energies and equilibrium partitioning chemical potential fugacity activity coef.

Envr 210, Chapter 3, Intermolecular forces and partitioning Free energies and equilibrium partitioning chemical potential fugacity activity coef. Envr 20, Chapter 3, Intermolecular forces and parttonng Free energes and equlbrum parttonng chemcal potental fugacty actvty coef. phase transfer- actvty coef and fugactes more on free energes and equlbrum

More information

Chemistry. Lecture 10 Maxwell Relations. NC State University

Chemistry. Lecture 10 Maxwell Relations. NC State University Chemistry Lecture 10 Maxwell Relations NC State University Thermodynamic state functions expressed in differential form We have seen that the internal energy is conserved and depends on mechanical (dw)

More information

( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.

( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2. Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.

More information

Entropy generation in a chemical reaction

Entropy generation in a chemical reaction Entropy generaton n a chemcal reacton E Mranda Área de Cencas Exactas COICET CCT Mendoza 5500 Mendoza, rgentna and Departamento de Físca Unversdad aconal de San Lus 5700 San Lus, rgentna bstract: Entropy

More information

Mass Transfer Processes

Mass Transfer Processes Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.

More information

y i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem

y i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem SOLUTION TO HOMEWORK #7 #roblem 1 10.1-1 a. In order to solve ths problem, we need to know what happens at the bubble pont; at ths pont, the frst bubble s formed, so we can assume that all of the number

More information

MS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7

MS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7 2017 Spring Semester MS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7 Byungha Shin ( 신병하 ) Dept. of MSE, KAIST Largely based on lecture notes of Prof. Hyuck-Mo Lee and Prof. WooChul

More information

A Self-Consistent Gibbs Excess Mixing Rule for Cubic Equations of State: derivation and fugacity coefficients

A Self-Consistent Gibbs Excess Mixing Rule for Cubic Equations of State: derivation and fugacity coefficients A Self-Consstent Gbbs Excess Mxng Rule for Cubc Equatons of State: dervaton and fugacty coeffcents Paula B. Staudt, Rafael de P. Soares Departamento de Engenhara Químca, Escola de Engenhara, Unversdade

More information

NAME and Section No.

NAME and Section No. Chemstry 391 Fall 2007 Exam I KEY (Monday September 17) 1. (25 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). Defne the terms: open system, closed system and solated system

More information

Lecture 8. Chapter 7. - Thermodynamic Web - Departure Functions - Review Equations of state (chapter 4, briefly)

Lecture 8. Chapter 7. - Thermodynamic Web - Departure Functions - Review Equations of state (chapter 4, briefly) Lecture 8 Chapter 5 - Thermodynamc Web - Departure Functons - Revew Equatons of state (chapter 4, brefly) Chapter 6 - Equlbrum (chemcal potental) * Pure Component * Mxtures Chapter 7 - Fugacty (chemcal

More information

Statistical mechanics handout 4

Statistical mechanics handout 4 Statstcal mechancs handout 4 Explan dfference between phase space and an. Ensembles As dscussed n handout three atoms n any physcal system can adopt any one of a large number of mcorstates. For a quantum

More information

Solutions Review Worksheet

Solutions Review Worksheet Solutons Revew Worksheet NOTE: Namng acds s ntroduced on pages 163-4 and agan on pages 208-9.. You learned ths and were quzzed on t, but snce acd names are n the Data Booklet you wll not be tested on ths

More information

Vapor-Liquid Equilibria for Water+Hydrochloric Acid+Magnesium Chloride and Water+Hydrochloric Acid+Calcium Chloride Systems at Atmospheric Pressure

Vapor-Liquid Equilibria for Water+Hydrochloric Acid+Magnesium Chloride and Water+Hydrochloric Acid+Calcium Chloride Systems at Atmospheric Pressure Chnese J. Chem. Eng., 4() 76 80 (006) RESEARCH OES Vapor-Lqud Equlbra for Water+Hydrochlorc Acd+Magnesum Chlorde and Water+Hydrochlorc Acd+Calcum Chlorde Systems at Atmospherc Pressure ZHAG Yng( 张颖 ) and

