Landolt-BrnsteinNumerical Data and Functional Relationships in Science and TechnologyNew Series / Editor in Chief: W. MartienssenGroup IV: Physical ChemistryVolume 21Virial Coefficients of PureGases and MixturesSubvolume AVirial Coefficients of Pure GasesJ. H. Dymond, K. N. Marsh, R. C. Wilhoit, K. C. WongEdited by M. Frenkel and K.N. MarshPrefaceThis critical compilation of virial coefficients of pure gases is a sequel to The Virial Coefficients ofPure Gases and Mixtures, by J.H. Dymond and E.B. Smith (Oxford University Press, 1979). This new andenlarged edition was prepared from the virial coefficient database at the Thermodynamics ResearchCenter, formerly at Texas A&M University, College Station, Texas and now located at the NationalInstitute of Standards and Technology, Boulder, Colorado. The virial coefficient data in this compilationwill be of interest to the theoretical chemist as it includes the many sets of accurate gas imperfection datawhich have been determined over the past twenty years by improved methods of gas densitydetermination, by isochoric Burnett coupling methods and from speed of sound measurements, as well asby the more traditional techniques. The needs of the industrial chemist are met by these more reliable dataand also the increased number of compounds for which data are now available.For each compound, the second and third virial coefficient data from different published sources aretabulated in increasing order of temperature, and an estimate of the uncertainty is given. Conversion to auniform set of units is undertaken where necessary. In the majority of cases, where the data cover asufficiently wide range of temperature, a weighted data fit has been made for the second virialcoefficients, and coefficients of the given equation are recorded. Values of the second virial coefficientgiven by the equation at selected temperatures are quoted.This volume includes material published up to the end of 1998. While every effort has been made tosee that the tables are free from error, it is unlikely that there will be no omissions or mistakes. We wouldappreciate it if corrections could be brought to our attention.Christchurch, New Zealand and Boulder, Colorado, USA, August 2001 The EditorsAcknowledgmentsThe authors wish to express their sincere appreciation to the University of Canterbury for the award ofa Visiting Erskine Fellowship to JHD to enable a leave at the Department of Chemical and ProcessEngineering and an award of an Erskine Grant to KNM.Our special thanks are due to Derek Caudwell, Barbara Clark, Christine Nichol and RubaVigneswaran for their assistance in formatting the text, preparing the graphs, checking the data, andcomposing the camera-ready copy of the manuscript. The facilities provided by the Department ofChemical and Process Engineering, University of Canterbury are gratefully acknowledged.Christchurch, New Zealand and Boulder, Colorado, USA, August 2001 J.H. Dymond, K.N. Marsh,R.C. Wilhoit, K.C. Wong1.1 Gas ImperfectionsLandolt-BrnsteinNew Series IV/21A10.00.51.01.52.00 5 10p/pcZ = pVm /RTT1T2T3Fig. 1. The compressibility factor Z1 IntroductionThe p-V-T behaviour of real gases is a topic that has concerned physicists and chemists for more than acentury. Some of this interest has arisen from the importance of the study of gas imperfections in theelucidation of the forces between molecules. From a more practical point of view, knowledge of p-V-Trelationships is essential for the resolution of problems in chemical engineering processes where gases arepresent.1.1 Gas ImperfectionsThe ideal gas is characterized by the equation of state:m/ 1 Z pV RT (1.1)where Z is termed the compressibility factor, or compression factor, p is the pressure, Vm the molarvolume, T the absolute temperature, and R the gas constant. Real gases may show significant deviationsfrom this equation of state even at low pressure. At low temperatures and pressures, Z is usually less thanunity whereas at high temperatures and pressures the converse is true.Typical dependence of Z on p/pc, where pc is thecritical pressure, is illustrated in Figure 1 for a series oftemperatures such that T1>T2>T3. The temperature T3 isjust above the critical temperature. The temperature T1at which the density dependence of Z is zero as p/pc zero is termed the Boyle temperature. For gases whichare neither quantum fluids nor strongly polar, thistemperature is about 2.7 times the critical temperaturefor monatomic substances, decreasing to around 2.3 forpolyatomic fluids.Many equations of state have been proposed torepresent the p-V-T behaviour of real gases but, from atheoretical point of view, the most satisfactory form, atall but the highest pressures, is the virial equation inwhich the compressibility factor is expressed as a seriesexpansion in either density (reciprocal molar volume)or pressure:2 