PHYSICAL PROPERTIES AND ASSOCIATION OF THE LIQUID HALOGEN FLUORIDES By Emerson E. Garver A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1957 ProQ uest Number: 10008509 All rights reserved INFO RM ATIO N TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy subm itted. In the unlikely event that the author did not send a com plete m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be removed, a note will indicate the deletion. uest ProQ uest 10008509 Published by ProQ uest LLC (2016). C opyright of the Dissertation is held by the Author. All rights reserved. This w ork is protected against unauthorized copying under Title 17, United States Code M icroform Edition © ProQ uest LLC. ProQ uest LLC. 789 East Eisenhow er Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346 ACKNOWLEDGMENT The author wishes to express his sincere appreciation to Professor Max T. Rogers, without whom this manuscript could not have been written. Throughout the course of this investigation he has offered encouragement, helpfulness and much-needed advice. He also wishes to make known his debt to J. L, Speirs for aid in instrumentation, to H. B, Thompson for his cogent observations, and to E, Forest Hood for some excellent glass blowing. The Atomic Energy Commission has made this work possible through a research grant. VITA Emerson E, Garver was born May 1, 1929 at Akron, Ohio. After attending Western Reserve Academy located at Hudson, Ohio, he spent one year at Swarthmore College and received the Bachelor of Science degree from Kent State University in 1951* He attended graduate school at the Ohio State University for a year and the following year enrolled at Michigan State University. He was a teaching assistant in chemistry 1952-3 and a research assistant from 1 9 5 U to 1 9 5 6 , Sigma Pi Sigma and Sigma Xi have honored him, and he is a member of the American Chemical Society. He will complete his work for the Doctor of Philosophy degree in the spring of 1957 with a major in physical chemistry and minors in inorganic chemistry, physics and mathematics. PHYSICAL PROPERTIES AND ASSOCIATION OF THE LIQUID HALOGEN FLUORIDES By Emerson E. Garver AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry Year Approved 195? ABSTRACT The viscosities of iodine pentafluoride, bromine pentafluoride, and bromine trifluoride have been determined over a temperature range of 15 to UO degrees Centigrade by means of a modified Ostwald viscometer made of Pyrex. The results have been fitted to a standard exponential equation which relates viscosity to the temperature, and various para­ meters such as energy, free energy, and entropy of viscous flow were computed. The results have been interpreted in terms of Eyring’s theory of viscous flow, and they indicate that bromine trifluoride, and to a lesser extent iodine pentafluoride, are associated liquids. Computations based on the data published thus far on the viscosity of iodine pentafluoride and chlorine trifluoride were included for the sake of com­ parison. Chlorine trifluoride and bromine pentafluoride are ’’normal” liquids. The surface tensions of iodine pentafluoride, bromine pentafluoride, and bromine trifluoride have been determined over the same temperature range by the capillary-rise method. The results were fitted to a standard, linear, surface tension-temperature relationship. Again the results indicated that bromine trifluoride, and perhaps iodine penta­ fluoride, are associated, while bromine pentafluoride and chlorine trifluoride are probably not. Various empirical relationships were employed to obtain estimated values of the critical temperatures of the'halogen fluorides. TABLE OF CONTENTS Page I. INTRODUCTION................................................ II. III. HISTORICAL REVIEW OF THE HALOGEN FLUORIDES................. THEORY....... '................................. Viscosity Surface Tension............... IV. V. .,. 2 8 8 Ill APPARATUS AND METHOD........................................ 19 Review of Methods....................................... Viscosity Measurements.......... Surface Tension Measurements......................... Construction Materials.................................. Apparatus............................................ Temperature Measurement and Control.................. Gas-Handling System. ............................. Procedure........................... Materials............................................ Treatment of Calibration Data........................... Viscosity Measurements .. ............................ Surface Tension Measurements. ..................... 19 19 22 2li 25 31 32 3h 37 38 38 U9 RESULTS AND DISCUSSION..................................... 93 Viscosity Measurements.................................. Results............................................... Treatment of Data .......................... Precision and Accuracy............................... Discussion............................................ Surface Tension Measurements ..................... Results .......................................... . Precision and Accuracy............................... Discussion........................................... VI. 1 SUMMARY................. 53 53 53 61 65 67 67 71 72 76 LITERATURE CITED................................... 77 APPENDICES..................... 83 vi LIST OF TABLES TABLE Page I . Melting and Boiling Points oT Halogen Fluorides........... II. Density-Temperature Relationships of Liquid Halogen Fluorides......... ........ . .................... h III. Dielectric Constants and Magnetic Susceptibilities of Liquid Halogen Fluorides.......................................... IV. 3 Molar Refractions and Electric Dipole Moments of Gaseous Halogen Fluorides................... 5 5 V. Viscosity Calibration Data for Apparatus III............... U2 VI. Viscosity Calibration Data for Apparatus I V ............... U3 VII. Data for Calculation of the Constant B ..................... bb VIII. Values of the Constant B ................................... 65 IX . Data for Calculation of Constant C Benzene inApparatus III. 66 X. XI. Data for Calculation of Constant C Waterin Apparatus IV..... 147 Calibration Data for Capillary Radii...................... 51 XII. Data to Check the Calibration of Pyrex Capillaries for use in Surface Tension Measurements............................ 52 XIII. Viscosity Data for Iodine Pentafluoride .............. 56 ....... 55 XIV. Viscosity Data for Bromine Pentafluoride. XV. Viscosity Data for Bromine Trifluoride............. •,...... ■ 56 XVI. Viscosities of Iodine Pentafluoride........................ 57 XVII. Viscosities of Iodine Pentafluoride fromApparatus I ....... 58 XVIII. Viscosities of Bromine Pentafluoride............ XIX. Viscosities of Bromine Trifluoride......................... XX. Thermodynamic Functions for Viscous Flow.................. vii 59 60 62 LIST OF TABLES - Continued TABLE Page XXI. Calculated and Observed Precision ofViscosity Results...... 63 XXII. The Surface Tensions ofIodine Pentafluoride................ 68 XXIII. The Surface Tensions of Bromine Pentafluoride.............. 69 XXIV. The Surface Tensions of Bromine Trifluoride................ 70 XXV. Calculated and Observed Precision of Surface Tension Results 71 XXVI. Surface Tension-Temperature Relationships for the Halogen Fluorides.................... .............................. 73 XXVII. Parachors of the Halogen Fluorides........................ 73 XXVIII. Atomic Parachors of the Central Halogen Atom............... 73 XXIX. Work of Cohesion of the Halogen Fluorides.................. 76 X X X . Estimated Critical Temperatures of the Halogen Fluorides (Centigrade)............................................... 76 XXXI. Viscosity and Surface Tension of the Halogen Fluorides at 20 C ........................................................ 76 a viii LIST OF FIGURES FIGURE Page 1. Ostwald Viscometer........................................ 20 2. Apparatus I for Measurement of Viscosity.................. 26 3. Apparatus III and IV for Measurement of Viscosity, and Surface Tension. ......... 29 U. Apparatus II for Measurement of Surface Tension.......... 30 5>. Vacuum System for Handling Halogen Fluorides............. 33 6 . Graph of 0 versus l/l for Apparatus III.................. I48 ix 1 INTRODUCTION The past ten years have seen considerable activity in the field of fluorine chemistry. The halogen fluorides, -which have excellent fluorinating abilities, have been widely used bat little information concerning their physical properties has been available. Although the great chemical reactivity that characterizes the halogen fluorides makes measurement of their physical properties difficult, modern techniques and materials now make accurate work possible. Two properties which it seemed desirable to determine are those of viscosity and surface tension. They give insight into the structure of the liquid phase, especially with regard to possible association. Accordingly, apparatus was designed and constructed to measure surface tension by the capillary-rise method and viscosity by the Ostwald method. Procedures were developed for measuring these proper­ ties with a precision of plus or minus one per cent or better over a temperature range of twenty-five centigrade degrees for those halogen fluorides that are liquids at room temperature. 2 HISTORICAL REVIEW The Halogen Fluorides In I8 7 O Gore (l) prepared the first halogen fluoride, iodine penta­ fluoride, Since that time five or six more such fluorides have been prepared. They are iodine heptafluoride, bromine pentafluoride, bromine trifluoride, chlorine trifluoride, chlorine monofluoride, and perhaps an unstable monofluoride of bromine. Ruff and Braida (2) suggested that, in the system bromine-bromine trifluoride, the species BrF existed. Fischer, ert ad. (3) in a study of the solid-liquid equilibria of the above system failed to find solid bromine monofluoride, but did demonstrate the existence of a different species, presumably bromine monofluoride, in the vapor of the above system (U). Iodine monofluoride has been detected only spectroscopically (5), and Aynsley, Nichols, and Robinson (6 ) observed a bright blue color which they attributed to an unstable trifluoride of iodine. Although the existence of such compounds is to be expected because halogen-halogen bonds are found in the elements themselves, the halogen fluorides possess unexpected thermal stability0 For example, bromine pentafluoride was found not to dissociate at temperatures as high as 350° C. (7). The great differences in electronegativities that exist among the halogens accounts in part for their stability. Since 1950 several review articles (8,9,10,11,12), as well as some books (7 ,1 3 ,lii,l5 )> concerning the chemistry of the halogen fluorides 3 have appeared, perhaps the most comprehensive being the two volumes edited by J. H, Simons (7*13). An excellent summary of the work pub­ lished to 195U has been given by Thompson (16). Therefore the emphasis in this review will be placed upon those physical properties that have been studied since 1 9 5 U. The melting points and boiling points of the halogen fluorides are summarized in Table I . Using highly purified iodine pentafluoride, R o g e rs eib aL., (17) found a freezing point of 9.U3° C, and a boiling point calculated from vapor-pressure measurements of 1 0 0 .5 ° C. Table II contains in summarized fashion the constants for empirical equations representing densities of liquid halogen fluorides as a func­ tion of temperature. It is unfortunate that more refined density measurements for iodine pentafluoride have not been made. TABLE I MELTING AND B O ILIN G POINTS OF HALOGEN FLUORIDES Compound if7 M.p., ° C. 6 B.p.j ° C. U.5 (subl.) 1 0 0 .5 9 , U3 BrF5 BrF 3 -60.5 8 -.75 J4 0 .7 125.75 CIF 3 -8 3 1 2 ,0 C1F -15U -1 0 0 .8 Other physical properties now known include the dielectric con­ stants, magnetic susceptibilities, molar refractions and electric dipole moments. They are listed in Table III and Table IV. Chlorine trifluoride was found to have a planar T-structure by Smith (30) from microwave spectroscopy. His results are supported by h TABLE II DENSITY-TEMPERATURE RELATIONSHIPS OF LIQUID HALOGEN FLUORIDES1 BrF5 BrF3 CIF3 18 2 19 a .38 3 .^ 96 3.623 2.729 o.ooa 0 . 003U6 0.00277 0.00307 Reference 20 21 22 a 2.3309 2.8311 1.8833 b 3 .U8U 2 .72 2.9U2U c 3.U3 0.00 3 .7 9 Compound IFs Reference 2 A B The liquid density in g./cc. is A-BT where_T is the absolute tempera­ ture, or in the second row, a-bxlO 3t -cxlO 6 t 2 where t is the temperature in degrees centigrade. X-ray diffraction work (31), infrared and Raman spectroscopic data (32), and electric dipole moment measurements (29). Rogers,,et a l .,(27) con­ firmed the dipole moment, hence supported the structure. Nuclear magnetic resonance absorption studies (3 3 ) at first failed to show the "chemical splitting" which is to be expected for a structure in which one fluorine atom is in a different electronic environment from the others (3 U),but later work (3 Ua) confirmed the planar structure of symmetry C 2V. The structure of bromine pentafluoride probably approximates an octahedron with one corner occupied by the unshared pair of electrons and all the fluorine atoms on the same side of a plane which passes 5 TABLE III DIELECTRIC CONSTANTS AND MAGNETIC SUSCEPTIBILITIES OF LIQUID HALOGEN FLUORIDES 1 Compound C1F3 X € b . 