A Method of Predicting the Thermal Conductivity of Some Hydrogen

Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1968 A Method of Predicting the Thermal Conductivity of Some Hydrogen Bonded Binary Solutions That Form Bimolecular Complexes Clayton Phillips Kerr Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Kerr, Clayton Phillips, "A Method of Predicting the Thermal Conductivity of Some Hydrogen Bonded Binary Solutions That Form Bimolecular Complexes." (1968) LSU Historical Dissertations and Theses 1496 https://digitalcommons.lsu.edu/gradschool_disstheses/1496 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons For more information, please contact gradetd@lsu.edu This dissertation h as b een microfilmed exactly as received 69-4479 KERR, Clayton P h illip s, 1939A METHOD OF PREDICTING THE THERMAL CONDUCTIVITY OF SOME HYDROGEN BONDED BINARY SOLUTIONS THAT FORM BIMOLECULAR COMPLEXES Louisiana State U niversity and Agricultural and M echanical C ollege, Ph.D., 1968 Engineering, chem ical University Microfilms, Inc., Ann Arbor, Michigan A Method of Predicting the Thermal Conductivity of Some Hydrogen Bonded Binary Solutions That Form Bimolecular Complexes A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Chemical Engineering by Clayton Phillips Kerr B.S., University of Oklahoma, M.S., Louisiana State University, 6 August, ACKNOWLEDGMENT The author is very grateful to Dr Jesse Coates, Professor of Chemical Engineering, for his guidance and assistance in carrying out this research The author wishes to acknowledge the financial support of the Department of Chemical Engineering and the National Science Foundation for financial support Grateful acknowledgment is made to the Dr Charles E Coates Memorial Foundation, donated by George H Coates, for financial support in publishing this dissertation Special thanks are due Miss Margaret Ann Koles for her skill and patience in typing the final copy The work of Mr Ronald W Ward in performing literature surveys and calculations is also acknowledged TABLE OF CONTENTS PAGE ABSTRACT ix CHAPTER I II III INTRODUCTION I REVIEW OF PREVIOUS WORK A Pure Liquids B Binary Solutions T C Reacting Mixtures THEORY 15 A The Nature and Types of Hydrogen Bonding 15 B Diffusion and Conduction Contributions to Thermal Conductivity l8 C Simplifying Assumptions 20 D Development of an Equation for Predicting Excess Thermal Conductivity 26 Recapitulation of Simplifying Assumptions 33 E IV DESCRIPTION OF APPARATUS AND OPERATING PROCEDURE 38 A Description of Apparatus 38 B Procedure h8 V EXPERIMENTAL RESULTS 51 VI DISCUSSION OF RESULTS 69 A Discussion of Errors 69 B Qualitative Discussion of Results 69 CHAPTER PAGE C D VII Spectroscopic Evidence for the Formation of Bimolecular Hydrogen Bonded Complexes 70 Sources of Data for Calculating Excess Thermal Conductivity 71 CONCLUSIONS AND RECOMMENDATIONS 95 A Conclusions 95 B Recommendations for Further Work SELECTED BIBLIOGRAPHY 97 APPENDIX A B C D E ERROR IN APPROXIMATING A FUNCTION WITH A INTERPOLATING POLYNOMIAL HERMITE 102 VIBRATIONAL FREQUENCY FOR A LINEAR HARMONIC OSCILLATOR 105 FREQUENCY RATIO FOR TWO SIMILAR M0LECU1AR SPECIES BASED ON A RIGID SPHERE MOLECULAR INTERACTION 108 THERMAL CONDUCTIVITY RATIOS FOR RIGID MOLECULES WITH SIMILAR SIZES AND SHAPES 112 EVALUATION OF THE EQUILIBRIUM CONSTANT FROM ACTIVITY COEFFICIENT DATA Ilk F NOMENCLATURE 117 G THERMAL CONDUCTIVITY VALUES UNCORRECTED FOR TEMPERATURE 119 AUTOBIOGRAPHY 125 iv LIST OF TABLES TABLE I II III IV V VI VII VIII IX X XI XII XIII XIV PAGE Solution Thermal Conductivity for Methyl Ethyl Ketone-Chloroform 53 Solution Thermal Conductivity for AcetoneChloroform 5^ Solution Thermal Conductivity for BenzeneChloroform 55 Solution Thermal Conductivity for 1,2 dichloroethaneMethyl Ethyl Ketone 56 Solution Thermal Conductivity for Ethyl Ether Chloroform 57 Solution Thermal Conductivity for Isopropyl Ether-Chloroform 58 Solution Thermal Conductivity for Diethyl Ketone-Chloroform 59 Solution