More information

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2015

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2015 Lecture 2. 1/07/15-1/09/15 Unversty of Washngton Department of Chemstry Chemstry 453 Wnter Quarter 2015 We are not talkng about truth. We are talkng about somethng that seems lke truth. The truth we want

More information

The Second Law of Thermodynamics (Chapter 4)

The Second Law of Thermodynamics (Chapter 4) The Second Law of Thermodynamics (Chapter 4) First Law: Energy of universe is constant: ΔE system = - ΔE surroundings Second Law: New variable, S, entropy. Changes in S, ΔS, tell us which processes made

More information

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2013

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2013 Lecture 8/8/3 Unversty o Washngton Departent o Chestry Chestry 45/456 Suer Quarter 3 A. The Gbbs-Duhe Equaton Fro Lecture 7 and ro the dscusson n sectons A and B o ths lecture, t s clear that the actvty

More information

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014 Lecture 16 8/4/14 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 214. Real Vapors and Fugacty Henry s Law accounts or the propertes o extremely dlute soluton. s shown n Fgure

More information

Chapter 5 rd Law of Thermodynamics

Chapter 5 rd Law of Thermodynamics Entropy and the nd and 3 rd Chapter 5 rd Law o hermodynamcs homas Engel, hlp Red Objectves Introduce entropy. Derve the condtons or spontanety. Show how S vares wth the macroscopc varables,, and. Chapter

More information

Q e E i /k B. i i i i

Q e E i /k B. i i i i Water and Aqueous Solutons 3. Lattce Model of a Flud Lattce Models Lattce models provde a mnmalst, or coarse-graned, framework for descrbng the translatonal, rotatonal, and conformatonal degrees of freedom

More information

A Modulated Hydrothermal (MHT) Approach for the Facile. Synthesis of UiO-66-Type MOFs

A Modulated Hydrothermal (MHT) Approach for the Facile. Synthesis of UiO-66-Type MOFs Supplementary Informaton A Modulated Hydrothermal (MHT) Approach for the Facle Synthess of UO-66-Type MOFs Zhgang Hu, Yongwu Peng, Zx Kang, Yuhong Qan, and Dan Zhao * Department of Chemcal and Bomolecular

More information

and Statistical Mechanics Material Properties

and Statistical Mechanics Material Properties Statstcal Mechancs and Materal Propertes By Kuno TAKAHASHI Tokyo Insttute of Technology, Tokyo 15-855, JAPA Phone/Fax +81-3-5734-3915 takahak@de.ttech.ac.jp http://www.de.ttech.ac.jp/~kt-lab/ Only for

More information

The ChemSep Book. Harry A. Kooijman Consultant. Ross Taylor Clarkson University, Potsdam, New York University of Twente, Enschede, The Netherlands

The ChemSep Book. Harry A. Kooijman Consultant. Ross Taylor Clarkson University, Potsdam, New York University of Twente, Enschede, The Netherlands The ChemSep Book Harry A. Koojman Consultant Ross Taylor Clarkson Unversty, Potsdam, New York Unversty of Twente, Enschede, The Netherlands Lbr Books on Demand www.bod.de Copyrght c 2000 by H.A. Koojman

More information

The Standard Gibbs Energy Change, G

The Standard Gibbs Energy Change, G The Standard Gibbs Energy Change, G S univ = S surr + S sys S univ = H sys + S sys T S univ = H sys TS sys G sys = H sys TS sys Spontaneous reaction: S univ >0 G sys < 0 More observations on G and Gº I.

More information

Chapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc.

Chapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Chapter 3 Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Concepts Energy functions F and G Chemical potential, µ Partial Molar properties

More information

V T for n & P = constant

V T for n & P = constant Pchem 365: hermodynamcs -SUMMARY- Uwe Burghaus, Fargo, 5 9 Mnmum requrements for underneath of your pllow. However, wrte your own summary! You need to know the story behnd the equatons : Pressure : olume

More information

Chapter 3 Thermochemistry of Fuel Air Mixtures

Chapter 3 Thermochemistry of Fuel Air Mixtures Chapter 3 Thermochemstry of Fuel Ar Mxtures 3-1 Thermochemstry 3- Ideal Gas Model 3-3 Composton of Ar and Fuels 3-4 Combuston Stochometry t 3-5 The1 st Law of Thermodynamcs and Combuston 3-6 Thermal converson

More information

CONVECTION AND MATTER TRANSPORT PROCESSES REVIEW: CLOSED SYSTEM

CONVECTION AND MATTER TRANSPORT PROCESSES REVIEW: CLOSED SYSTEM CONVECTION AND MATTER TRANSPORT PROCESSES REVIEW: CLOSED SYSTEM Simple substance i.e., no reacting components internal energy U = U(S,V,m) constant mass makes this a two-port capacitor one port for each

More information

PETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium

PETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium ETE 30 Lectures # 24 & 25 Chapter 2 Gas Lqud Equlbrum Thermal Equlbrum Object A hgh T, Object B low T Intal contact tme Intermedate tme. Later tme Mechancal Equlbrum ressure essels Vale Closed Vale Open

More information

applied to a single-phase fluid in a closed system wherein no chemical reactions occur.

applied to a single-phase fluid in a closed system wherein no chemical reactions occur. The basc relaton connectng the Gbbs energy to the temperature and pressure n any closed system: (ng) (ng) d(ng) d dt (nv)d (ns)dt T T,n appled to a sngle-phase flud n a closed system wheren no chemcal

More information

Computation of Phase Equilibrium and Phase Envelopes

Computation of Phase Equilibrium and Phase Envelopes Downloaded from orbt.dtu.dk on: Sep 24, 2018 Computaton of Phase Equlbrum and Phase Envelopes Rtschel, Tobas Kasper Skovborg; Jørgensen, John Bagterp Publcaton date: 2017 Document Verson Publsher's PDF,

More information

Process Modeling. Improving or understanding chemical process operation is a major objective for developing a dynamic process model

Process Modeling. Improving or understanding chemical process operation is a major objective for developing a dynamic process model Process Modelng Improvng or understandng chemcal process operaton s a major objectve for developng a dynamc process model Balance equatons Steady-state balance equatons mass or energy mass or energy enterng

More information

TP A SOLUTION. For an ideal monatomic gas U=3/2nRT, Since the process is at constant pressure Q = C. giving ) =1000/(5/2*8.31*10)

TP A SOLUTION. For an ideal monatomic gas U=3/2nRT, Since the process is at constant pressure Q = C. giving ) =1000/(5/2*8.31*10) T A SOLUTION For an deal monatomc gas U/nRT, Snce the process s at constant pressure Q C pn T gvng a: n Q /( 5 / R T ) /(5/*8.*) C V / R and C / R + R 5 / R. U U / nr T (/ ) R T ( Q / 5 / R T ) Q / 5 Q

More information

Physics 607 Exam 1. ( ) = 1, Γ( z +1) = zγ( z) x n e x2 dx = 1. e x2

Physics 607 Exam 1. ( ) = 1, Γ( z +1) = zγ( z) x n e x2 dx = 1. e x2 Physcs 607 Exam 1 Please be well-organzed, and show all sgnfcant steps clearly n all problems. You are graded on your wor, so please do not just wrte down answers wth no explanaton! Do all your wor on

More information

Topic 3 : Thermodynamics

Topic 3 : Thermodynamics GEOL360 LECTURE NOTES: T3 : THERMODYNAMICS 1/20 GEOL360 Topc 3 : Thermodynamcs 3.1 Introducton and vocabulary Thermodynamcs deals wth the physcal and chemcal changes of matter due to work and hear flow

More information

Mixtures. Partial Molar Quantities

Mixtures. Partial Molar Quantities CHEM 331 Physical Chemistry Fall 2017 Mixtures Our current discussion takes up some general results for systems that are mixtures and/or open. The former involve systems that contain multiple components;