7 5h - 0 .0 l 8 t ( 2) 8 .2 0 - o.ouy t 10 (L M U l .09 - 0 .1 9 8 t e.g.s. units x 10 6 -26.5 (2 5) -33.9 (25) (23) -1*5.1 (25) (214) -58.1 (25) BrF 3 BrF 5 M 1 References are given in parentheses after the value. TABLE IV MOLAR REFRACTIONS AND ELECTRIC DIPOLE MOMENTS OF GASEOUS HALOGEN FLUORIDES 1 Compound M d GIF 7.6 2 (cc./mole) at t C. j 14 (Debye) 2h ° C . (26) 0. 8 8 ( 28 ) CIF 3 10.31* 26 0 C. ( 26 ) 0.551*, 0 . 6 5 (29,27) BrF 3 13 .22 25 0 c. ( 26 ) 1 .1 9 (27) BrF 5 1 5 . 1*1 25 0 c. (2 6 ) 1. 5 1 (23) 7.62 2h ° C. (2 6 ) 2.18 (2 7) 1 References are given in parentheses after the value. 6 through the bromine atom and is perpendicular to the fourfold axis of symmetry. Mellish and Linnett (350 draw the above conclusion from their observations on directed valency; they show that in the fluorides some factor is operating which is more important than the mutual repul­ sion of the fluorine atoms and which causes a decrease in the bond angles. They cited in support of the above structure that infrared and Raman spectra (36) indicate a similar symmetry for bromine pentafluoride and that the known structure of the SbF 5 the same as the one mentioned. ion in the compound K 2SbF5 is The nuclear magnetic resonance absorption spectrum indicates that one fluorine atom is bonded differently than the other four (3U?3Ua). Also, dipole moment studies (23) support the distorted octahedral structure. The electric dipole moment studies (27) are in agreement with a planar structure of C 2V symmetry for bromine trifluoride. Infrared studies (3 ?) support this structure. The most probable configuration for iodine pentafluoride is a dis­ torted octahedron in which the iodine atom is slightly displaced toward the corner occupied by the lone electron pair. The large measured dipole moment, 2.18 D, (27) eliminates any symmetrical configurations. magnetic resonance absorption data (3 U;,3 Ua) rule Nuclear out the pentagonal pyramidal form, because at least one fluorine atom is in a different electronic environment from the rest. Iodine heptafluoride is the only known molecule of the type AB 7 . A pentagonal bipyramidal structure has been inferred from the infrared 7 and Raman spectra (38), although again the nuclear magnetic resonance spectram (3 U) contraindicated this configuration when it failed to show the expected "chemical splitting" due to the two different positions occupied by fluorine atoms. 8 THEORY The liquid, state lacks a comprehensive theoretical development such as we have for the gaseous and solid states. The simplifying assumptions employed for the latter states do not apply well to liquids (39). Two properties which have helped elucidate the structure of the liquid state and the nature of the intermolecular forces are viscosity and surface tension. Viscosity may be defined as the resistance which a liquid exhibits to the flow of one layer over another (I4O). In 1867 Newton (Ul) postu­ lated that this resistence to the flow of the layers is independent of the pressure } proportional to the area, and proportional to the relative velocity. Most liquids conform to these assumptions and accordingly are known as Newtonian liquids. This discussion will be limited to them, Poiseuille (1*2 ) investigated the flow of water through capillary tubes and found the relationship 4 for the volume V flowing in time j , where C is a constant and P is the pressure difference between the ends of the tube of length L and radius r. For a given tube C was found to depend only on the temperature and upon the liquid used. many authors Equation (1) has since been theoretically deduced by and the coefficient of viscosity shown to be tt/ 8 1 (U2 ). - i The dimensions of the coefficient of viscosity are mass x length ■ x time _ i 9 and the unit, which is dyne-second per centimeter squared in the e.g.s. system, is the poise, after Poiseuille. viscosity, the fluidity, is used. Sometimes the reciprocal of In general it has more convenient valuess Kinematic viscosity is the viscosity divided by the density. Perhaps the most striking characteristic of viscosity is the rapid change observed when the temperature changes. An increase in temperature of 100 degrees Centigrade reduces the viscosity of water to one-tenth of its original value (U3 )j and for some fluorocarbons the change is even greater (Uh). Many formulae have been proposed to represent the viscositytemperature relationship. For example, Partington (Ul) lists 76 equations, most of which are strictly empirical, containing up to five arbitrary constants and relating viscosity to other physical properties such as density, molecular weight, vapor pressure, and heat of vaporization. One of the more useful empirical equations was proposed by Hovorka^et^ a l . } in analogy with Kirchoff!s formula for vapor pressure as a function 1 of temperature, log 0 = A-B/T -C *log T (2) where 0 is the fluidity and T is the absolute temperature. Some authors have regarded the change of viscosity with temperature as due entirely to volume effects. *1 = k / (v-b)° Macleod (U6 ) proposed the equation ^ 1 Throughout this thesis A, B, and C represent arbitrary constants. See Appendix A. 10 where v is the specific volume and b, the volume of the molecules them­ selves, is analogous to Van der Waal’s b, Mukherjee (U7) used the equation log 0 = A► Blog p(mm.) - 3/21og T (h) In 1930 Andrade (J48 ) introduced the equation B/T \ - Ae (9) He derived it by assuming a quasi-lattice structure for the liquid with flow taking place by smooth slippage between two sheets of molecules. Resistance to flow was assumed to originate from molecular agitation which was introduced statistically by the Boltzmann energy distribution. There have been many modifications of this formula (see 3 9 , ^1 and U9). Perhaps the most widely used form is that of Eyring and (9 0 ), whoconsidered viscous flow from the point of view of co-workers a chemical reaction that requires an energy of activation before a molecule flows past its neighbors into a vacant space. They deduced, after making certain assumptions about the energy barrier and distances between units of flow, that tLt n - — af*/rt e m where h ’ is Planck’s constant, N is Avogadro's number, is the molar volume, R is the universal gas constant, T is the absolute temperature, and A AF x is the standard free energy of activation per mole. - T & S^, where A and Since are the standard 11 enthalpies and entropies of activation. Equation (6 ) may be written e (7) = m If then A S t is assumed constant, since the molar volume does not vary much with temperature, Equation (6 ) reduces to Equation ( 9 ) . After making certain assumptions about the partition function in the liquid state, they showed that (8) m v where M is the molecular weight, is the experimentally observed activation energy per mole for viscous flow, ^ E is the energy of evaporation, and the other symbols have their previous meanings. At first glance the pre-exponential factor in Equation (8 ) is temperature dependent. However, Ewell (9l) has showed that this is not the case, and the term is essentially independent of the temperature. ®vis Although Is a slowly varying function of temperature, generally it varies less than experimental error— except close to the freezing point of the liquid (39). Also, as the exponent increases, the pre-exponential factor decreases (9 3 ). From data on a large number of liquids, Eyring found several empirical relations among the parameters in Equations (6 ), (7), and (8 ). The ratio of & E / ^ F^ is 2.U5 f o r most liquids, but it ranges from 1.7 to U.7 , the value for water. He suggested that when the ratio is not close to 2 .U9 the unit of flow is not the unit of evaporation (9 2 ). 12 For most non-polar molecules of spherical symmetry the ratio of A ^v/^Vis = n is in the neighborhood of three, whereas for polar molecules, the ratio is nearer four. Eyring (£2) proposed that l/n signifies the fraction of the size of a unit of flow which must be available as adjacent space in order for viscous flow to take place. "Whenever hydrogen bonding is present, n is generally less than three (5>2,5>3). However, it is 7.9 for molten cadmium chloride, which Harrap (5>U) interpreted as indicating that cadmium chloride in the liquid state exists to a certain extent as complex conglomerates that dissociate upon vaporization. Therefore the ratio n, as an indication of associ­ ation in the liquid state, must be used with caution. Association of any kind in liquids is evidenced by the fact that ^vis shows a marked temperature dependence. Also, although there is no direct relationship known, associated liquids tend to have higher values of E ^ g than "normal” liquids. Another method of showing whether association occurs in the liquid state was developed by Grunberg and Nissan (55>). They noted that if the work of cohesion, W^, in kcal./mole, as determined by the relationship, W where c = U.78 xlo ' 8 y V 2' 3 i f h m , (9) is the surface tension in dynes/cm., is divided into Ev ^_s , the ratio is approximately one. Since is found from static measure­ ments, it contains no energy terms derived from the breaking of bonds such as may be present in ^vis ■ ^or associated liquids, then, E ^ s is noticeably larger than the work of cohesion. 13 Obviously the viscosity of a liquid is dependent on the size and shape of molecules as well as the intermolecular forces. The first exhaustive attempt to relate the viscosity of a pure liquid to its chemical structure was by Rodger and Thorpe (56,57), who compared viscosities at different temperatures and at different reduced tempera­ tures but found trends only within homologous series. In analogy with the parachor (See Surface Tension), Friend and Hargreaves (58) proposed a "rheochor" [R] [R] = | V /o (10) [ft] was found to be an additive function of atomic rheochors, but the appearance of viscosity to the one-eighth power makes [R] insensitive to small changes in viscosities. For a wide range of liquids, Souder (5U) found that log(log where ^ ) = md-2.9 (11) is viscosity in millipoise , d is density in g./ce., and m is a constant which, when multiplied by the molecular weight, can be re­ solved into atomic and structural constants. The above relationships are only approximate. Some authors believe that no simple, true relation between viscosity and chemical structure can be found because of the complexity of the liquid state. Bondi (59) proposed that attempts to relate viscosity data to chemical structure by means of structural constants be limited to geometrically similar compounds. Frenkel (60) postulated that the activation energy Evis is lb the fundamental variable which is related to the structure of the liquid^ rather than the viscosity coefficient itself. For the viscosity of an ideal binary solution, Eyring (5 3) proposed the following relationship: 0m = v N 20 2 (12) where 0^ is the fluidity of the mixture and N stands for the molefraction of a component. According to Harrap (5b) * however, the viscosity- composition isotherms generally show negative deviations from linearity, even at low concentrations of one component. Eyring proposed that the activation energy of a mixture is also a linear function of the composi­ tion. That is, Evis= Ni *viBi - Nz (U) For non-ideal solutions Eyring added another term, N 1N 2 Evj_sl2, to express the effect of interaction between the components. According to Harrap (5b) there is no adequate means of estimating the magnitude of this term. Surface tension is the second mentioned physical property that has been used in investigating the liquid state and molecular structure. The surface tension of a liquid, Y , is the force per centimeter on the surface of a liquid which opposes the expansion of the surface area (bO). This force arises because the molecules at the surface are not attracted equally in every direction as those molecules in the body of the liquid are. There is a net attraction for the surface molecules 15 toward the bulk of the liquid resulting in the liquid assuming a shape with a minimum of surface area (6 l). Therefore, as can be seen intuitively, surface tension depends on the intermolecular forces of a liquid. In 192b Sugden (62) empirically derived a quantity from surface tension which he named the "parachor" [?]. It is obtained from the relation r ^ = M d-d' ^ where M is the molecular weight, d is the density of the liquid and d' is vapor density. When the vapor density is negligible in comparison 1/ with the liquid density, the parachor relationship reduces to 3 where is the molar volume. Therefore a comparison of parachors is equivalent to comparing molecular volumes at equal surface tensions (6 3 ). The parachor being a form of molecular volume, it is not surprising that Bayliss (6 U) found one parachor unit to be equivalent to the volume of o a sphere 0.210 A in radius. At first it was considered that the parachor of a compound could be obtained by adding together atomic constants, and this is roughly true. Using only the atomic constants, one can, calculate parachors which agree to within one or two per cent with observed values (62-). After it became evident that certain constitutive features, such as double bonds and steric effects, had to be taken into account, calculated values agreed to within 0 .2 per cent with observed values for most organic liquids (6 3 ). 