Thermal Conductivity for TolueneChloroform 60 Solution Thermal Conductivity for Methyl Isobutyl Ketone-Chloroform 6l Effect of Increasing Steric Hindrance on the Excess Thermal Conductivity for Several KetoneChloroform Solutions Predicted Versus Experimental Excess Thermal Conductivity for the Chloroform-Isopropy1 Ether System 75 Predicted Versus Experimental Excess Thermal Con­ ductivity for the Methyl Ethyl Ketone-Chloroform System 76 Predicted Versus Experimental Excess Thermal Conductivity for the Acetone-Chloroform System 77 Predicted Versus Experimental Excess Thermal Conductivity for the Benzene-Chloroform System 78 TABUS XV XVI XVII XVIII XIX XXI XXII XXIII XXIV XXV XXVI PAGE Predicted Versus Experimental Excess Thermal Conductivity for the Ethyl Ether-Chloroform System 79 Predicted Versus Experimental Excess Thermal Conductivity for the Toluene-Chloroform System 80 Predicted Versus Experimental Excess Thermal Conductivity for the Diethyl Ketone-Chloroform System 81 Predicted Versus Experimental Excess Thermal Conductivity for the 1,2 dichloroethaneMethyl Ethyl Ketone System 82 Predicted Versus Experimental Excess Thermal Conductivity for the Chloroform-Methyl Isobutyl Ketone System 83 Experimental Thermal Conductivity Values for Mixtures of Chloroform and Methyl Ethyl Ketone 119 Experimental Thermal Conductivity Values for Mixtures of Chloroform and Toluene 120 Experimental Thermal Conductivity Values for Mixtures of Chloroform and Methyl Isobutyl Ketone 121 Experimental Thermal Conductivity Values for Mixtures of Chloroform and Diethyl Ketone 122 Experimental Thermal Conductivity Values for Mixtures of 1,2 dichloroethane and Methyl Ethyl Ketone 123 Experimental Thermal Conductivity Values for Mixtures of Chloroform and Isopropyl Ether 124 vi LIST OF FIGURES FIGURE PAGE Structure of Acetic Acid Dimer l8 Thermoconductimetric Apparatus for Liquids 39 General View 1+0 1+ Top View of Hot Bar, Water Connections, Micrometers, and Jack Screws i+1 Cell Disassembled 1+2 Cell Assembled 1+3 Hot and Cold Baths, Water Circulators, and Thermoregulators 1+1+ Precision Refractometer 1+5 Thermal Conductivity versus Composition for Mixtures of Isopropyl Ether and Chloroform at 25°C and Atm 62 10 Thermal Conductivity versus Composition 63 11 Thermal Conductivity versus Comgosition for Mixtures of Benzene and Chloroform at 20 C and Atm 61+ Thermal Conductivity versus Composition for Mixtures of Ethyl Ether and Chloroform at 25°C and Atm 65 Thermal Conductivity versus Comgosition for Mixtures of Acetone and Chloroform at 25 C and Atm 66 ll+ Thermal Conductivity versus Composition 67 15 Excess Thermal Conductivity versus Mole Fraction for the Chloroform-Isopropy1 Ether System 8k Excess Thermal Conductivity versus Mole Fraction for the Toluene-Chloroform System 85 Excess Thermal Conductivity versus Mole Fraction for the Chloroform-Ethyl Ether System 86 12 13 16 17 vii FIGURE 18 19 20 21 22 25 PAGE Excess Thermal Conductivity versus Mole Fraction for the Methyl Ethyl Ketone - 1,2 Dichloroethane System 8? Excess Thermal Conductivity versus Mole Fraction for the Acetone-Chloroform System 88 Excess Thermal Conductivity versus Mole Fraction for the Chloroform-Benzene System 89 Excess Thermal Conductivity versus Mole Fraction for the Methyl Ethyl Ketone-Chloroform System 90 Excess Thermal Conductivity versus Mole Fraction for the Chloroform-Diethyl Ketone System 91 Excess Thermal Conductivity versus Mole Fraction for the Chloroform-Methyl Isobutyl KetoneSystem 92 APPENDIX D THERMAL CONDUCTIVITY RATIOS FOR RIGID MOLECULES WITH SIMILAR SIZES AND SHAPES Equation (3-37) should be applicable to the prediction of the ratio of thermal conductivities of pure liquids whose molecules are approximately rigid and which have similar shapes and sizes For example, molecular species such as benzene and toluene which have similar sizes and shapes, the binding constants should be equal and the frequency ratios should be inversely proportional to the square root of