3m m m m/ 1 / / / ........... pV RT B V C V D V + + + + (1.2)* * 2 * 3m/ 1 ............. pV RT B p C p D p + + + + (1.3)It is normal practice to define B, C, D, .... in the density (or volume) series as the second, third,fourth, virial coefficients. They are all temperature dependent. The importance of these virialcoefficients lies in the fact that they are related directly to the interactions between molecules. The secondvirial coefficient represents the departure from ideality due to interactions between pairs of molecules, thethird virial coefficient gives the effects of interactions of molecular triplets, and so on. The coefficients ofthe two series are simply related:1.1 Experimental MethodLandolt-BrnsteinNew Series IV/21A2*B B RT (1.4)*2 * 2( )( ) C B C RT = + (1.5)*3 * * * 3( 3 )( ) . D B B C D RT = + + (1.6)B(T) is defined as follows:( ) m m1/ 0 1/ 0m m( ) lim / 1 limV VB T pV RT V A (1.7)and B(T) is zero at the Boyle temperature. The general manner of the variation of B(T) with temperatureis shown in Figure 2. At low temperatures B(T) is large and negative, whereas at high temperatures it hassmall positive values which, at very high temperatures (corresponding to twenty times the criticaltemperature for helium), pass through a maximum.The third virial coefficient is given by the following limit:m1/ 0mlim ( ) .VC A B V (1.8)However, because of the difficulty in determining p-V data at constant temperature with sufficiently highaccuracy at very low densities, values for this coefficient are usually determined from gas-compressibilitydata by fitting the results at a given temperature to a polynomial in the reciprocal volume. Thecoefficients of this polynomial are then identified with the coefficients of the infinite series. The generaldependence of C(T) on temperature is illustrated in Figure 3.It should be noted that values for the virial coefficients obtained in this way depend on the degree ofpolynomial used and on the density range of the compressibility data. The resulting uncertainties in thesecond virial coefficient are small, but they are much larger for the third virial coefficient, and theuncertainty in the fourth virial coefficient is such that even the sign cannot be determined with certaintyfrom most measurements.-600-500-400-300-200-1000100T/ KB(T)/cm3. .. . mol-1Fig. 2. Second virial coefficient of methane500 1000 -3-2-1012345T/ K10-3. . . . C(T)/cm6. .. . mol-2Fig. 3. Third virial coefficient of methane 200 400 6001.1 Gas ImperfectionsLandolt-BrnsteinNew Series IV/21A3Table 1. Values of pVm /RT for methane(i) at 200 K (B = 104.64 cm3mol-1 ; C = 4020 cm6mol-2 )p/MPa Vm/cm3mol-11+B/Vm1+B/Vm+C/Vm2Zexp (1)0.2 8209.100 0.98725 0.98731 0.987320.5 3219.000 0.96749 0.96788 0.967891 1553.700 0.93265 0.93431 0.934322 716.460 0.85394 0.86178 0.861703 431.840 0.75768 0.77924 0.779064 282.830 0.68028 0.681305 182.790 0.54785 0.549635.5 138.520 0.45409 0.458166 97.913 0.35061 0.35329(ii) at 300 K (B = 42.23 cm3mol-1 ; C = 2410 cm6mol-2 )p/MPa Vm/cm3mol-11+B/Vm1+B/Vm+C/Vm2Zexp (1)0.2 12430.000 0.99660 0.99662 0.996620.5 4946.600 0.99146 0.99156 0.991571 2452.400 0.98278 0.98318 0.983202 1205.600 0.96497 0.96663 0.966674 582.910 0.92755 0.93465 0.934776 376.220 0.88775 0.90478 0.904968 273.820 0.87792 0.8781910 213.400 0.85503 0.8555515 136.870 0.82011 0.8230820 103.320 0.81703 0.8284125 86.125 0.83457 0.86320(1) 96-wag/derFortunately, for calculation of gas densities up to moderate pressures it is generally necessary toinclude only the second and third virial coefficient terms in the virial equation. This is illustrated in Table1 in the case of methane at 200 K (just above the critical temperature, 190.4 K) and at 300 K.Termination of the virial equation after the second virial coefficient term gives reasonable values for Zat densities up to about 0.25 times the critical density. This can be seen from Table 1. Methane has acritical volume of 99.2 cm3mol-1. Inclusion of the third virial coefficient term gives satisfactoryagreement at higher densities, even approaching the critical density.Values for the virial coefficients are derived from experimental measurements which can beconveniently classified as follows: low pressure p-V-T measurements; high pressure p-V-T measurements;speed of sound measurements; vapour pressure and enthalpy of vaporization measurements; refractiveindex/dielectric constant measurements and Joule-Thomson experiments. These will be discussed inChapter 1.2, and methods of data evaluation described in Chapter 1.5. Much attention has been paid to thecorrelation of virial coefficient data and the more satisfactory methods are considered in Chapter 1.3,together with a brief discussion of the theoretical calculation of the second virial coefficient from pairpotential energy functions which have been derived a priori or by consideration of other dilute