16 Of necessity, the atomic and structural parachors are averages obtained from many compounds. Sugden (62), Quayle (6 3 ), Mumford and Phillips (65), and Vogel (6 6 ), all have published values which can be considered reliable for organic liquids. For inorganic liquids, however, some discrepancies appear. Liquid nitric oxide has a parachor twice the value calculated from the atomic constants determined from organic compounds (6 7 ). construct the parachor of phosphorus phosporus and phosporus trichloride. Nor is it possible to pentachloride from data on liquid "When atomic parachors are derived from compounds in which the central atom is in different valencies, different values are obtained. Samuel (6 8 ) proposed that separate atomic constants be assigned to each of the different valencies of an atom and showed that this procedure restored agreement between calculated and observed molecular parachors for inorganic liquids. However, as a result of these discrepancies and the relative insensitivity of the parachor to structure, it is not considered a reliable criterion for distinguishing between alternative structures. The parachor is useful in other ways. Herzog (6 9 ) has determined empirical relationships between the parachor and the critical constants of temperature, volume and pressure, and Langemann (70) has shown that there is a linear relationship between the parachor and molecular sound velocity, molar refraction, Souder’s viscosity constant m, and Van der Waal1s b . Although the parachor is generally insensitive to temperature changes, when it does change with temperature, it is probably as a 17 result of association in the liquid state. For a typical associated liquid, e.g. ethanol, the parachor increases from 12U.2 at -37° C. to 131.0 at 200 o C. 1 This behavior is probably due to the fact that the surface tensions vary more rapidly with temperature for associated liquids than for unassociated liquids. Another equation involving surface tension that has been widely applied is that proposed by Eotvos (71). ' / ( M v f t = k(tc-t) where t (15) is the critical temperature in ° C . and t is the temperature at which the surface tension and the specific volume v are measured. The constant k is 2.1 for most liquids, but it decreases to around unity for highly associated liquids. To fit the experimental data better, Ramsay and Shields (72) altered equation (15>) to ■^(Mv) = k(tc ~t-6 ) (T6 ) It was once thought that an association factor x could be obtained by the process of setting k equal to 2 . 1 for all liquids, solving for the molecular weight, and then calculating x from the ratio M(observed)/ M(simplest formula). However, as Partington (l|l) stated, "Although low values of k mean association, it is fairly well agreed that calculation of association factors from the Ramsay-Shields k is unjustified." Again inorganic liquids furnish unusual exceptions. The parachor of palladium in compounds of the type (RgS^ ^ ^ 2 ro03-113 X halogen) changes rapidly with temperature (73). 18 The variation of surface tension with temperature has no sound theoretical basis at the present. 'While experimental evidence indicates that many compounds have surface tensions that vary linearly with the temperature, there are many compounds for which the relationship is not linear over a large temperature range. Equations (17-20) are but a few of the empirical relationships proposed. reference (7U) y = A-BT y B = A(l-T/T ) (75) (1 8 ) = A-BT (76) (19) log 9^ - A i-B/T-ClogT (77) (20) 5/ I T 76 (17) Even though the surface tension disappears at or near the critical temperature, then, extrapolation of data to zero surface tension can yield but estimates of the critical temperature. 19 APPARATUS AND METHODS Review of Methods Viscosity Measurements Many methods have been developed for measuring viscosity. The shear of a liquid by rotating cylinders, oscillating bodies, falling bodies, and capillary tubes have been used. However, only a few methods can be treated with sufficient mathematical precision to warrant absolute measurements. The Ostwald type viscometer (Figure 1) is the simplest and most precise method. A known amount of liquid is drawn into the upper reservoir, and the time required for the meniscus to flow between two reference points is noted. to calculate the viscosity. Poiseuille's law, Equation (1), is then used Because the liquid head is the driving force, and it constantly changes, some sort of average head times the density is taken for the constant pressure. ^ ^ 1 “k 2 ) p p Meissner's formula (7 8 ), ^ Tni-prp /nn \ (21) where h x and h 2 are the hydrostatic heads at the beginning and the end of the flow, has been most often applied. Because of Poiseuille^ s equation it was assumed that there is no acceleration of the liquid as it flows through and that the liquid emerges from the capillary with zero velocity, two corrections are necessary for calculating absolute viscosities. Couette (hi) studied FIG U R E OSTWALD 1 VIS C O M E TE R 21 the consequences of the acceleration of the fluid entering the capillary from the reservoir, and he concluded that the length of the capillary should be increased by a factor 1.6Ur, where r is the radius. Also Hagenbach (79) derived a correction for the kinetic energy of the emerging liquid. Poiseuille’s equation then becomes 4 Because the factors mentioned above tend to cancel when two liquids are compared in the same apparatus, good relative measurements of viscosity are possible. If the same volume of sample is used, then Equation (1) becomes Adj (23) where A is a calibration constant of the instrument. A two-constant equation given by Barr (80) permits more accurate correction for the kinetic energy effect: = Cdj-Bd/j (21*) Two calibrating liquids are necessary to determine the constants B and C. Another method capable of yielding absolute results is the measure­ ment of the torque required to rotate a cylinder immersed in a liquid. Barr (80) and Fischer (81) have derived the equations which relate the viscosity to torquej they found ^ ^ 60 = m V X 1 PL X T (r .p'.m (25) where r is the radius and L the length of the cylinder, and T is the 22 torque which produces a constant rate of rotation measured in revolu­ tions per minute (r.p.m.). In Equation (25) ^ surface tension and end effects were neglected, but they can be minimized by proper design and manufacture of the apparatus. This method has been applied most successfully to systems of highly viscous liquids (8 1 ). Measurement of the rate of fall of a body through a fluid is another means of determining viscosities. Heiks and Orban (82) used a solid cylinder falling through a close-fitting tube to determine the viscosity of benzene up to the critical temperature. For measuring relative viscosities, they used the following equation: ■^ n^Q (c^o~8.2) Jo (26 ) where ( T represents the density of the solid cylinder, d the density of the liquid, j the time, and the subscript zero refers to a standard calibrating liquid. This method is suitable for high pressure and temperature investigations (82). Surface Tension Measurements The most accurate method for determining the surface tension of a liquid consists in measuring the height to which it rises in a capillary tube (UO). If the contact angle is less than 90° , the liquid rises until the force due to surface tension tending to pull up the liquid is balanced by the force of gravity. If 9 is the angle of contact between the wall and the liquid, the force.upward is 2 nr*y*cos 9, where r is the radius of the capillary, and 2nr is the perimeter. The force downward, 23 is the weight of the liquid above the bottom of the meniscus is neg­ lected, is rrr2hdg, where h is the rise, nr2h is the volume of the suspended liquid, d is the density of the liquid, and g is the accelera­ tion of gravity. At equilibrium the forces are equal, and 2tTr cos© = Trr2hdg, or } 2 cos 9 For very accurate work, certain corrections are made (See 77). A meniscus correction may be made by adding a term r/l to the measured height. The effect of vapors over the meniscus is accounted for by sub­ traction of the vapor density from the liquid density. When a capillary of radius r x is contained in another tube of radius r 2, the effective radius becomes the reciprocal of l/rx - l/r 3 (8 3 ). The method is capable of high precision only when the angle of contact is small or zero. This is a consequence of the fact, as Harkins (8U) claims, that contact angles can only be measured to within 25 per cent. With the above factors taken into account, Equation (27) becomes Y' = ■! nV~d '\ l/r2 / h 'r/3) 2 1/r-,- (28) Another method, often used because of its convenience, is called the maximum bubble-pressure method. A capillary tube, which has one end ground flat, is mounted vertically with that end immersed in the liquid, and an inert gas is forced through it. The pressure at which the bubbles break away from the tip has been reiateb to the surface tension by many 2k authors. In theory, this method should yield the greatest accuracy, because of the constant forming of a new surface in the body of the liquid. However, no exact expression has been developed. Two recent modifications of this method in which the pressure does not have to be measured are given by Shah and Pathak (85) and Cuny and Wolf (8 6 ). An obvious disadvantage of the maximum bubble-pressure method is that it cannot be applied in a sealed system. The drop-weight method of measuring surface tension consists of weighing a known number of drops falling slowly from the tip of a capillary. The weight has been related to the surface tension by factors described by Harkins (8 U), whose detailed studies have made this an accurate method. Many other methods have been used to measure surface tension (See 8I4), but they are of doubtful accuracy. Construction Materials The study of the physical properties of halogen fluorides, as it has been mentioned earlier, is hampered by their chemical reactivity. Materials for construction of equipment must be chosen to prevent corrosion and consequent contamination of the samples. Nickel and Monel metal are suitable for containing halogen fluorides in the liquid form, but once corroded, require mechanical action to clean the surface. brass are useful when the only contact is with the vapors. Copper and When visi­ bility is required, fluorothene (polychlorotrifluoroethylene), a plastic 25 that machines readily and is transparent when thin, is a possible construction material. It was once thought that the halogen fluorides attacked glass. However, iodine pentafluoride was prepared and stored in Pyrex 1 (8 7 ). Bankes and Maddock (2 0 ) found that chlorine trifluoride and bromine pentafluoride did not attack glass if all moisture was excluded. Also, Johnston, et al., (8 3 ) used Pyrex in their determination of the surface tension of fluorine at low temperatures. Bromine trifluoride 2 was found to react slowly with Pyrex, but not with Vycor. Therefore, glass or Vycor can be considered possible materials for constructing apparatus. Apparatus The first attempt to measure the viscosities was by the rotating cylinder method. The apparatus, which was designed and built by J. L. Speirs, is shown in Figure 2. It features good temperature control and direct reading of viscosities. 3 The upper part A was a Brookfield viscometer, which is powered by a small, self-starting, synchronous motor that drives the nickelplated spindle B at four different speeds. the motor is a beryllium-copper spring. Between the spindle and As the motor turns the spindle, the spring moves a pointer in proportion to the drag exerted on the Trademark of Corning Glass Works, Corning, N. Y. 2 3 Ibid. Model LVF made by Brookfield Engineering Laboratories, Inc., Stoughton, Mass. 26 FIG URE APPARATUS 2 I , V IS C O S IT Y I SUPPLY IN E R T COOLANT DRAIN C R O S S - S E C T IO N . SIDE 27 annular cylinder C. The cylinder, made of Monel, is 2.28 inches long, 1 . 5 8 0 inches in diameter, 0 . 