More information

Identify the intensive quantities from the following: (a) enthalpy (b) volume (c) refractive index (d) none of these

Identify the intensive quantities from the following: (a) enthalpy (b) volume (c) refractive index (d) none of these Q 1. Q 2. Q 3. Q 4. Q 5. Q 6. Q 7. The incorrect option in the following table is: H S Nature of reaction (a) negative positive spontaneous at all temperatures (b) positive negative non-spontaneous regardless

More information

Chem 2A Exam 1. First letter of your last name

Chem 2A Exam 1. First letter of your last name Frst letter of your last name NAME: PERM# INSTRUCTIONS: Fll n your name, perm number and frst ntal of your last name above. Be sure to show all of your work for full credt. Use the back of the page f necessary.

More information

10.40 Appendix Connection to Thermodynamics and Derivation of Boltzmann Distribution

10.40 Appendix Connection to Thermodynamics and Derivation of Boltzmann Distribution 10.40 Appendx Connecton to Thermodynamcs Dervaton of Boltzmann Dstrbuton Bernhardt L. Trout Outlne Cannoncal ensemble Maxmumtermmethod Most probable dstrbuton Ensembles contnued: Canoncal, Mcrocanoncal,

More information

Module 3: The Whole-Process Perspective for Thermochemical Hydrogen

Module 3: The Whole-Process Perspective for Thermochemical Hydrogen "Thermodynamc Analyss of Processes for Hydrogen Generaton by Decomposton of Water" by John P. O'Connell Department of Chemcal Engneerng Unversty of Vrgna Charlottesvlle, VA 2294-4741 A Set of Energy Educaton

More information

Basic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos

Basic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos Introducton to Toshhsa Ueda School of Scence for Open and Envronmental Systems Keo Unversty, Japan Combuston Mxng and reacton n hgh vscous flud Applcaton of Chaos Keo Unversty 1 Keo Unversty 2 What s reactve

More information

CHEMICAL ENGINEERING

CHEMICAL ENGINEERING Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton

More information

Lecture 10: Euler s Equations for Multivariable

Lecture 10: Euler s Equations for Multivariable Lecture 0: Euler s Equatons for Multvarable Problems Let s say we re tryng to mnmze an ntegral of the form: {,,,,,, ; } J f y y y y y y d We can start by wrtng each of the y s as we dd before: y (, ) (

More information

4) It is a state function because enthalpy(h), entropy(s) and temperature (T) are state functions.

4) It is a state function because enthalpy(h), entropy(s) and temperature (T) are state functions. Chemical Thermodynamics S.Y.BSc. Concept of Gibb s free energy and Helmholtz free energy a) Gibb s free energy: 1) It was introduced by J.Willard Gibb s to account for the work of expansion due to volume

More information

Using Spectrophotometric Methods to Determine an Equilibrium Constant Prelab

Using Spectrophotometric Methods to Determine an Equilibrium Constant Prelab Usng Spectrophotometrc Methods to Determne an Equlbrum Constant Prelab 1. What s the purpose of ths experment? 2. Wll the absorbance of the ulbrum mxture (at 447 nm) ncrease or decrease as Fe soluton s

More information

3) Thermodynamic equation to characterize interfaces

3) Thermodynamic equation to characterize interfaces 3) Thermodynamc equaton to characterze nterfaces 3.1) Gbbs Model Realty: rapd contnuous change of chemcal and thermodynamc propertes Replaced by model (constant propertes up to the surface) uv bulk uv

More information

Lecture 16 Statistical Analysis in Biomaterials Research (Part II)

Lecture 16 Statistical Analysis in Biomaterials Research (Part II) 3.051J/0.340J 1 Lecture 16 Statstcal Analyss n Bomaterals Research (Part II) C. F Dstrbuton Allows comparson of varablty of behavor between populatons usng test of hypothess: σ x = σ x amed for Brtsh statstcan

More information

Department of Physical Chemistry, Faculty of Chemistry, University of Bucharest, Bd. Regina Elisabeta 4-12, , Bucharest, Romania