gasproperties. So far, this calculation is only applicable to molecules with a spherically symmetricintermolecular potential energy function, for which1.1 Experimental MethodLandolt-BrnsteinNew Series IV/21A4-0.400.4RU(R)( ) ( )( )/ 22 1 dU R kTAB T N e R R (1.9)where NA is the Avogadro number and U(R) is thepotential energy of a pair of molecules at separation R.The general form of the dependence of U(R) on R isgiven in Figure 4.Fig. 4. Pair potential energy function1.2 Experimental MethodsMethods for the determination of virial coefficients can conveniently be classified as (a) p-V-Tmeasurements, (b) speed of sound measurements, (c) Joule-Thomson measurements, (d) refractive indexand relative permittivity measurements and (e) vapour pressure and enthalpy of vaporizationmeasurements.The great majority of the virial coefficient data come from a variety of experimental techniques for p-V-T measurement, both low pressure and high pressure. In principle, the results should be reliable and inagreement, and this is certainly true at temperatures above the critical temperature, but only where thehigh pressure measurements extend to pressures down to around 0.1 MPa. In recent years, the Burnettexpansion method [36-bur] has become the favoured high-pressure technique. It has been used by manygroups, including those at the National Research Council, Ottawa, Canada (W.G. Schneider), TexasA&M University, College Station, U.S.A. (J.C. Holste, K.R. Hall, K.N. Marsh and P.T. Eubank), KeioUniversity, Yokohama, Japan (T. Sato, K. Watanabe), and the National Institute for Standards andTechnology, Gaithersburg, U.S.A. (L.A. Weber and D.R. Defibaugh).Below the critical temperature there is a major problem in all p-V-T methods, apart from achieving therequired accuracy in the measured variables, which arises from adsorption and particularly from capillarycondensation. This problem has been overcome by Wagners group in Bochum using the methoddescribed in section 1.2.1.3, which is based on the buoyancy principle with two sinkers to compensate forthese effects.The alternative solution is to use a method where this problem does not arise. Of the possibilitieslisted under classifications (b) to (e), speed of sound measurements have the great advantage of highaccuracy in the measured variable (frequency). Even for compounds where vibrational relaxation may bestrong, requiring significant corrections for dispersion, there is still high precision in the measurements.Advances in the method of data analysis has lead to reliable acoustic virial coefficients and deriveddensity virial coefficients. Groups making measurements by this method include those at UniversityCollege, London (M.B. Ewing), the National Institute of Standards and Technology, Gaithersburg, U.S.A.(A.R.H. Goodwin and M.R. Moldover), Imperial College, London (J.P.M. Trusler), Ruhr-UniversittBochum, Germany (W. Beckermann and F. Kohler) and Keio University (H. Sato and K. Watanabe).Examples of the various techniques are described in the following sections. Since Mason and Spurling[69-mas/spu] have given an excellent summary of the methods employed up to 1969, attention will befocused here on the most important of those methods and on experimental work since that time.1.2 Experimental Methods 5Landolt-BrnsteinNew Series IV/21A1.2.1 p-V-T Measurements1.2.1.1 Low Pressure MeasurementsThe application of the virial equation to determine values for the virial coefficients requires a knowledgeof the pressure, volume, temperature and the number of moles of the gas. It is generally assumed that forpressures below 0.1 MPa, terms beyond the second virial coefficient can be neglected. For a fixed massof gas, measurements are usually made of the pressure when the gas either occupies different knownvolumes at constant temperature, or is heated to different known temperatures at constant volume.The simplest example of the first of these methods is the thermostatted Boyles Law apparatus wherea gas is confined by mercury in one side of a U-tube, which is calibrated and sealed at the upper end. Thegas pressure is measured as the difference in height of the mercury menisci in the two limbs. Mercury canbe added (or removed) at the bottom of the U-tube to vary the gas volume, and hence a set of p-Vmeasurements at constant temperature can be obtained.In order to define the gas volumes more precisely, and overcome the problems associated with themercury in contact with the gas and the limited temperature range because gas and mercury were at thesame temperature, expansion methods were later devised where the gas was allowed to expand from onevessel into another, previously evacuated, vessel (and in some cases into a series of other vessels). Thevolumes had previously been accurately determined by weighing with water or mercury. The gas wasseparated from the manometer, which