0 6 5 inches thick, and rotates with a clearance of 0.030 inches. inches. It was machined to a tolerance of t 0.001 The length of the cylinder was adjusted uniil direct readings were obtained on the scale with water The cooling jacket and housing D as a standard. and all the lower partexcept the fluorothene level indicators E and F were constructed of Monel metal. In order to reproduce a constant levelof immersion for the cylinder, an overflow drain G was incorporated. The total volume of sample required for operation is 25 cc. The entire apparatus is suspended within a large tripod, andthe lower part supported on three adjustable legs by means of which the upper and lower parts can be aligned and leveled. For prefluorinating the apparatus, a seal around the spindle is necessary and is accomplished by screwing cap H down on washer J, forcing it against a Teflon gasket. A spring arrangement allows for the necessary extension in the spindle. cap H is raised, and the washer turns When the viscometer is operating, with the spindle. Toprovide an inert atmosphere, helium is blown over the liquid. A vacuum-tight seal was never attained, and corrosion products accumulated at points x. Although carbon tetrachloride was used to rinse out the viscometer, it could never be adequately cleaned, and corrosion became severe. For these reasons the method was employed. outlined below 28 The apparatus by which both the surface tension and the viscosity were measured is shown in Figure 3 . It was patterned after the one used by Doescher and Elvrum (7 8 ) when they determined these properties for liquid fluorine. To measure the surface tension, the rise in the capillary is observed, and to measure the viscosity, the time of flow through the capillary is obtained. In Apparatus III, used for measurements on iodine pentafluoride and bromine pentafluoride, the reservoir A holds 3cc. of liquid. cision -bore Pyrex capillary B is 3 / b mm. in diameter. The pre­ The outer shell or container C was readily constructed from a large, standard-taper glass joint D, which greatly facilitated cleaning. Through the bottom of C was inserted a thermocouple-well made of thin-wall tubing. The standard- taper joints F allow the apparatus to be attached to the gas-handling system described in a later section. In Apparatus IV, used for measurements on bromine trifluoride, the reservoir holds 8 cc. of liquid. Two capillaries were used. a precision-bore Pyrex capillary, again 3/U mm. in diameter. One was The other one, used for viscosity measurements, was made of Vycor and was 1.16 mm. in diameter. The container C is also made of Vycor. In other respects, Apparatus IV Is like Apparatus III. For surface tension measurements the first apparatus, Apparatus II (Figure U), was made from a block of fluorothene. The capillary was formed by a 1 / 3 2 inch drill extended by silver-soldering a length of steel wire to it. To provide thin walls for transparancy excess plastic was removed by milling. All joints were sealed with fluorothene wax to 29 FIG U R E 3. A P P A R A T U S HI AND I Y V I S C O S I T Y AND SU R FA C E TEN SIO N A, R E SER V O IR - 3 cc . in I I I , 8 c c . in I V . B, C A P I L L A R Y - 4 . 3 cm. in I I I , 7.7 c m . in I Y . D, T E, TH E R M O C O U P L E -W E L L F, 7 2 9 / 4 2 in I I I , "5 3 4 - / 4 9 1 0 / 3 0 in III a n d IY . in I Y . 30 F IG U R E 4 A P P A R A T U S II . S U R F A C E MADE A, R E S E R V O IR C . 3 /8 E ,F , X 5 /8 " 3 /8 AND PLUG 1/4" OF TEN SIO N FLUOROTHENE B / 1 /3 2 " D . 3/8 X 3 /8 " PLUGS C A P IL L A R Y PLUG 31 make vacuum-tight seals. When it became evident that bromine penta­ fluoride dissolved some of the wax and bromine trifluoride did not wet the plastic, this apparatus was rejected. Temperature Measurement and Control Temperature measurements were made with a copper-constantan thermo1 couple which was made by fusing together the ends of number 22 wire. 2 The output was measured on a precision potentiometer circuit. The icepoint reference was prepared by rinsing crushed ice with distilled water, then mixing the ice with de-ionized water in a clean Dewar flask. The potentials were converted to Centigrade degrees by interpolation on an expanded plot constructed from tables (8 8 ). The thermocouple was compared with a mercury thermometer previously calibrated by a platinum resistance thermometer 3 and was found to be accurate to ± 0.1 o C. Temperature control was maintained by means of two baths. The bath apparatus in which the viscosity-surface tension apparatus was immersed consisted of a clear Dewar flask that was detachable. In the bottom half of the flask was placed an aluminum coil through which water was circulated by a small, impeller-blade pump submerged in a five-gallon reservoir. The wires were purchased from the Wheelco Instrument Company, Chicago, 111. A type K-2 potentiometer with a type E galvanometer made by the Leeds and Northrup Company, Philadelphia, Pa. Appendix B contains the data for the calibration of the thermometer. 32 In addition to the pump, the second bath contained two knife-edge heaters serving as the heating elements. An auxiliary heater of 500-watts capacity, operated from an auto-transformer, served to heat the baths rapidly and to aid maintainance of temperatures from 30° C. to U5° C. A single 2^0-watt heater was controlled by the thermoregulating system and served to maintain the thermostat between 13 to 30° C. For temper­ atures less than room temperature and above 1 3 ° C ., a copper coil which circulated tap water was added. The thermoregulator was identical to the one described by Pruett (89). The temperature-sensitive element was a thermistor in a Wheatstone- bridge circuit, and the heater current was controlled by a saturable reactor. The circuit was an adaptation of that published by Burwell et_ al. (90). Regulation of the temperature was possible to ± 0.09° C. in the large reservoir and in the Dewar flask. The Gas-Handling System The vacuum system designed for the handling and final purification of the halogen fluorides is shown schematically in Figure 5- The viscosity-surface tension apparatus was attached at points A by means of 10/30 standard-taper joints, the male part being machined from Monel. At point B was a Monel Swagelok 1 union which allowed the apparatus to be tightened into place free of residual torque. Except for a copper expansion loop C, all tubing (l/U inch in Manufactured by the Crawford Fitting Company, Cleveland, Ohio. VACUUM SYSTEM FOR HANDLING HALOGEN FLUORIDES 33 hi K 3 CO CO ac uj CL o o< h- o fO -J -I X ® ® — 3k diameter) was made of Monel, as were the valves (Hoke model M1132). Valve E opened to the gas handling system described by Thompson (16). The only change from his description was the addition of a pro­ tective cold-trap placed before the vacuum pump. Although this trap was of Pyrex, no sign of etching occurred at any time. of liquid was allowed to accumulate. Not more than two cc . The remainder of the system is described in the following section. Procedure The entire system was first pre-fluorinated by the introduction of 2 chlorine trifluoride to a pressure of 500 mm, The gases were then pumped off, valves G and H closed and about 6 cc. of liquid drawn from the fluorothene storage container D into the Monel trap F. Valves J and K were closed, and, when valve G was opened, the liquid slowly vaporized into the rest of the system. The tube L contained sodium 3 fluoride pellets vapors. which removed any hydrogen fluoride present in the After an estimated 0.5 cc. of liquid had been pumped away, a Dry-ice-acetone mixture in a Dewar flask was raised around the cell, and solid distillation products allowed to collect on the glass walls. A fluorothene trap E was added to provide one additional stage of purification in the case of bromine trifluoride. 1 Manufactured by Hoke, Inc., Englewood, N. J. 2 . Pressure was measured by a Helicoid gage made by American Chain and Cable Company, Chicago, 111. 3 The l/ 8 inch pellets were purchased from the Harshaw Chemical Company, Cleveland, Ohio. 35 When enough material had collected in the cell (as solid) the distillation was halted by closing valve G, dry air was admitted, and the solid allowed to melt. If insufficient- sample had collected the liquid was distilled back into trap F, because an open capillary was necessary to maintain a pressure at which a reasonable rate of distil­ lation occurred. Next the thermocouple was attached and the thermostat raised into position. Thermal equilibrium was considered to be attained when successive measurements of the temperature at ten minute intervals showed no change. Capillary rise was measured by means of a cathetometer that was capable of measuring length to plus or minus 0.002cm. Before each measurement it was leveled, the cross-hairs aligned with a plumb-bob line, and the plumb of the capillary checked. At each temperature both levels of the liquid were determined from three to five times, depending upon how reproducible the readings appeared to be. Before each measurement the valves N and K were opened to equalize the pressure in both tubes of the apparatus and the meniscus was agitated to cause it to seek its own level. For viscosity measurements the reservoir was filled in two dif­ ferent ways. Either valve N was closed and dry air admitted through valve K to force the liquid up, or valve K was closed and the liquid was drawn up slowly by evacuating the reservoir througn. valve N. The methods were alternated to maintain a pressure as near to that of the atmosphere as possible, Great care was exercised to insure that the 36 lev-el of the liquid never rose high enough to touch the Monel standardtaper joint. Valve P was then closed, and the pressure was equalized in both sides of the viscometer by opening valve N or K (whichever was closed). The time of flow between the two marks made above and below the reservoir was measured with a stopwatch, 1 checked by time signals from station WWV. the accuracy of which was Measurements were repeated until three times were obtained which differed by no more than 0 . 1 seconds. Immediately after flow ceased, the temperatures were recorded, then the level of the capillary tip and level of liquid were determined by use of the cathetometer. A procedure for handling the halogen fluorides in glass was de­ veloped in this laboratory. All glass components were first cleaned, rinsed well with distilled water, and dried at 150° C. They were then assembled in position in the vacuum system, all ground joints being sealed with fluorothene wax. The system was evacuated to a pressure of 0 . 5 mm. or less and gently flamed, care being taken not to melt the wax. Next chlorine trifluoride was introduced to a pressure of 500 mm., and was condensed as a liquid wherever possible. New metal parts created a white fog which settled on the glass when the chlorine trifluoride was first introduced. However, the glass was not etched, if the process was done slowly, and the powder was easily removed by disassembling the apparatus and washing with water. \y p e N. Y. New apparatus required from two to 200B, made by A. R. and J. E. Meylan Stopwatch Co., New York, 37 three repetitions of the above process before no white powder appeared. To dispose of a sample of halogen fluoride, dry air was admitted to the cell, which was then removed from the system and the liquid poured into a fluorothene beaker and allowed to evaporate. The cell was immediately sealed back into position and evacuated to remove last traces of liquid. At this point the cell was ready to be cleaned. Materials All halogen fluorides were purchased from the Harshaw Chemical Company. They were purified by distillation in a Monel still described by Thompson (16) and then were stored in fluorothene beakers. Previous samples of halogen fluorides had been distilled in the same Monel still. According to Malik (91), iodine pentafluoride was 0 .0025 > mclal in impurities, bromine pentafluoride 0 .0 2 molal, and bromine trifluoride around 1-2 molal. Although the samples used here were a different lot, they were believed to have essentially the same concen­ tration of impurities, except for bromine trifluoride, which probably was less than one molal in impurities. The additional step of distill­ ation into the viscosity cell helped to eliminate previous impurities, but occasionally some dirt or water vapor in the cell would contaminate the liquid. Direct measurement of the impurity content of the material in the apparatus was not possible since it was not designed for precision melting point measurements. A useful qualitative criterion of purity was the color of the sample. If the apparatus was not prefluorinated, highly colored reaction products 38 of the halogen fluorides appeared. Mien iodine pentafluoride was pure it was colorless, and when it was contaminated it assumed a yellowish to light blue tinge. Colorless bromine pentafluoride took on a faint yellow tinge which became orange upon further contamination, and bromine trifluoride, straw-yellow when pure, turned first a bright orange, then a cherry-red as the concentration of impurities increased. For iodine pentafluoride and bromine pentafluoride no observable increase in the flow time was noted with the appearance of a slight color. For bromine trifluoride, however, bubbles appeared, smooth operation of the viscometer was impeded, and no further readings were recorded on that sample. Another part of the procedure in checking for impurities was noting any residue left in the apparatus in those cases where the sample was not immediately disposed of but distilled into some container. Only for bromine trifluoride did a visible residue ever appear in the apparatus. Treatment of Calibration Data Viscosity Measurements The calibration of the cell for viscosity measurements involved few changes in the procedure and apparatus from that already described for handling the halogen fluorides. The gas-handling system was altered by removal of the sodium fluoride and by the substitution of a different vacuum pump. Instead of the calibration liquids being distilled into the cell, they were poured in after several rinsings were made. Also, to reduce chance of contamination, no wax was used to seal the joints. 