molecular weight The distance between centers can be obtained from density and molecular weight data Ma \Ma Mb \ The result is: Mb Pa Ma Pb A test of the above relation for similar substances is shown below: Substances Ma Mb Mb P a ku \ mT Ma Pb Source of Thermal Conductivity Data 0.919 0.872 Methyl Ethyl Ketone Methyl Isobutyl Ketone* 1.178 1.248 Author Ethyl Ether* Isopropyl Ether 1.310 1.303 Ethyl Ether-2 Isopropyl EtherAuthor Cyclohexane* Methyl Cyclohexane ikz 1.140 Chlorobenzene* Bromobenzene 1.15 1.195 Iodobenzene* Bromobenzene O.9 O 0.872 Chlorobenzene* Iodobenzene 1.268 1.385 Benzene Toluene Refers to component a 112 APPENDIX D REFERENCES N V Tsederberg, Thermal Conductivity of Gases and Liquids, (Cambridge, Massachusetts: M.I.T Press, Massachusetts Institute of Technology, ) p 1992 L P Fillippov and N S Novoselova, "The.Thermal Conductivity of Solutions of Normal Mixtures," Vestnik Moskovskogo Universiteta, Seriya Fiziko-Matenatecheskikhi Estestvennykk Nauk, No j X (1955), P 37 113 APPENDIX E EVALUATION OF THE EQUILIBRIUM CONSTANT FROM ACTIVITY COEFFICIENT DATA The formation of the hydrogen bonded complex A B from the acid A and the base B will be written as A + B s AB The equilibrium mixture of A,B, and AB will be assumed to be ideal The chemical potential of component A written in terms of the actual mole fraction of A is: l-'A = ^a ( T ’P ) + R T l n XA • The chemical potential of component A can also be written in terms of the apparent mole fraction of A and an activity coefficient ^A: M*A = M-A^T,pN; + R T l n Y a xa ° Equating these two results: i M-a (T,P) + RT In 11 y a xa ° = M-a (T,P) + RT In xA When xA = 1, the activity coefficient yA equals unity and " hence (J«a (T,P) = p-A (T,P), Therefore: RT In Ya x a° = RT In xA Hence the activity coefficient is the ratio of the actual mole fraction to apparent mole fraction: 115 An equilibrium constant K will be defined as: K A B For each mole of complex formed, a mole of acid or base is consumed: where nA = nA nAB nB = nB nAB n ^ is the number of moles ofcomplex are respectively the moles of acid and formed, n^ and n° base initiallypresent, and n^ and n^ are respectively the number of moles of acid and base present at equilibrium From the preceding, the mole fractions of each component can be expressed as: x A X B x AB nA " nAB o , o nA B nAB o i nB " nAB o , o nA B nAB nAB o , o nA B nAB Making use of the above and equation (-5), the equilibrium constant can be expressed as: " K = ' ya YA(!-2x° + yAx° ) APPENDIX E REFERENCES ■*T Prigogine, Chemical Thermodynamics, (London: Green, and Co., 195*0 > P • 116 Longmans, APPENDIX F NOMENCLATURE a Distance between centers ofmolecules c Total molar concentration D lm Mutual diffusion coefficient of component i in a mixture m D3 Mutual diffusion coefficient of component in infinitely dilute in o D3i Mutual diffusion coefficient of component in infinitely dilute in f Hooke's law constant HL Partial molal enthalpy I< Equilibrium constant ki Thermal conductivity of component k2 Thermal conductivity of component k3 Thermal conductivity of component k£ Thermal conductivity without chemical reaction ks Thermal conductivity of the solution M Molecular weight N^ Molar flux- R Gas constant U Velocity of sound V Molar volume x Mole fraction z Distance 117 li8 Greek Symbols K Boltzmann1 v Frequency p density constant APPENDIX G THERMAL CONDUCTIVITY VALUES UNCORRECTED FOR TEMPERATURE Table XXI Experimental Thermal Conductivity Values for Mixtures of Chloroform and Methyl Ethyl Ketone M o l e F r a ction C hloroform Temperature F Sol u t i o n T h e r m a l Conductivity at 25°C 0 0 42 0.0853 0.0870 0.2171 0.0754 0.0770 0.4261 O.O7 0.0719 O 6 87.27 0 O.O 0.8154 87.19 o.o64o O.O V 0 0 87.24 0 0.0671 Thermal conductivity has units of BTU/(HR)(FT)(°F) 119 120 Table XXII E xperi m e n t a l Therma l C o n d u c t i v i t y Values for Mixtures of C h l o r o f o r m and Tolu e n e Mole Fraction Chloroform Temperature F Solution Thermal