can be at room temperature, by a differential pressure gauge.Greater accuracy is obtained in relative measurements when the expansion of the test gas is comparedwith that of a reference gas such as nitrogen where departure from ideal-gas behaviour is small. For thetwo gases at identical initial pressures below 0.1 MPa, undergoing expansion between vessels of matchedvolumes at constant temperature, the final pressure change is related to the difference between the secondvirial coefficients. This method has been used by the groups at Heidelberg, Germany (B. Schramm) [82-sch/mue] and Armidale (K. N. Marsh and M. B. Ewing) [79-ewi/mar].The quasi-isochoric method [94-mil/hen, 87-spi/gau] has been used by groups at Rostock, Germany(G. Opel and J. Millat) and Darmstadt, Germany (J. Gaube). A known mass of liquid is introduced intothe cell, made of quartz in the case of the first group or stainless steel for the second group, of previouslydetermined volume which is maintained at constant temperature. Pressures are measured with a highprecision mercury manometer, with a pressure transducer between the vapour and gas above themanometer, after thermal equilibrium has been established following increases in temperature. Values forthe second virial coefficient were obtained from the virial equation terminated after the third virialcoefficient term by a graphical method, a surface fit of the data or by estimation of the third virialcoefficients.The isochoric method has also been used in a relative mode [91-sch/web] by the group at Heidelberg,Germany (B. Schramm). Two vessels of equal volume are filled, one with the sample of test gas and theother with a gas with well-defined volumetric behaviour, to the same pressure at the same temperature.The pressure was less than 0.1 MPa so that only the second virial term was considered necessary. Thetemperature was changed and the resulting pressure difference between the two gases was accuratelymeasured. This is related to the difference between the second virial coefficients of the two gases at theoriginal temperature and at the new temperature. Thus, it is necessary to know the values of the secondvirial coefficient of the reference gas at each temperature and of the test gas at the original temperature.1.2.1.2 High Pressure MeasurementsThe simple and relative isothermal methods referred to just above can be used at high pressures also. Theapparatus of the group at Ohio State University, Columbus, U.S.A. (W.B. Kay) [83-mar/lin] consists of avertical tube with two volume-calibrated sections of different diameters, sealed at the upper end, in whichthe gas is confined by mercury. Thermal equilibrium was maintained by circulating a purified boilingliquid through an outer jacket around the tube. The weighed sample was admitted in sealed glassampoules. Change in volume was achieved by variation in nitrogen pressure on the mercury external tothe tube and the gas volume determined from measurement of the mercury height in the tube. Highestpressure (a few MPa) points were removed as necessary until the data were satisfactorily given by thevirial equation with just the second virial coefficient term.6 1.2 Experimental MethodsLandolt-BrnsteinNew Series IV/21APressureMeasurementVacuum / feedThe classic apparatus for high pressure gas p-V-T studies [66-tra/was], where high pressure nowrefers to pressures up to 300 MPa, was that of the group of A. Michels at the van der Waals Laboratory,Amsterdam. Known as a piezometer, the central glass gas burette consists of a series of bulbs separatedby fine capillary tubing in each section of which is a contact wire of platinum. The volumes betweensuccessive contacts is accurately known. The burette is sealed at its upper end, and the gas is confined bymercury in a known volume by raising the mercury level until electrical contact is made with one of thewires. The pressure is measured at each of these points. The piezometer is surrounded by mercury or oilto reduce the pressure difference across the glass. The data are fitted to a multi-term virial equation, thenumber of terms depending on the pressure range of the measurements.Another series of highly accurate virial coefficient determinations from high-pressure p-V-T studies[61-dou/har] which is worthy of note is that of the group of D.R. Douslin at the previous BartlesvillePetroleum Research Center, Oklahoma. The volume of a pre-weighed sample in a single globe isconfined by mercury and the pressure is noted using a free-piston gauge after the addition of a measuredvolume of mercury. The highest pressures here were about 40 MPa.The uncertainties of the effects of interaction of mercury vapour with the gas are overcome in theBurnett expansion method [36-bur]. This method has the further advantage that only pressuremeasurements are required - there is no need for mass