39 Because the volume of halogen fluoride distilled into the cell differed for each sample, it was necessary to know precisely the effect of the level of the liquid upon the time of flow. Therefore, the apparatus was calibrated with different amounts of liquid, the height of the surface above the tip of the capillary tube being measured by the cathetometer , At each level the times of flow were determined as a function of temperature over a 20 degree range. Apparatus H I tetrachloride. (Figure 3) was calibrated with benzene and carbon Although water was tried, its surface tension prevented complete drainage of the reservoir. However, in Apparatus IV, (Figure 3) the Vycor capillary was sufficiently long to allow the use of water, and benzene was used for the second calibrating fluid. The water samples were from the laboratory distilled water supply, i further purified by passage through an ion-exchange column. Its conductivity indicated less than one part per million impurities. The benzene, Baker’s A. R. Grade, was partially crystallized then distilled from calcium hydride in an efficient packed-column. At 25 C. the density was found to be 0 . 8 7 3 5 5 g*/cc*> about the mean of the values listed by Egloff (92). The carbon tetrachloride, Baker’s A. R. Grade, was distilled over calcium chloride in the previously mentioned packedcolumn, its boiling-point range being 7 6 .O-7 6 .5 pressure. C. at 723.8 mm. All liquids were used shortly after purification. Deeminizer, product of Crystal Research Laboratories, Inc., Hartford, Conn. 2 The benzene was supplied by Dr. T, L. Brown. iiO A check on the purity of these calibration liquids was made on each sample in ments. If the apparatus by meansof the surface tension measure­ the value differed by more than 0.3 dyne/cm. from the accepted value, the sample was discarded and the apparatus cleaned. The data obtained are listed in Tables V and V I . In order to find the constants B and C in Equation (2U)^ first log dj was plotted versus the reciprocal of the absolute temperature. A family of straight, parallel lines resulted, one line for each level of liquid used. When the vertical distances between lines for a single liquid were compared, it became obvious that the intercepts were directly proportional to the level of liquid in the apparatus. Therefore all time-density data for one liquid were condensed into one empirical equation of the form log dj = I* - b +■ c(m-f) (29) where a is the slope, m is the liquidlevel or mark, and b, c, f are constants. The constant f is actually the lowest mark measured for the calibrating liquids, and the constant b is the intercept calculated for that level. Calculations of the slopes and intercepts were done by a least squares method described by Wilson (93). For Apparatus III, log dj - U00/T-0.026U + O.llU(m-l.OO) (30) dj = U96/T-0.3U90 ^ 0 ,0h6(m-l.75) (3i) For Apparatus IV, By means of Equation (30) or (3 1 ) the flow-times of one calibrat­ ing liquid were calculated for those liquid levels at which flow-times were measured for the second liquid. Then the constant B was calculated from the equation given by Barr (80) j2 ) i .8*2 d1 (32) where the subscripts refer to the different calibration liquids and the other symbols have their previous meanings. Pertinent data for these calculations are listed in Tables VII and VTII. The values of density and viscosity were obtained by interpolation from graphs of literature data versus the temperature. For benzene and carbon tetrachloride values from Timmermans (9U) were used^ and for water values from the Handbook of Chemistry and Physics (95) were used. Next the constant C was calculated at each temperature and level of liquid used experimentally, by means of the following equation: C - % ♦ Bd/.j dj (33) Data from which C was calculated are listed in Tables IX and X. Unlike the constant B 5 which was a constant of the apparatus under all con­ ditions y the constant C was a function of temperature and of the level of liquid. When C was plotted versus the reciprocal of the absolute temperature a family of lines was obtained as shown in Figure 6. Values of C were read directly from such a graph. b2 TABLE V VISCOSITY CALIBRATION DATA FOR APPARATUS III Sample Benzene Benzene Level Mark (cm .) I II 1.0 1.5 Millivolts 1.101 1.000 1.002 23,6 2h.? 1.618 1.608 20.9 20.7 1.630 20.7 l.U 2I4.8 2 h. 7 21.8 21.7 21.7 21.0 0.(19 26.8 28.6 0.720 O.76 I4 28.5 28.1 1.0U7 1.0U7 26.3 0.990 1.517 1.525 1.5U6 1.556 III 23.7 23.7 0.780 0.780 0.777 1.350 1.350 1.350 1.587 1.290 1.286 Benzene Time (sec.) 26.h 25.2 25.1 2 J4.3 2 h .2 214.0 23.9 1.060 I.OI46 25.6 25.7 1.058 25.6 0.807 27.0 27.1 29. U 29.2 29. h 2I4.O 23.9 0.810 0.582 0.582 0.580 1.U67 1.U90 1.130 1.310 1.310 2h. U 214.5 2 I4 .U 53 TABLE VI VISCOSITY CALIBRATION DATA FOR APPARATUS IV Sample Level Mark (cm.) Water I 1.75 Water II 2.59 Millivolts 0.526 0.550 0.575 0.790 0.795 0.795 1.035 1.037 I.OJ4O 1.335 1.335 1.335 1.539 1.126 1.126 0.735 0.735 1.502 1.502 1.502 Water III 2.20 2.20 2.21 2.22 Benzene I Benzene II 2.32 2. Ul 0.630 0.630 0.892 0.898 0.898 1.105 1.320 1.322 1.322 0.990 0.992 O .989 0 .665 Time (sec .) 25.5 25.3 25.1 21 .9 21.9 21.9 20.5 20.5 20.3 18.7 18./ 18.6 17.7 21 .3 21.5 25.5 25.3 19.2 19.3 19.3 25.5 25.5 22.5 22 .5 22.5 21.5 19.5 19 .6 19.5 18.6 18.6 18.7 0.667 O .669 19.7 19 .6 19.6 0.690 1.118 19.7 18.8 hh TABLE VII DATA FOR CALCULATING CONSTANT B Liquid Level Mark (cm.) Temp. °c. Density g./cc. Time (sec .) , cp. Apparatus Ill Benzene 1.30 1.30 1.10 19.7 26.3 26.8 33.5 19.3 0.879 0.872 0.872 0.865 25.3 •26.9 25.2 23.7 0.880 25.6 0 .652 0 .591 0 .587 0 .532 0 .656 1.30 1.30 1.30 1.30 1.10 19.7 26.3 26.8 33.5 19.3 1.595 1.582 1.581 1.568 1.596 23.1 21.9 21.8 20.8 22.1 0 .977 0 .891 0 .887 0 .811 0 .986 1.30 1 .30 Carbon Tetra­ chloride Apparatus IV Benzene 2.32 2 .32 2.Ul 2.hi 2h.8 17.0 25.7 17.6 0.07h O.88I4 0.873 0.882 22.0 19.6 18.8 19.7 0 .603 0 .682 0 .596 0 .675 Water 2.32 2h.8 17.0 25.7 0.997 0.999 0.997 0.999 22.0 2h .7 22.0 2h.h 0 .898 1 .083 0 .880 1 .066 2.32 2.hi 2.hi 17.6 66 TABLE VIII VALUES OF THE CONSTANT B Level Mark, cm. Apparatus III Temp., C. B 1,30 19.7 2.08 1.30 26.3 1.30 Apparatus IV Temp.. °C . B 2.32 25 5.09 2.03 2 .32 17 5.59 26.8 1.8? 2.61 26 5.U1 1.30 33.6 2 .0l| 2.61 17 5.10 1.10 19.3 2.26 Average 2.1 Average 5.3 Level Mark, c m . TABLE IX DATA FOR CALCULATION OF THE CONSTANT C BENZENE IN APPARATUS III Level Mark (c m .) 1.00 1.50 103 T 0 3.318 3.3^0 3.350 3.1413 3 .1+11+ 3.1+15 3.257 3.257 3.257 3.199 3.191 3.191+ 3.187 3.353 3.1+31 3.1+31 3.1+17 3-338 3.338 3.273 3.271+ 3.216 3.211+ 3.209 3.208 1.50 —^ K. 3.331+ 3.338 3.331+ 3.1+05 3.1+05 3.1+01+ 3.1+71 3.1+71 3.1+72 3.228 3.223 3.221+ 3.268 3.268 7£c p. 0.598 0.600 0.600 0.651 0.652 0.653 0.530 0.530 0.530 0.1+86 0 .1+81 0.1+83 0.1+79 0.602 0.667 O .667 0.655 0.590 0.590 0.51+2 0.51+3 0.1+99 0.1+98 0.1+91+ 0.1+93 0.588 0.590 0.588 0.61+3 0.61+3 0.61+2 0.709 O .709 0.710 0.508 0 .501+ 0.505 0.538 0.538 Density g./cc. dj g.-sec,/cc . C 0.873 0.873 0.873 0.879 0.879 0.880 0.865 0.865 0.865 0.858 0.858 0.858 0.857 20.55 20.59 20.59 21.82 21.85 21.86 18.90 18.90 18.90 17.91 17.78 17.83 17.72 0.0328 0.0329 0.0329 0.0332 0.0332 0.0333 0.0325 0.0325 0.0325 0.0319 0.0320 0.0319 0.0319 O .878 0.881 0.881 0.880 0.872 20.78 25.29 25.29 25.97 23.22 23.22 21.87 21.89 20.75 20.71 20.62 20.60 0.0322 0.0289 0.0289 0.0288 0.0285 0.872 0.866 0.866 0.860 0.860 0.860 0.859 0.872 0.872 O .872 0.879 0.879 O .878 0.885 0.885 0.885 0.861 0.861 0.861 0.865 0.865 22.53 22.61 22.53 23.51 23.51 23.59 25.56 25.56 25.59 20.55 20.3U 20.36 21.20 21.20 0. 02 83 0.0281 0.0281 0.0276 0.0271 0.0276 0.0276 0.0293 0.0 2 9 2 0. 0 2 9 3 0. 03 02 0.0302 0.0302 0.0302 0. 030 2 0. 0 3 0 2 0.0285 0.0285 0.0285 0.0289 0.0289 b7 TABLE X DATA FOR THE CALCULATION OF THE CONSTANT C WATER IN APPARATUS IV Level Mark (cm.) 103 T o -1 K. *1 CP- Density g./cc. C g.-sec,/cc. 3.U88 3 .1*81 3.b73 3.U09 3.U08 3.U08 3.3bl 3.3U1 3.350 3.262 3.262 3.262 3.210 1.187 1.168 1.11*9 1.002 1.000 1.000 0.871 0.871 0.870 O.7I46 O.7J46 0.7l|6 0.677 0.999 0.999 0.999 0.998 0.998 0.998 0.997 0.997 0.997 0.995 0.995 0.995 0.993 2b. 05 23 .86 23.61 21.97 21.95 21.95 20.33 20.33 20.30 18.58 18.58 18.58 17 .51 0.0566 0.0566 0.0556 0.0556 0.0557 0.0553 0.0553 0.055U 0.0556 2,h9 3.317 3.317 3.1*26 3.U23 3.220 3.220 3.220 0.831 0.831 1.037 1.033 0.689 0.689 0.689 0.996 0.996 0.999 0.999 0.993 0.993 0.993 21.39 21.39 2b.23 2b. 15 19.15 19.15 19.23 0 .05 0 b 0 .05 0 b 0.0518 0.0518 0.0503 0. 0 5 0 2 0.0501 2.21 3.U58 3.U51 3.381 3.379 3.379 3.3b7 3.265 3.265 3.265 1.327 1.310 1.180 1.176 1.176 1.127 1.020 1.019 1.020 0.999 0.999 0.998 0.998 0.998 0.997 0.995 0.995 0.995 2u.ao 2U .21 0.05bb 0.05bl 22.31 0.0527 0. 05 27 0.0527 0 .052 b 0.0520 0.0520 0.0520 1.75 22.32 22 .32 21.51 19.61 19.61 19.61 0.0583 0.0581 0.0579 0.0566 o o’ h9 The precision of the calibrations was checked by calculating the viscosities of the calibrating liquids from experimental data and com­ paring them with values given in the literature. The root-mean-square 1 deviation was 0.005 cp. for Apparatus III and 0.011 cp. for Apparatus IV. Surface Tension Measurements The radii of all capillaries were measured using the method of Young which is summarized by Harkins (8U). By means of a glass pipette which 2 had a f i n e , curved tip, a column of mercury placed in the clean capillary. about 5 cm. in length was A travelling microscope was used to measure the length of the column to within 0.01 mm. Then the mercury was weighed and its volume determined from the known density of mercury at room temperature. If it were not for the volume of the menisci, the volume of the column divided by its length would give the mean cross section of the capillary. Instead of that calculation being made, a slug of mercury approximately 2.5 cm, in length was introduced into one-half of the section formerly occupied by the column. This length was measured, the slug weighed, and the mean radius of the initial section not then occupied was given by the formula w 1-w2 v2 (3U) The root-mean-square deviation cT is calculated from the expression where A is the difference of a single observation from the nT average, n 1 the number of observations. Triply distilled mercury was purchased from the Chicago Apparatus Co., Chicago, 111. 50 where w x and w 2 are respectively the weights of the column and the slug of mercury, l x and 1 2 the respective lengths, and d is the density of mercury at room temperature. Finally a bead of mercury 1.2 cm. in length was introduced into a section of known radius . The length as it was measured in that section was assumed to be correct, and the percentage deviation from that length as the bead was moved stepwise down the capillary, was calculated. The radius was assumed to vary by the same percentage. Because the precision-bore Pyrex capillary tubing was found to be more uniform in radius than required considering the precision of the cathetometer readings, the mean radius was used directly. Although the Vycor tubing was never used for surface tension measurements, a two-foot length was calibrated in order to locate a 9 cm. length with the smallest radius. The data for this are listed in Table XI. For checking the values of the radii, the surface tension of the benzene was determined at room temperature. Data for this calibration is summarized in Table XII. The close agreement between the calculated values and those interpolated from Sugden's (62) data is probably fortuitous. The formula used was the same as that used by Johnston} et al. (8 3 ) , (35) where r x is the radius of the capillary and r2 is the radius of the larger tube. 51 TABLE XI CALIBRATION DATA FOR CAPILLARY RADII Reference Tip j |-— Part 1 - Part 2 • Part n «----------- \— \ * • i v • Pyrex III Vycor IV Pyrex IV Room Temperature, °C. 21^.0 23.5 22 .1 Density of Mercury, g./cc. 13.536 13.538 13.551 Length of Column, mm. 65.161 53.681 58.25 0.3818 Weight of Column, g. 0.6375 0.3692 Length of Slug in Part 1. 32.397 23.638 25.90 Length of Slug in Part 2. 32.359 23.707 25.50 Weight of Slug, g. 0.1885 0.3533 0.1682 Radius in Part 1., cm. 0.0372 0.05875 0.0380 Radius in Part 2., cm. 0.0373 0.05882 0.0382 Radius in Part 3 . cm. a The list is continued in Appendix C. a 52 TABLE XII DATA TO CHECK THE CALIBRATION OF PXREX CAPILLARIES FOR USE IN SURFACE TENSION MEASUREMENTS Apparatus III Apparatus IV Radius of Capillary, cm. 0.0372 0.0382 Radius of Large Tube, cm. 1.02 1.28 l/r1-l/r2 25.91 25. h i Temperature, ° C . 25.8 2 0 . 14 Density, g./cc. 0.8729 O .8786 Average Rise, cm. 1.706 1.707 Calculated Surface Tension, dynes/cm. 28.17 28.88 Surface Tension from Sugden (62), dynes/cm. 28.19 28.83 1These data were obtained after the rise for bromine trifluoride had been determined. 