Conductivity 0.0000 87.40 0.0777 O.O7 8 87.33 0.0718 0.0728 4 87.31 0.0665 0.0676 6624 87.24 0.0637 0 1.0000 87.24 O.O 65 0 Thermal conductivity has units of BTU/(HR)(FT)(°F) Thermal Conductivity at 25°C 121 Table XXIII Experimental Thermal Conductivity Values for Mixtues of Chloroform and Methyl Isobutyl Ketone Mole Fraction Chloroform Temperature F 0 0 87.33 0.0730 0.0739 6 87.30 O.O O 9 87.35 0.0667 0.0679 0.6840 8 O.O O 0 6 87.24 0.0643 0 6 0.84-75 8 o.o64o 0 0 0 87-24 0 0 Solution Thermal Conductivity Thermal conductivity has units of BTU/(HR)(FT)(°F) * at 25°C Table XXIV Experimental Thermal Conductivity Values for Mixtures of Chloroform and Diethyl Ketone Mole Fraction Chloroform Temperature F 0 0 87.23 0 0 0.24l4 87.05 0.0747 0.0755 O A 566 87.07 0.0707 0.0717 0.6572 0 0.0684 0.8478 0.0664 0 7 0 0 87.24 0 0 Solution Thermal Conductivity Thermal conductivity has units of BTU/(HR)(FT)(0F ) Thermal Conductivity at 25°C 123 Table XXV Experimental Thermal Conductivity Values for Mixtures of 1,2 dichloroethane and Methyl Ethyl Ketone Mole Fraction 1,2 dichloroethane Temperature F Solution Thermal Conductivity Thermal Conductivity at 25°C 0 0 ^ 0.0853 0.0870 20 2 0.0815 O.O8 O k27k- 8 0 0 6 3 ^ 0.0772 0.0783 0.8305 k 0.0767 0 7 0 0 87.29 0.0773 0 o Thermal conductivity has units of BTU/(HR)(FT)(°F) 12k Table XXVI Experimental Thermal Conductivity Values for Mixtures of Chloroform and Isopropyl Ether M o l e F r a ction Chloroform T e mperature F Sol u t i o n T h e r m a l ' Conductivity T h e r m a l Conductivity at 25 °C 0.0000 87.10 0.0606 0608 0.2963 O.O588 0.0594 O.536O 87.18 0.0600 0.0606 0.8 77 2 0.0625 O.O638 1.0000 87.24 0659 0.06 Thermal conductivity has units of BTU/(HR)(FT)(°F) AUTOBIOGRAPHY The author was born February 27, 1939, in Picher, Oklahoma, the oldest of three sons of Clayton H and Mildred Phillips Kerr He attended the public schools of Miami, Oklahoma and graduated from Miami High School in 1957In September, 1957 the author enrolled in Northeastern A and M College in Miami, Oklahoma In June, 1958 the author enrolled at the University of Oklahoma at Norman, Oklahoma and subsequently graduated in June, 196 l with a Bachelor of Science Degree in Chemical Engineering From June until February, 19^5 the author was employed by Humble Oil and Refining Company in Baton Rouge, Louisiana as a chemical engineer In February, 1965 the author started graduate school in the Department of Chemical Engineering at Louisiana State University in Baton Rouge, Louisiana and was simultaneously appointed for one semester to fill a temporary vacancy as an undergraduate instructor of chemical engineering In August, 6 the author received a Master of Science Degree in Chemical Engineering The author is presently a candidate for the degree of Doctor of Philosophy in Chemical Engineering Upon graduation, the author plans to join the Department of Chemical Engineering at Tennessee Technological University in Cookeville, Tennessee as an assistant professor of chemical engineering 125 EXAMINATION A N D THESIS REPORT Candidate: Clayton Phillips Kerr Major Field: Chemical Engineering Title of Thesis: A Method of Predicting the Thermal Conductivity of Some Hydrogen Bonded Binary Solutions That Form Bimolecular Complexes Approved: a Major Professor and Chairman D ean of the Graduate School EXAMINING COMMITTEE: Date of Examination: J u ly 18, 1968 ... the case of thermal conductivity, the flux is heat and the driving force is the gradient of temperature An approximation to the thermal conductivity of binary solutions might be to take the thermal. .. and the deviation from the experimental values are often as high as lOOfo B Binary Solutions The thermal conductivity of real solutions is always less than the ideal thermal conductivity or the. .. Fick's Law and the conduction contribution to thermal conductivity is evaluated from the thermal conductivity of the pure components and an estimated value of the thermal conductivity of the complex