or volume measurements. Here two different-sizedvessels are connected via narrow tubing with a valve, as shown in Figure 5.Fig. 5. Schematic Burnett apparatusThe larger vessel A contains the gas at a relatively high pressure, which is accurately measured, andthe smaller vessel B is evacuated. Valve C is then opened and the gas expands into B and the newpressure is determined. By repeating the process of closing the valve, evacuating B, opening the valveand recording the new pressure, a series of pressure readings is obtained. There are various data reductionmethods (88-pat/jof) for deriving values for the virial coefficients, both computational and graphical,from plots of the pressure ratios pi-1/pi, before and after the i-th expansion, versus the pressure, where1 1/ /i i i i ip p N Z Z- -= (1.10)and Ni , the cell constant, is the ratio of the total volume to the volume of A, given by the pressure ratio asthe pressure tends to zero. Ni should have the same value irrespective of the sample in the cell;differences, for example with organic vapours, from the value given by a gas such as helium are evidenceof adsorption.This method has the disadvantage at temperatures below the critical temperature because of thesignificant decrease in the pressure range within which measurements along an isotherm can be made. Asa result, it has become general practice to use a relatively high temperature Burnett expansion as a base,ABC1.2 Experimental Methods 7Landolt-BrnsteinNew Series IV/21Aand to follow this with isochoric measurements at the lower temperatures. The scheme can be explainedusing Figure 6.Vessel A is initially filled to pressure 11p and temperature T1 and the temperature is lowered to T2 (anisochoric run) and the pressure 21p is measured. The temperature is then raised to the initial T1 and aBurnett expansion is made to pressure 12p . An isochoric run is made to temperatures T2 and T3 and thecorresponding pressures measured. The temperature is then increased to T1 and another Burnett expansionis made to pressure 13p , followed by an isochoric run to temperatures T2 , T3 and T4. The Burnett-isochoric coupling procedure is repeated until the minimum measurable pressure is reached. The data foreach isotherm effectively constitute other Burnett runs, and a similar analysis [88-pat/jof] can be made.Fig. 6. p - T diagram for coupled Burnett-isochoric experiments1.2.1.3 Gas Density DeterminationsThis technique has been considered separately because of recent significant developments which have ledto p-V-T measurements of the highest accuracy. Historically, accurate gas density measurements weremade at different pressures to remove the effects of molecular interaction by extrapolation to zeropressure and hence to determine atomic weights. Second virial coefficients were derived from these databut the results for organic vapours had large uncertainties due to adsorption. Gas balances have been usedspecifically for second virial coefficient determination [82-zam/ste].The development [86-kle/wag] which has led to the substantially-improved accuracy is to base themethod on Archimedes buoyancy principle but to have two sinkers of identical mass and surface area,with the same surface material (gold) but with much different volumes. This leads to compensation of alleffects, including gas adsorption, which lowers the accuracy of measurements with a single sinker. Theapparatus is shown schematically in Figure 7.The measuring cell was filled with gas within the operational temperature range of 50 K to 350 K andat pressures up to 8 MPa. The sinkers were, independently, placed on the cage or removed from it. Fromthe readings on the microbalance, which was connected to the cage by a thin bar via a magnetic-suspension coupling, the resulting differential buoyant force F was determined.The density was calculated from the relationship( ) ( )S R/ / F g V V (1.11)T5 T4 T3 T2 T1TpC11p12p13p14p21p22p23p24p32p33p34p54p44p43p11p8 1.2 Experimental MethodsLandolt-BrnsteinNew Series IV/21AFig. 7. Schematic drawing of the Wagner apparatuswhere g is the acceleration due to gravity and VS ,VR are the volumes of sphere and ring respectively. Bymeasuring these volumes with an accuracy of better than 0.01 %, and the buoyant force to better than0.01 % or 410-5 g, whichever is the greater, it is estimated that the uncertainty in the gas density is lessthan 0.02 % or 0.002 kg m-3, whichever is greater. Virial coefficients derived from densities measured inthis way are amongst the most accurate made.1.2.2 Speed of Sound MeasurementsThe rise in importance of this method results from the high accuracy with which the speed of sound cannow be measured from the spherical modes of a spherical resonator, and the fact that the results are notsubject to errors from gas adsorption. One form of apparatus [89-ewi/tru] is shown schematically