1 53 RESULTS AMD DISCUSSION Viscosity Measurements Results The data obtained for viscosity measurements are listed in Tables XIII,. XIV, and XV for iodine pentafluoride, bromine pentafluoride, and bromine trifluoride respectively. Tables XVI, XVIII, and XIX contain various derived quantities and the calculated viscosities for each compound. The viscosities were calculated from the data by means of the calibration for the instrument obtained from Barr ’s equation--Equation (2h), Some data for the viscosities of iodine pentafluoride were obtained on the rotating cylinder apparatus, Apparatus I . They are listed in Table XVII together with values calculated for the same temperatures from results with the Pyrex viscometer for the sake of comparison. "When the first observation was made, some mechanical friction was noted and the cap of the viscometer removed. The friction disappeared, but the sample was then exposed to the moist atmosphere and turned a deep blue. Also the calibration was no longer applicable. Thus the data obtained on Apparatus I were not considered reliable. Treatment of Data The viscosities calculated from the data and the calibration con­ stants were fitted by a least-squares method to Equation (5)* which shows that a graph of the logarithm of viscosity versus the reciprocal of 5a TABLE XIII VISCOSITY DATA FOR IODINE PENTAFLUORIDE Sample I Level Mark , c m . 1.30 Millivolts 1.002 1.010 I .oia 0.737 0.737 0.737 1.160 1.161 1.162 1.126 1.505 1.501* 1.501* II III IV 1.10 1.30 1.30 1.01*2 1.01*1 1.01*0 0.738 0.7 35 0.735 1 . 1*1*5 1.1*1*5 1.1*1*5 1.515 1.515 1 .5 15 0.737 0.71*3 0.71*5 0.987 0.983 1.257 1.257 1.257 1.605 1 .6 05 1.605 1.615 1.612 1.032 I .032 1.032 0.720 0.717 0.715 Time, sec . 25.5 2 5 .a 2 5 .a 27.8 27 .8 27.8 2a . 3 2U.2 26.3 2 a.5 22 .0 22.1 22 .1 2a . 0 2a .1 2a . 0 26.6 26.7 26.7 2 1 .a 21.3 21.3 20.9 20.6 20.9 27.7 27.8 27.8 25.7 25.7 23.2 23.3 23.3 21.1 21.0 21.0 21.7 21.7 2 5 .a 2 5 .a 25.3 2 8 .a 2 8 .a 28.5 55 TABLE XIV VISCOSITY DATA FOR BROMINE PENTAFLUORIDE Sample I Level Mark, cm. 1.55 l.UO II 1.35 0.775 0.770 1.30 0.700 1.20 1.316 12 .2 1.20 1.15 1.52 1.55 i.Uo 1 1.067 Time, sec. 13.5 13.5 13.6 13.7 13.7 ' 13.8 1.25 III Millivolts 1.010 1.000 0.225 15.7 0.206 0.211 15.6 0.768 0.900 0.905 1.500 1.500 15.6 13.5 13.5 13.5 13.5 13.5 12.8 12 .7 0.135 0.157 o.i5i 0.757 0.770 0.775 0.962 0.957 15-9 15.5 15.5 15.5 15.0 15.0 13.7 13.7 0.775 0.775 IV 1.50 0.575 15.3 V 1.50 0.580 0.580 0.580 0.600 0.600 1.128 i.i5o 0.079 0.072 0.090 15.3 15.3 15.5 15.1 15.1 13.1 1.55 1.30 1.20 1 Impure sample. 13.0 15.5 15.6 15.5 56 TABLE XV VISCOSITY DATA FOR BROMINE TRIFLUORIDE Sample I Level Mark , cm. 1.80 Millivolts 0.887 0.890 1.219 1.202 II III 2.00 2.67 Time, sec . 20.3 20.3 18.6 1.207 18.7 18.7 0.798 0.805 0.805 1,051 1.060 1.065 21.2 21.1 21.2 19.8 19.6 19.7 1.812 18.8 1.396 1.803 18.2 18.3 0.517 0.515 0.515 0.991 0.991 0.991 0.667 0.665 1.598 1.595 1.595 28.1 28.0 23.9 20.7 20.7 20.7 23.1 23 .1 18.5 18.6 18.5 57 TABLE XVI VISCOSITIES OF IODINE PENTAFLUORIDE Mark cm. , 1.30 1 Temp.C. 25.3 25.5 25.6 18.9 18.9 18.9 29.0 29.0 29.0 28.3 37.6 37.6 37.6 1.10 26.3 26.3 26.3 18.7 18.7 18.7 32.9 32.9 3.2.9 37.7 37.7 1.30 Liquid Density 3.18? 3.186 3-186 3.212 3.212 3.212 3.172 3.172 3.172 3.175 3.138 3.138 3.138 3.183 3.183 3.183 3.213 3.213 3.213 3.156 Time, sec. Sample I ” 25.5 25. 6 2 5 .U 27.8 27.8 27.8 26.3 26.2 26.3 26.5 22.0 22.1 22.1 »le II 2660 26.1 26.0 26.6 3.156 3.137 26.7 26.7 21.6 21.3 21.3 20.9 3.156 C Viscosity, cp. 0.0302 0.0302 0.0302 0.0306 2.191 2.191 2. 1 8 1 0.0306 0.0306 0.0300 2.689 2.689 2.689 2.038 0.0300 2.029 0.0300 0.0300 2.038 2. 06 2 0.0295 0.0295 0.0295 1.768 0.0319 0.0319 0.0319 0.0326 0.0326 0.0326 0.0315 0.0315 0.0315 3.137 20.6 37.7 3.137 20.9 0.0312 0.0312 0.0312 1 8 .7 1 8 .9 1 8 .9 21*.9 21*.8 3 1 .5 3 1 .5 3 1 .5 39.9 39.9 3 9 .9 3.213 3.213 3.213 3.188 3.1 88 3.162 3.1 62 3.162 3.1 28 3.1 28 3.128 Sample III 27.7 27.8 27.8 25.7 25.7 23.2 23.3 23.3 21.1 2 1 .0 2 1 .0 0.0306 0.0306 0.0306 0.0302 0.0302 0.0298 0.0298 0.0298 0.0293 0.0293 0.0293 1.739 1.768 2.159 2.169 2.159 2.526 2.526 2.526 1.817 1.807 1.807 1.726 1.696 2 . 1*80 2.690 2 .1*90 2.211* 2.222 1.901 1.911 1.911 1.621 1.621 1-621 1.726 58 TABLE XVI VISCOSITIES OF IODINE PENTAFLUORIDE (continued) Mark, cm. 1.30 Tginp. C. Liquid Density UO.O ho .0 3.128 3.128 3.181* 3.181* 3.181* 3.215 3.215 3.215 26.1 26.1 26.1 18.3 18.2 18.2 Time, sec . Sample V 21.7 21.7 25. h 25. h 25.3 28. h 28. k 28.5 l C Viscosity, cp. 0.0293 0.0293 0.0301 0.0301 0.0301 0.0307 0.0307 0.0307 1.686 1.686 2.171 2.171 2.162 2.565 2.565 2.575 'b is 2.1 . TABLE XVII VISCOSITIES OF IODINE PENTAFLUORIDE FROM APPARATUS I Temperature, Corrected 36.1 36.1 25.0 15.6 Scale 0-.5 direct direct direct Reading, cp. 1.8U 2 .00 2 .32 2.96 Correction, cp. -0.02 -0.12 -0.12 -0.12 Viscosity, cp. 1.82 1.88 2.20 2.8A Values calculated from results with Apparatus III. Viscosity, cp . 1.82 1.82 2.22 2. 6Lt 59 TABLE XVIII VISCOSITIES OF BROMINE PENTAFLUORIDE Mark, cm. 1.55 1.50 1 .U0 1.35 1.35 1.30 1.20 1.25 1.25 1.25 1.20 1.20 1.20 1.20 1.20 i.i5 1.15 i.5o 1.50 1.55 1.55 i.Uo i.5o i.5o i.5o 1.50 1.55 1.30 1.30 1.20 1.20 B is 2.1. Temp. °C. Liquid Density 26.9 25.5 25.3 19.7 17.8 2.3 2.558 2.1+63 2.1+61+ 2.U83 2.U83 2.1+89 2.51+3 5.8 5.3 5.5 19.7 19.7 19.5 22.8 22.9 28.9 28.9 2.531 2.532 2.532 2.1+83 2.1+83 2.1+83 2.1+72 2.1(72 2.1+51 2.1+51 19.6 3.8 3.7 19.6 19.7 25.3 25.2 12.3 12 .3 12.3 15.3 28.5 28.5 2.0 1.8 2.537 2.538 2.1+83 2.1+83 2.1+67 2.1+67 2.508 2.508 2.508 2.1+98 2.1+53 2.1+52 2.51+1+ 2.51+5 Time j sec. Sample I lt.l+ 13.5 13.5 1 c 0.0288 0.0293 0.0293 13.6 0.0301 13.7 0.0301 0.0307 0.0327 13.8 lli.lj Sample II it.7 11+ .6 11+.6 13.5 13.1+ 13.h 13.1+ 13.1+ 12 .8 12 .7 Sample III 15.5 15.5 15.0 15.0 13.7 13.7 Sample V 15.3 15.3 15.5 15.1 13.1 13.0 15.5 15.6 0.0320 0.0320 0.0320 0.0315 0.0315 0.0315 0.0313 0.0313 0.0313 0 .0 3 1 3 0.0299 0.0299 0.0293 0.0293 0.0295 0.0295 0.0293 0.0293 0.0293 0.0296 0.0300 0.0300 0.0327 0.0327 Viscosity, cp. 0.575 0.591 0.601 0.653 0.653 0.675 0.825 0.829 0.819 0.819 0.670 0.659 0.659 0.658 0.658 0.580 0.602 0.832 0.823 0.657 0.657 0.621 0.619 0.683 O .683 0.692 0.669 0.571 0.560 0.827 0.859 60 TABLE XIX VISCOSITIES OF BROMINE TRIFLUORIDE 1.80 2.00 2.U7 Wo <1)0 Eh Mark, cm. 22. 5 22.6 30.5 30.2 30.3 Liquid Density 2 .805 2.805 2.783 2.785 2.783 20.3 20.5 20.5 26.5 26.7 26.8 35/2 j 5*9 35*0 2 .8 1 1 2.810 13.2 13 .2 13.2 25.0 25.0 17.0 16.9 39.6 39.6 39.6 2.830 l B is 5 .3 . 2.810 2. 795 2.793 2.793 2.769 2.768 2.768 2.830 2.830 2.798 2.798 2.820 2.820 2.757 2.757 2.757 1 Time, sec . Sample I 20.3 20.3 18.6 18.7 18.7 Sample II 21.2 21.1 21.2 19.8 19.6 19.7 18.5 18.2 18.3 Sample III 25.1 25.0 23.9 20.7 20.7 23.1 23.1 18.5 18.6 18.5 C Viscosity, cp. 0.0558 2.555 2.555 2.055 0.0558 0.0550 0.0550 0.0550 2 .073 2. 0 7 3 0.0558 0.0558 0.0558 0.0539 0.0539 0.0539 0.0535 2.563 2.553 2.963 2.235 2.196 2.215 1.935 0.0536 1.902 0.0535 1.915 0.0539 0.0539 3.055 3.036 3.018 2.219 2.219 2.760 2.760 1.770 1.789 1.770 0.0530 0.0507 0.0507 0.0 5 2 3 0.0523 0.0502 0.0502 0.0502 61 absolute temperature is a straight line. It was assumed that the temper­ atures were accurate and any deviations from the straight line were due to errors in the viscosity values only. Values for the constants A and B, are assembled in Table XX, together with the energies of viscous flow and similar derived constants. Precision and Accuracy of Results The precision of the results may be said to depend upon the pre­ cision of the calibration. For Apparatus III the root-mean-square deviation was 0.00^ cp., and for Apparatus IV it was 0.011 cp., both values being around one per cent of the viscosity of the calibrating liquid used. These results conformed to expectations when compared with results obtained by Elvrum and Doescher (7 8 ) with this type of apparatus. The expected precision of a particular viscosity measurement was calculated by the perfect differential method (9 3 )> that is, the error in the viscosity is given by the expression [ where f B f p 1 ^ e error and 4 I 0 ' 1 ‘A < » > is the partial derivative of the analytical expression for the viscosity, f(^)^ with respect to each of the parameters, x^, affecting the viscosity. The following is a sample calculation for Equation (3 6 )with iodine pentafluoride as the liquid. 2 (A *^ ) 2 2 = [(Cd * B d / j 2) A j 2 *■ (d j A C ) ( A d f (C j-B /jf ] , <■ ( d / j . A B) c • (37) 62 TABLE XX THERMODYNAMIC FUNCTIONS FOR VISCOUS FLOW a Compound GIF 3 BrF 3 BrF& Sloped U28.5 810* .1 519.1 B 986.8 19U. 1195. 796.3 183b. 1 .U8 0.351 1 .1 1 o.b? Evis(kcal./mole) 1.970 3.860 3 *6 I4.J4 A H (kcal./mole) 6.58d 2.371* f 7.31 9 .88 g A E^c(kcal./mole) 6.01 9.67 6 .69 9.28 AF^(kcal ./mole) 2.32 3.35 2.76 3.51 -1 . 2 2 1.73 -1.31 0.39 A xlO (poise ) AS^( e .u.) 1 0 .3e ^ E^/Evis(n ) 3.07 2.5 2.8 2.5 A E /a V 2.59 2.88 2.U3 2 .6 b f^ fData reported by Bankes^ at al_. (96) . The slope was calculated for a graph of log vs. l/T. The constants apply to Equation (5). CA E was calculated from the relation A E = A H^ - R T . TheVtemperature was chosen to represent the range for which the vapor .pressurej from which A H was calculated^ is valid. Keference (1 3 ). V ^Reference (97). Reference (98). ^Reference (17). 62a TABLE XX (Cont.) THERMODYNAMIC FUNCTIONS FOR VISCOUS FLOW Compound a SbF5 H 20 Slope^ 10 3 0 . 908. B 23?U. 4 A x 10 (poise) 1U-3 c 2090. 0.0805 Evj_s(kcal ./mole) U.72 U. 15 £ H v (kcal ./mole) 10.37 10.5U A E v (kcal ./mole) 9 .80 9.95 A F +(kcal ./mole) 6.57 0 .88 -6.U3 11.ia 2 .08 2 .ao 1.U6 a .7 (e .u.) ^V/£vis(n ) A e ^/a f * ^Calculated from data reported by references (105) and (106) for 16 C. Calculated from data in reference (7 ) for 0.0 C. Q ^Calculated from data in reference (95) and (55) for 20 C , The slope ■was calculated from a graph of log 1/T. 63 B = 2.10 l 0.11, C = 0.03 ± 0.0001, j ■= 25 ± 0.1 seconds, and d = 3.0 t 0.001 g./cc. When these values are substituted into Equation (37), > (A ^ ) 2 = [ 0.56 x 10~4 . 1.7/ x 10'"4 .- 1.0 x 10‘4 * 0 J - 0.018 cp. For Apparatus IV the estimated error in constant C was 0.0001 and the constant B, 0.20. Table XXI compares the calculated and observed precisions. TABLE XXI CALCULATED AND OBSERVED PRECISION OF VISCOSITY RESULTS Compound Calculated Precision, cp. r j a Per Cent Observed Precision, cp. Pera Cent 0.018 0.9 0.028 1.3 BrF5 0.023 3.U 0.02/ 3.5 BrF3 0.036 1.6 0.0/2 1.9 a Based upon the mean viscosity. Thus for Equation (2/) the calculated and observed estimates roughly agree. According to Wilson ( 9 3 ) y agreement is a good check on the accuracy of error estimates, the small times of flow. The reason for the poor precision lies in Although a longer capillary would have in­ creased the times of flow, it would have caused the apparatus to be unwieldy for distillation. large a sample. A larger reservoir would have required too While a decrease in the radius of the capillary was 6h the most potent means of increasing times of flow,, such a decrease would have hindered the use of the capillary as a surface tensiometer. In addition to Equation (2li), the one-constant equation was em­ ployed in calculation of the viscosities of halogen fluorides. The constants obtained from the calibration data were plotted as a function of temperature, and interpolated values were read from the graph in the viscosity calculations. While precision of the calibration increased, and the deviation for bromine pentafluoride and trifluoride decreased to one per cent or less, it was thought that the two-constant equation yielded sufficiently more accuracy to warrant its use. Comparison of the energies of viscous flow obtained by the different methods showed that the two constant equations yielded higher results by about 8.2 per cent for iodine pentafluoride and 7.3 bromine pentafluoride. For bromine trifluoride there were no calculations based upon the oneconstant equation. In terms of absolute viscosities, the two calibra­ tions yielded essentially the same results for iodine pentafluoride and bromine trifluoride, but the bromine pentafluoride results were much higher for the one-constant equation, as one would expect if the kinematic viscosities were much lower than those of the calibrating liquids. Thus the use of the two-constant equation apparently improved the accuracy of the measured viscosities at the expense of the precision. A requisite for accuracy was the maintenance of viscous flow. That the conditions were fulfilled is proved by the fact that the Reynold^s numbers (99) were less than 1000 for each apparatus. For Apparatus III the number was 35>0, and for Apparatus IV it was 370. 