Department of Physical Chemistry, Faculty of Chemistry, University of Bucharest, Bd. Regina Elisabeta 4-12, , Bucharest, Romania ISOTHERMAL LIQUID-VAOR EQUILIBRIUM IN ACETONITRILE-WATER SYSTEM Rodca Vlcu, Zoca Cenuse abstact: The study of ths system started from the mportance that acetontrle has as the component of some mxtures

More information

MME 2010 METALLURGICAL THERMODYNAMICS II. Partial Properties of Solutions

MME 2010 METALLURGICAL THERMODYNAMICS II. Partial Properties of Solutions MME 2010 METALLURGICAL THERMODYNAMICS II Partial Properties of Solutions A total property of a system consisting of multiple substances is represented as nm = n i M i If the system consists of a liquid

More information

Thermodynamics. Section 4

Thermodynamics. Section 4 Secton 4 Thermodynamcs Hendrck C. Van Ness, D.Eng., Howard. Isermann Department of Chemcal Engneerng, Rensselaer olytechnc Insttute; Fellow, Amercan Insttute of Chemcal Engneers; Member, Amercan Chemcal

More information

CHEMISTRY Midterm #2 answer key October 25, 2005

CHEMISTRY Midterm #2 answer key October 25, 2005 CHEMISTRY 123-01 Mdterm #2 answer key October 25, 2005 Statstcs: Average: 70 pts (70%); Hghest: 97 pts (97%); Lowest: 33 pts (33%) Number of students performng at or above average: 62 (63%) Number of students

More information

Chapter 4: Partial differentiation

Chapter 4: Partial differentiation Chapter 4: Partial differentiation It is generally the case that derivatives are introduced in terms of functions of a single variable. For example, y = f (x), then dy dx = df dx = f. However, most of

More information

Modelli Clamfim Equazioni differenziali 22 settembre 2016

Modelli Clamfim Equazioni differenziali 22 settembre 2016 CLAMFIM Bologna Modell 1 @ Clamfm Equazon dfferenzal 22 settembre 2016 professor Danele Rtell danele.rtell@unbo.t 1/22? Ordnary Dfferental Equatons A dfferental equaton s an equaton that defnes a relatonshp

More information

5.60 Thermodynamics & Kinetics Spring 2008

5.60 Thermodynamics & Kinetics Spring 2008 MIT OpenCourseWare http://ocw.mt.edu 5.60 Thermodynamcs & Knetcs Sprng 2008 For nformaton about ctng these materals or our Terms of Use, vst: http://ocw.mt.edu/terms. 5.60 Sprng 2008 Lecture #29 page 1

More information

Biophysical Chemistry

Biophysical Chemistry Bophyscal Chemstry 155 (211) 89 13 Contents lsts avalable at ScenceDrect Bophyscal Chemstry ournal homepage: http://www.elsever.com/locate/bophyschem Recommendatons for termnology and databases for bochemcal

More information

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng

More information

Physics 115. Molecular motion and temperature Phase equilibrium, evaporation

Physics 115. Molecular motion and temperature Phase equilibrium, evaporation Physcs 115 General Physcs II Sesson 9 Molecular moton and temperature Phase equlbrum, evaporaton R. J. Wlkes Emal: phy115a@u.washngton.edu Home page: http://courses.washngton.edu/phy115a/ 4/14/14 Physcs

More information

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look

More information

Relationship between Refractive Index and Molar Concentration of Multi-Component Solutions Zhu Xingyu 1, a, Mai Tiancheng 2, b and Zhao Zilong 2, c

Relationship between Refractive Index and Molar Concentration of Multi-Component Solutions Zhu Xingyu 1, a, Mai Tiancheng 2, b and Zhao Zilong 2, c Advances n Computer Scence Research, volume 71 4th Internatonal Conference on Machnery, Materals and Informaton Technology Applcatons (ICMMITA 2016) Relatonshp between Refractve Index and Molar Concentraton

More information