65 Discussion It can be seen from Table XX that the four halogen fluorides under discussion fall into two groups on the basis of the thermodynamic properties for viscous flow. For chlorine trifluoride and bromine pentafluoride the energies of viscous flow are around two kllocalories per mole, and for bromine trifluoride and iodine pentafluoride the values are nearly four. A typical non-associated liquid like benzene has a of approximately 2.5 kilocalories per mole whereas water, a typical associated liquid, has a E^yg per mole. at room temperature of h.O kilocalories Comparison indicates that chlorine trifluoride and bromine pentafluoride are similar to benzene in flow properties, and the bromine pentafluoride and chlorine trifluoride are more like water. Inspection of the data shows that A pair and positive for the second. is negative for the first This fact further supports the thesis that chlorine trifluoride and bromine pentafluoride are similar In flow properties and different from bromine trifluoride and iodine pentaA t fluoride. Large positive values of A S are usually observed for associated liquids whereas ZS. is negative for non-associated liquids. According to theory, the ratio of A E /Ey-is should be in the neighborhood of three for symmetrical, non-polar molecules, and should be lower for associated liquids (53). The ratio is near three for the chlorine trifluoride pair, but for the other pair the ratio is 2.q, which is close to the value 2,3 found for water at room temperature (53). If iodine pentafluoride and bromine trifluoride are associated liquids these values are reasonable. 66 The ratio A E ^ / A f " is near 2 M S for most of the liquids dis­ cussed by Eyring (51) and the halogen fluorides have values of this ratio close to 2 M S also. Although bromine trifluoride has a value of 2.88, the value of U-7 f°r water is considered by Eyring to be valid for the rule (53). The graph of log *7^ versus l/T for bromine trifluoride seems to have a slight curvature convex to the temperature axis just as observed in the case of water (95) . However, the precision of the data does not warrant attributing this curvature to association. Since this research was completed, Robinson and Hetherington (100) have reported values for the viscosity of iodine pentafluoride. They used a differently modified Ostwald viscometer, obtained data over a temperature interval of 15 to 70° C ., but used only two different samples. At h S ° C. the results are identical to those reported here, but at 15° C., they reported a viscosity of 2.6? cp. In this paper the value reported is 2.73 cp., a 2.2 per cent difference that is within experimental error for both determinations only if the maximum allowed errors are added. the curve log T.nus they report a smaller value for the slope of versus l/T than is reported in this paper. The value reported here for the slope should be more accurate since more samples were utilized in obtaining the data and a correction for the kinetic energy term, which tends to yield a larger slope, was made. Favoring the smaller slope are the facts that errors in viscometric determinations tend to yield high values and Robinson et_ aA. used a larger temperature range . 66a Listed in Table XX for purposes of comparison are the thermo­ dynamic functions for antimony pentafluoride and water. Water is typical of liquids that have hydrogen bonding, and because the same factors which influence the association of the liquid halogen fluorides presumably are operating in antimony pentafluoride, this liquid is included. It should be emphasized that the functions for antimony pentafluoride may be in error, because the available data is sparse and probably not accurate. Nevertheless the conclusion can be drawn that the derived functions Ey-is n do 311 associated liquid. It can be seen from Table XX that the values of ^rV ± 5 and n of bromine trifluoride and iodine pentafluoride tend toward those of associated liquids, whereas those values of chlorine trifluoride and bromine pentafluoride do not. Muetterties and Phillips (3l|.a), who have studied the nuclear magnetic resonance spectra of the halogen fluorides as a function of temperature, concluded that dimerization is the mechanism by which fluorine exchange occurs. If their assumptions are correct, they show that the order of dimer stability is Bri?3>ClF3 >lF5>BrF5 . One might conclude then that viscosity results should show the same order. However, the rates of exchange do not depend only upon the concen­ tration of species involved. Fewer dimers taking part in a faster reaction could account for the same observed rate of exchange. 0 6 A concentration of dimers from 10 to 10 molar can account for the observed rates (107)- Thus the relative degree of association of the halogen fluorides on a bulk scale as determined by viscosity measurements in this work is not contradicted. 67 Surface Tension Measurements Results The data obtained for surface tension measurements are listed in Tables XXII, XXIII, and XXIV for iodine pentafluoride, bromine penta­ fluoride , and bromine trifluoride respectively. The equation chosen for representation of the data was the linear form, Equation (1?). This equation represents the data within experimental error and is the simplest to apply. The constants for Equation (17) are listed in Table XXV. Because the samples on which the surface tension measurements were made were from the same source as those for viscosity measurements and received the same treatment, the purity estimates utilized for viscosity measurements are assumed to be applicable. For bromine trifluoride, the surface tension measurements were made in a Vycor apparatus with a Pyrex capillary (Apparatus IV). The liquid did not wet the Vycor surface properly, and a Pyrex capillary had to be used. Since bromine trifluoride attacked the Pyrex slowly with the formation of bubbles, each sample was discarded immediately as soon as the formation of bubbles signaled contamination. Measurements were obtained on only two samples before contamination took place. It was found that exposure of cold bromine trifluoride to a partial vacuum for twelve hours previous to the distillation produced a light yellow liquid that did not form bubbles for three or four hours after contact with the Pyrex. Measurements of the capillary radius at the points where the menisci fell were made after exposure. No measurable corrosion occurred. 68 TABLE XXII THE SURFACE TENSIONS OF IODINE PENTAFLUORIDE Sample I II Temp. °C. 5 1.002 25.2 0.593 3.187 29.7 3 0.725 18. 5 0.507 3.215 3 0 .8 5 1.161 ■ 29.2 0.589 3.171 29 .2 h,b cm. Densityj g./cc . Surface Tension, dynes/cm. This sample was impure 1.032 26.1 0.588 3.185 29.5 5 1.175 26.5 0.590 3.182 29.5 6 1.535 38.2 0.576 3.135 28.2 5 1.025 25.9 0.590 3.185 29.5 5 0.759 19.2 0.508 3.211 3 0 .8 3 1.613 50.1 0.565 3.127 27.5 3 1.032 2 6 .0 0.583 3.185 29.2 3 0.717 1 8 .2 0.597 3.215 3 0 .2 III IV a Milli­ volts Weight a _ The weight represents the number of observations at that temperature and is used in obtaining the average. b . The symbol h represents the capillary rise. 69 TABLE XXIII THE SURFACE TENSIONS OF BROMINE PENTAFLUORIDE Sample I b 11 III Weighta Milli­ volts Temp. °C. 3 0.855 2 1 .5 O.I488 2.1477 22.9 1 1 .0 7 8 27.2 0.585 2.1+97 22.5 5 1.069 27.0 0.581 2.1+98 22.5 3 1.337 33.5 0.552 2.1+39 20.8 3 0.776 19.7 0.592 2.1+83 23 .1 5 0.821 20.8 0.590 2.1+79 23.0 1 0.360 9.2 0.510 2.921 25.3 1 0.371 9.6 0.5 05 2.919 25.1 1 0.390 10.0 0 .5 1 0 2.917 25.3 1 0.560 1)4.3 o.5oo 2 .9 0 1 23.6 1 0.568 IJ4 .5 0.595 2 .9 0 1 23.5 1 0.573 III.7 0 .5 0 0 2 .9 0 0 23.5 1 0.576 lh.7 0 .5 0 0 2 .900 23.5 3 1.057 26.7 0.586 2.1+99 22.6 1 .3 0 0 32.6 0.568 2.1+1+2 21.6 0.963 25.3 0.591 2.1+67 22.9 0 .6 3 0 1 6 .1 0.595 2 .1+81+ 23.5 2 h, c cm. Density, g./cc Surface Tension, dynes/cm. aThe weight represents the number of observations at that temperature, the data being averaged. ■l This point was discarded on a statistical basis. c The symbol h represents the capillary rise. 70 TABLE XXIV THE SURFACE TENSIONS OF BROMINE TRIFLUORIDE b Sample 1 II III Temperature on a C ., corr. cm. Density, g./cc. 12 .0 0.715 2 .8 3 3 37.1 18.9 0 .6 9 0 2 .8 X6 36 .5 27.1 0 .6 8 0 2 .789 35.6 55.0 0.670 2.7ltl 33.8 2 6 .1 0.690 2.797 35.1 3 6 .6 0.680 2.767 35.6 111. 2 0.710 2 .8 2 7 3 6 .8 Surface Tension dynes/cm. Bubbles developed aA calibrated thermometer was used to measure bath temperatures Lor the surface tensions of bromine trifluoride in Apparatus IV. ^The symbol h represents the capillary rise. 71 Precision and Accuracy When th^ perfect differential equation for estimating errors, Equation (36), was applied to the formula for surface tension, rgdh/2, and maximum values for r, d, and h were properly substituted, the esti­ mated r.m.s. error in the surface tension values was found to be as shown in Table XXV. The table also contains the observed r.m.s. deviations for each compound. Only in the case of bromine pentafluoride are the calculated and ooserved deviations much different. According to Wilson (93) agreement is a check on the accuracy of the error estimations. TABLE XXV CALCULATED AND OBSERVED PRECISION OF SURFACE TENSION RESULTS Compound Calculated Precision, dynes/cm. Per Cent Observed Precision, dynes/cm. Per Cent if5 0.33 1.1 0.29 1.0 BrF5 0.28 1.2 0.16 0.7 BrFa 0.32 0.9 0,30 0.8 Thus a deviation of ± 0.3 dynes/cm. may be assigned to the surface tensions of iodine pentafluoride and bromine trifluoride and of t 0.2 dynes/cm, to bromine pentafluoride and chlorine trifluoride (96). 72 Discussion The surface tensions of the halogen fluorides are presented as functions of temperature in Table XXVI. They are intermediate between water at 70 dynes per centimeter and fluorocarbons at 10 dynes per centimeter at room temperature. A linear relationship between ' f ' and T represents the data within experimental error. Table XXVII shows the parachors of the halogen fluorides. The values are averages of those calculated at 10, 20 and 30 degrees Centigrade. Little variation with temperature was noted. From the values of the parachors, the atomic parachors of the central atom with different valencies can be calculated assuming a constant value for the atomic parachor of fluorine. Samuel (68) first applied this technique, Bahkes, e_t a l (96) extended it to the chlorine fluorides, and they showed how the values obtained fit fairly well into a series of phosphorus and sulfur atomic parachors. From Table XXVIII it can be seen that the halogens form a series with obvious trends themselves. The atomic parachors shown for tervalent iodine and pentavalent chlorine have been estimated. According to Grunberg and Nissan (95) the ratio of ^vj_s to the work of cohesion, W^, as computed from surface tension data, is approxi­ mately one. For water and ethanol the ratio is 2.3 and 1.5 respectively. Table XXIX lists the work of cohesion and the ratio of E^is the four liquids under discussion here. to it for It should be noted that bromine trifluoride has the highest value (1.9)> iodine pentafluoride next (1.8), and the last two have the same value (1.5). Here is another indication 73 TABLES XXVI SURFACE TENS ION -TEMPERAT JRE RELATIONSHIPS FOR THE HALOGEN FLUORIDES3" A B C1F3 BrF3 BrF5 26.7 38.3 25.a 0.16 r.m.s . dev. a For the equation ±0.2 IT = A - Bt 0,100 33.0 0.113 ±0.3 ±0.2 0.130 ±0.3 dynes/cm. TABLE XXVII PARACHORS OF THE HALOGEN FLUORIDES C1F3 Tp J 111.5 BrF3 BrF5 120.6 15a. a 162.5 TABLE XXVIII ATOMIC PARACHORS OF THE CENTRAL HALOGEN ATOMS Valence Br I 3 68.0 90.0 36.5 a5.6 Cl 1 5 (19) 29.5 (60) 37.9 7h TABLE XXIX WORK OF COHESION OF HALOGEN FLUORIDES W (kcal/mole) +A EVwc CIF3 BrF3 BrF5 1 .2 6 2 .0 1 1.59 2.03 1.5 1.9 1.5 1 .8 TABLE XXX CIF3 BrF 3 BrF5 1—1 01 ESTIMATED CRITICAL TEMPERATURES OF THE HALOGEN FLUORIDES (CENTIGRADE) Reference 167 383 225 252 a. 15U 327 197 2J4O (1 0 1 ) b. 208 397 237 327 (102) 17U 330 2ua 267 (103) 170 368 217 315 (10U) 170 360 220 280 best value a Linear extrapolation of surface tension data. ■u 0 3/2 Td , where T~ is the boiling point in D £5 K. 7ha TABLE XXXI VISCOSITY AND SURFACE TENSION OF THE HALOGEN FLUORIDES AT 20°C. Compound Viscosity (c.p.) Surface Tension (dynes/cm.) GIF 3 BnF 3 BrF5 IT's O.U29 2.^7 0.530 2 .U 3 23.£ 37.8 23.1 3 0 .a that the former pair of liquids is associated compared to the latter, although the high value of the ratio for the latter pair casts some doubt on the certainty of the conclusion. There is no reliable method for estimating critical temperatures of inorganic compounds. In most cases the methods compounds or non-associated compounds. apply only to organic From the many empirical approaches, five of the best have been chosen to estimate the critical temperatures for the halogen fluorides. for these quantities. No direct measurements have been reported The results are assembled In Table XXX. The "best value” was obtained by choosing a value between the extremes, emphasizing the method that seemed to apply best. Linear extrapolation of the surface tension data was ignored for bromine trifluoride and iodine pentafluoride because of possible association effects. As a quali­ tative check, the "best values" were used in the Eotvos equation, Equation (15), to calculate the constant k. The values were 2.15, 1.90, 2.02, and 1.97 for chlorine trifluoride, bromine trifluoride, bromine pantafluoride, and iodine pentafluoride in order. The average value for several hundred compounds is 2.12 (Jjl). If the halogen fluorides are not much associated, the estimated critical temperatures are nearly correct. 76 SUMMARY The viscosities of iodine pentafluoride, bromine pentafluoride, and bromine trifluoride have been determined over a temperature range of 15 to I4O degrees Centigrade by means of a modified Ostwald viscometer made of Pyrex. The results have been fitted to a standard exponential equation which relates viscosity to the temperature, and various para­ meters such as energy, free energy, and entropy of viscous flow were computed. The results have been interpreted in terms of Eyring1s theory of viscous flow, and they indicate that bromine trifluoride, and to a lesser extent iodine pentafluoride, are associated liquids. Computations based on the data published thus far on the viscosity of iodine penta­ fluoride and chlorine trifluoride were included for the sake of com­ parison. Chlorine trifluoride and bromine pentafluoride are ’’normal" liquids. The surface tensions of iodine pentafluoride, bromine pentafluoride, and bromine trifluoride have been determined over the same temperature range by the capillary-rise method. The results were fitted to a standard, linear, surface tension-temperature relationship. Again the results indicated that bromine trifluoride, and perhaps iodine pentafluoride, are associated, while bromine pentafluoride and chlorine trifluoride are probably not. Various empirical relationships were employed to obtain estimated values of the critical temperatures of the halogen fluorides. ri LITERATURE CITED (1) G. Gore, Proc. Roy. Soc., 1 9 , 235 (1870). (2) 0. Ruff and A. Braida, Z. anorg. u. allgejn, Chem., 2 1 k , 91 (1933) (3) J. Fischer, R. K. Steunenberg and R. C. Vogel, J. Am. Chem 76, 1U97 (195U). So--* (i|) J. Fischer, J. Bingle and R. C. Vogel, ibid., 7 8 , 902 (1956). (5) R. A. Durie, Proc. Roy. Soc. (London), 20?, 388 (1951). (6) E. E. Aynsley, R. Nichols and P. L. Robinson, J. Chem. Soc., 623 (1953). (7) J • H. Simons, Ed., "Fluorine Chemistry,” Vol. I, Academic Press, Inc., New York (1950). (8) H. J.'Emeleus, Ball. Soc. Chim. France, 909(1953). (9) N. N. Greenwood, Revs. Pure and Appl. Chem.(Australia), (10) V. 1_, 8 J4 (1951). Gutman, Angew. Chem., 62^, 312 (1950). (11) A. G. Sharpe, Quart. Reys., I4 , 115 (1950). (12) Ht. S. Booth and J. T. Pinkston, Chem. Revs., J41 , 1*21 (19^7). (13) J. H. Simons, Ed., ’’Fluorine Chemistry,” Vol. II, Academic Press, Inc., New York (195U)• (III) E. B. Maxted, "Recent Advances in Inorganic Chemistry,” Clarendon Press, Oxford, England (19U7)(15) H. Hazeldine and A. G. Sharpe, "Fluorine and Its Compounds,” - John Wiley and Sons, Inc., New York (1951). (16) H. B. Thompson, Ph. D. Thesis, Michigan State University (1953). (17) M. T. Rogers, J. L. Speirs, H. B. Thompson, and M. B. Panish, J. Am. Chem. Soc., 7 6 , U81j3 (195U). (18) 0. Ruff and W. Menzel, Z. anorg. u. allgem. Chem., 202_, Ii9 (1931). (19) C. F. Swinehart and F. J. Burton, private communication to H. S. Booth and J. J. Pinkston, See Simons, Vol. I. 78 (20) A. A. Bankes and J, J. Maddock, J. Chem. Soc., 2779 (1955). (21) L. Stein, R. C. Vogel and ¥. H. Ludewig, J. Am. Chem. Soc . 76 U28 (1955). ’ (22) A. A. Bankes and A. J. Rudge, J. Chem. Soc., 191 (1950). (23) M. T. Rogers, R. D. Pruett, H. B. Thompson and J. L. Speirs, J. Am. Chem. Soc., 7 8 , 55 (1956). — (2U) M. T. Rogers, J. L. Speirs, and H. B. Thompson, ibid., 7 6 , 5851 (1955). ~ — (-25) M. T. Rogers', M. B. Banish and J. L. Speirs, ibid., 7_7 , 5292 (1955). — (26) M. T. Rogers, J. G. Malik and J. L. Speirs, ibid., 7 8 , 56 (1956). _~~(27) M. T. Rogers, R. D. Praett, and J. L. Speirs, ibid., 7 7 , 5280 (1955). (28) ’’Table of Electric Dipole Moments of Substances in the Gaseous State,1r Bureau of Standards Circular 537, Washington, D. C. (1953). (29) D. W. Magnuson, J. Chem. Ph.ys.. 20, 229 (1952). (30) D. F. Smith, ibid., 21, 609 (1953). (31) R. D. Burbank and F. N. Bensey, (32) R. L. Potter, ibid., 1 7 , 957 (1959). (33) H. S. Gutowsky and C. J. Hoffman, ibid., 19, 1259 (1951). ibid., 21, 602 (1953). (35-) H.'S. Gutowsky, D. W. McCall and C. P. Slighter, ibid., 21, 279 (1953). (3Ua)E. L. Mu et ter ties and W. D. Phillips, J. Am. Chem. Soc., 79, 322 (1957). (35) C. E .Mellish and J. W. Linnett, Trans. Faraday Soc., 53_, 1311 (1955). (36) C. V. Stephenson and E. A. Jones, J. Chem. Phys., 20, 1830 (1952) (37) H. H. Claassen,-J..G. Malm, and-B. Weinstock, paper presented before the -Dympdsncuu on Molecular Structure ana opectra, The Ohio State University, Columbus, Ohio, June 11-15 (1956). (38) R.C. Lord, J. Am. Chem. Soc., 72_j> 522 (1950) . (39) E. N. Da C. Andrade, Endeavour, 13, H 7 (1955). 79 (UO) F. Daniels, "Outlines of Physical Chemistry/ 1 John Wiley and Sons Inc., New York (19U8). , (UD J • R* Partington, "An Advanced Treatise on Physical Chemistry," Vol. II Longman Green and Co., New York (1951). (142) J. L. M. Poiseuille,Mem. Acad. Sci., Paris. £, U33 (I8 q6 ) . (il3) E. C. Bingham and H. S. Jackson, Nat. Bur. Standards (U.S.) Tech. News Bull., II4, 75 (1918). (UU) L. L. Burger and G. H. Cady, J. Am. Chem. Soc., 77, h2h3 (1951). (U5) F. Hovorka, H. P. Lankelma and S. C. Stanford, ibid., 60, 820 (1938). (J46 ) D. B. Macleod, Trans. Faraday Soc., 19, 6 (1923). (U7) A. K. Mukherjee, J. Indian Chem. Soc., 29, 56 (1930). ([48) E. N. da (U9) U. Rost, Kolloid Z., 1^2, 132 (1955). (50) C. Andrade, Nature (London), 125, 125 (1930). S. Glasstone, K. Laidler and H. Eyring, "The Theory of Rate Processes," Chapter 9, McGraw-Hill Book Co., New York (19U1). (51) R. H. Ewell, J. Applied Phys., 9_, 252 (1938). (52) J. F. Kinkaid, H. Eyring and E. A. Stearn, Chem. Revs., 28_, 301 (19U1) . (53) W. E. Roseveare, R. E. Powell and H. Eyring, J. App. Phys., 12_, 669 (19U1). (5U) B. S. Harrap and E. Heyman, Chem. Revs., I48 , 56 (1951). (55) L. Grunberg and A. H. Nissan, Trans. Faraday Soc., U5, 125 (19b9). (56) T. E. Thorpe and J. W. Rodger, Phil. Mag., 185A, 397 (1895). (57) T. E. Thorpe and J. W. Rodger, ibid., 189A, 71 (1897). (58) J. N. Friend and W. D. Hargreaves, ibid., 37, 120, 201 (59) A. Bondi, Ann. N. Y. Acad. Sci. £3, $70 (1951). (6 0 ) (19h6) . J. Frenkel, "Kinetic Theory of Liquids," OxfordUniversity Press, Oxford (19U6). 80 (61) N. K. Adam, ’’The Physics and Chemistry of Surfaces/' Oxford University Press, Oxford (1938). (62) S. Sugden, "The Parachor and Valency/' G. Rutledge and Sons, Ltd London (1930). (63) 0. R. Quayle, Chem. Revs.3 £3* hh3 (1953). (6 U) N. S. Baylissj J. Am. Chem. Soc., 5£, hhk (1937). (65) S. A. Mumford and J. W. C. Phillips, J. Chem. Soc., 2112 (1929). (6 6 ) A. I..Vogel, ibid., 625 (1958). (6 7 ) G. H. Cheesman, ibid., 889 (1932). (6 8 ) R. Samuel, J . Chem. Phys., !£, 167 (1955). (69) R. Herzog, Ind. Eng. Chem., 36, 997 (I9 J4U ). (70) R. T. Lagemann and W. S. Dunbar, J. Phys. Chem., 59, 528 (1955). (7 1 ) Eotvos, Ann. Phys., 2£, UU8 (1886). (72) W. Ramsay and J. Shields, Trans. Roy. Soc. (London, AI 8 I4, 6 I47 (1893). (73) F. G. Mann and D. Purdie, J.Chem. Soc., 1559 (1935); 8731 (1936). (75) R. H. Fowler, Proc. Roy Soc. (London), A159, 229 (1937). (75) A. Ferguson, Trans. Faraday Soc., 1£, Ul (1923). (76) S. S. Mitra and N. K. Sanyal, J. Chem. Phys., 23, 1737 (1955). (77) S. S. Mitra and D. N, Chakravarty, Z. physik. C.hem., A205 1 (1955). (7 8 ) R. N. Doescher and G. W. Elvrum, J. Chem. Phys., 20_, 1835 (1952). (79) E. C. Bingham, "Fluidity and Plasticity," McGraw-Hill Book Co., New 'York (1951) . (80) G. Barr "A Monograph of Viscometry," Oxford University Press, London (1931) . (81) E. K. Fischer, "Colloidal Dispersions," John Wiley and Sons, New York (1950). (82) J. R. Heiks and E. Orban, J. Phys. Chem., 60, 1025 (1956) . 81 (83) H. L. Johnston, D. L. "White, and J. Heng Hu, J. Am. Chem So76, 2^86 (1952). ' ^ (86) A. Weissberger, ’'Techniques of Organic Chemistry,” Vol. I, Interscience Publishers, New York (1965). * (85) G. M .Shah and P. D. Pathak, Current Sci. (India), 2 6 , 11 (1955). (8 6 ) K. H. Cuny and K. L. Wolf, Ann. Physik, 1 7 , 57 (1956). (8 7 ) R. E. Dodd and P. L. Robinson, "Experimental Inorganic Chemistry," Elsevier Press, Inc., New York (1953). (8 8 ) "Reference Table for Thermocouples," National Bureau of Standards Circular 508. (89) R. D. Pruett, Thesis, Michigan State University (1955). (90) R. L. Burwell, Jr., A. H. Peterson and G. B. Rathman, Rev. Instr. 6 0 , 608 (1 9 6 8 ). Sci. (91) Jim G. Malik, Thesis, Michigan State University, Ph. D. (1956). (92) G. Egloff, "Physical Constants of Hydrocarbons," lishing Corp., New York (1939). Reinhold Pub­ (93) E, Bright Wilson, Jr., "An Introduction to Scientific Research," McGraw-Hill Book Co., Inc., New York (1952). .(96) J. Timmermans, "Physico-chemical Constants of Pure Organic Compounds," Elsevier Publishing Co., New York, (1950). (95) "Handbook of Chemistry and Physics," Chemical Rubber Publishing Co., Cleveland, 31st Edition. (96) A. A. Bankes, A. Davies, and A . J . Rudge, J. Chem. Soc., 731 (1953). (97) G. D. Oliverand J. W. Grisard, (98) M. T. Rogersand J. L. Speirs, J. Phys.Chem., 60, 1662 (1956). (99) W. L. Badgerand W. L. McGraw-Hill Book Co., New York, J. Am.Chem. Soc., 76, 2705 (1952). M c C a b e , "Elementsof Chemical Engineering," (100) G. Hetherington and P. L. Robinson, J. Chem. Soc., 3681 (1956). (101) C. M. Guldberg, Z. physik. Chem., 5, 376 (1890). 82 (102) Herzog, Ind. Eng. Chem., 36, 997 (19UU). (103) W. T. Smith, Jr., S. Greenbaum, G. P. Rutledge, J. Phys. Chem., 5 8 , U53 (1955). (IOJ4) R. F. Marschner and J. B. Beverly, J. Chem. Ed., 33_, (105) A. A. Woolf and N. N.Greenwood, J. Chem. Soc., 2200 (1950)* (106) R. C. Shair and W. F.Schurig, Ind. and Eng. Chem., 53, 1625(1951)- (107) M. T. Rogers, privatecommunication (1957). 60 J4 (1956). APPENDICES APPENDIX A List of Symbols Used Angstrom units Empirical constants Empirical constants Van der Waal■s b Liquid density Vapor density Energy of vaporization Energy of activation for viscous flow (experimental) Free energy of activation for viscous flow Gravitational constant Heat of vaporization Heat of activation for viscous flow Capillary rise Planck's constant Mean hydrostatic head Hydrostatic head Time in seconds Eotvos constant Length of capillary Lengths of mercury slugs Molecular weight 8i4 m1 Souder's viscosity constant m Calibration mark N Avogadro’s number N x ,N2 Mole fractions n The ratio ^ n7 The number of observations P Pressure head fP] SugdenTs parachor P Vapor pressure (mm. Hg.) r Capillary radius R Universal gas constant mrd Molar refraction for sodium light E / A E^~ v/ [R] Rheochor RT Alkyl group T Absolute temperature T c Critical temperature, °K T1 Torque t Temperature, °C t Critical temperature, °C c Volume of flow V V m Unit volume V W Molar volume c Work of cohesion Wi,W2 Weight of mercury slugs X Halogen atom 85 Surface tension in dynes/cm. £ Dielectric constant 41\_ Viscosity Jb L . Electric dipole moment Root-mean-square deviation (Tu 0~2 0 Solid density Fluidity Molar magnetic susceptibility © Angle of contact between liquid and solid log logarithm to the base 10 In logarithm to the base e 86 APPENDIX B Mercury Thermometer Calibration The temperature control used was described on page thermometer was immersed to the -3.0 C. mark. 32. The mercury The platinum resistance 1 thermometer had been calibrated by the National Bureau of Standards and the data fitted to the following equation: Rt = Ro [ 1 k u t + uv ( 1 - Too ) Too 1 where R is the resistance of the thermometer at t° C. R 0 was found to be 25.5031 ohms (1 6 ), and u and v were given as 0 .0 0 3 9 2 6 0 b and. 1.5919, respectively. A method of successive approximations was used to find t to the nearest 0.01° C. from the measured resistance. R_k (ohms) 28.2951 28.2971 28 ,1 2 2 j? 27.8559 27.6185 27.5625 27.3535 27.0505 26.7975 28.5651 2 8 .8 1 5 2 2 8 .8 1 8 1 29.2505 29.5650 Temperature of Platinum Resistance Thermometer Temperature of Mercury Thermometer 27.58 26.96 27.56 27 .61 2 5 .8 8 2 3 .1 2 2 0 .8 8 2 7 .0 0 2 5 .3 0 2 2 .5 3 2 0 .2 8 2 7 -6 0 19.35 18.75 17.67 lit. 70 1 8 .2 6 1 5 .2 6 1 2 .7 6 30.27 32.75 32.78 37.08 50.77 1 2 .1 8 29.70 3 2 .1 0 32.15 3 6 .U3 5 0 .1 t a corrected 25.90 2 3 .1 0 20.87 19.35 18.27 1 5 .2 8 12 .76 30.31 32 .72 32.77 37.08 5 0 .8 ,!t corrected'* is the temperature calculated by applying the stem correction and adding 0.60° C. to the observed reading. 1Leeds and Northrup serial number 1016073 platinum resistance thermometer was used with No. 1011517 Mueller bridge, type G-l. APPENDIX G Calibration Data for the Vycor Capillary Inches from Reference Tip 0.0-0.5 0.5-1.0 1.0-1.$ 1.5-2.0 2.0-2.$ 2.5-3.0 3.0-3.5 3.5-lt.O h.o-h.s 14.5-5.0 5.0 -5 .5 5.5-6.0 6 .0 -6 .5 6.5-7 .0 7.0-7.5 7.5-8.0 8.0-8.5 8.5-9.0 '9.0-9.5 9.5-10.0 10.0-10.5 1 0 .5 -1 1 . 0 1 1 .0 -1 1 . 5 1 1 .5 -1 2 . 0 1 2 .0 -1 2 .5 1 2 .5 -1 3 . 0 1 3 .0 -1 3 . 5 1 3 .5-ilj .0 1 U.0 -H 4 .5 lh.5-15.0 15.0-15.5 1 5 .5 -1 6 . 0 1 6 .0 -1 6 . 5 1 6 .5 -1 7 . 0 1 7 .0 -1 7 . 5 1 7 .5 -1 8 . 0 1 8 .0 -1 8 . 5 1 8 .5 -1 9 . 0 Length of Sing (cm,) Per Cent Deviation ■15.58 15.56 15.53 15.50 15.30 15.33 0.00 0.13 0.32 0.51 1.80 2.25 ----- --- 15. OU lit.99 111.99 ’ 15.96 15.96 15.03 15.08 15.15 15.25 15.50 15.55 15.55 15.65 15.73 15.72 3.56 3 .66 3.66 3.98 3.92 3.53 3.21 2.82 2 .12 1.16 0.91 0.26 -0.55 -0 . 9 6 -0 . 9 0 1 5 .8 0 -l.hl 15.82 15.79 15.71 15.59 15.52 15.31 15.15 15.88 15.53 15.55 15.57 15.57 15.55 15.50 15.57 -1.55 -1.35 -0 . 8 7 -0 . 0 6 1 .0 3 1.73 2.82 50 6.75 6.61 7.12 7.12 7.25 6.93 6.58 Corrected (Radius (c: 0.05875 0.05882 0.05893 0.05905 0.05980 0.06006 0.06077 O.O6 O89 0.06189 0.06108 0.06105 0.06081 0.06063 0.06050 0.05999 0.05952 0.05927 0.05889 0.05858 0.05818 0.05821 0.05791 0.05785 0.05795 0.05823 0.05836 0.05935 0.05976 0.06050 0.06138 0.06270 0.06263 0.06292 c . 06292 0.06300 0.06281 0.06255