inFigure 8. The sealed resonator is constructed from two hemispheres of aluminium alloy, mounted on acopper support. It has two ports machined at an angle of 90o to take the electroacoustic transducers.In the absence of dispersion, the speed of sound, u, in a gas can be expressed in terms of thetemperature and molar volume:( ) ( ) 2 pg 2m a m a m, / 1 / / ... u T V RT M V V + + + (1.12)where pg = Cp,m /( Cp,m - R), superscript pg refers to the perfect gas state and Cp,m is the perfect-gas molarheat capacity at constant pressure. a, a, ... are the second, third, ... acoustic virial coefficients which arerelated to coefficients in the pressure virial equation of state and their temperature derivatives:MicrobalanceMagnetic-suspension couplingGold ringQuartz glass sphereMeasuring cell Measuring cellRadiation shield1.2 Experimental Methods 9Landolt-BrnsteinNew Series IV/21A( ) ( ) 2pg pg pg 2 2 2a2 2 1 (d / d ) 1 / (d / d ) B T B T T B T + + (1.13)and( ) ( ) ( ) 2pg pg pg pg 2 2 21 / 2 1 (d / d ) 1 (d / d )a B T B T T B T + + ( ) ( ) ( ) 2pg pg2 pg 2 2 2 pg2 1 1 (d / d ) 0.5 1 (d / d ) . C T C T T C T + + + + (1.14)Fig. 8. Schematic diagram of a spherical resonatorThe speed of sound in compressed gases is determined from the lowest-order radial modes of aspherical-resonator [89-ewi/tru, 81-meh/mol] of mean radius a0 at the given temperature and zeropressure, since (u/a0) is given by( ) ( )( ).0 0 0, 0,/ 2 / /n i i nu a a a f f v (1.15)Here, a is the radius at pressure p, f0,n are the frequencies of the radial modes, i if is the sum of smallcorrection terms and 0,n is a known eigenvalue. From isothermal measurements at different pressures, theperfect gas isobaric molar heat capacity and the second and third acoustic virial coefficients can bederived by regression analysis, using an iterative procedure. Initially, molar volumes are determined fromthe perfect gas equation and coefficients a determined. By use of a model potential-energy function, suchas the square-well potential, values for the molecular parameters in the expression for the second virialcoefficient (see 1.3) can be determined by fitting the second acoustic virial coefficient data by theequation given above. Knowledge of the second virial coefficient gives a more accurate density andhence internal consistency can be obtained by iteration in this manner. It is not necessary to know thethird virial coefficient providing the densities are sufficiently low.For direct information on the compression factor, without any assumptions about the form of theintermolecular potential energy function, the differential equations which link the speed of sound and thevirial equation of state can be numerically integrated, with known initial conditions. Specifically [96-to vacuum, gas supply and pressure transducervacuum vesseltransducer portscopper radiation shieldspherical resonatorto vacuum gauge10 1.2 Experimental MethodsLandolt-BrnsteinNew Series IV/21Aest/tru], the following two expressions are used to obtain Z and CV, m inside the (T, ) region where speedof sound measurements were made:( ) ( ) ( ) ( ) 22,m/ / / /nn n VTu RT M Z Z R C Z T Z T , ] + + + , ] ]( )( ),m/ /n V n TR C (1.16)( ) ( )2 2 22 / / .n nT Z T T Z T + (1.17)Here, n is the amount-of-substance density, equal to the reciprocal molar volume. To carry out thenumerical integration of these equations, initial values are required for two of the three quantities CV, m , Zand (Z/T)n . For example, values for Z and (Z/T)n can be determined at evenly spaced densitiesalong an initial isotherm when accurate gas-density data are known. Then, (Z/n)T can be calculatedand combined with speed of sound data to give values for CV,m at each density from the first of theequations above, and then T2(2Z/T2)n can be determined from the second equation. A simple predictor-corrector method is then used to determine Z and (Z/T)n at a temperature T from the referenceisotherm. This process is then repeated to cover the range of thermodynamic states of the speed of soundmeasurements. Accurate coefficients in the virial equation of state can then be derived from thecompression factors.1.2.3 Joule-Thomson MeasurementsFlow calorimetric measurements of the isothermal Joule-Thomson coefficient of a vapour also provideinformation on gas non-ideality which is free from adsorption errors. Basically, all that is required is afixed-throttle flow calorimeter, free of heat leaks, fitted with an electric heater as shown in Figure 9 sothat isothermal measurements can be made [77-alb/wor].Fig. 9. Schematic diagram of an isothermal Joule-Thomson apparatusThe quantity determined in the experiments is p , which is related to the enthalpy change, given bythe electric power, P, required to maintain isothermal conditions divided by the flow rate, f, and the smallpressure difference (p2 p1) across the stainless-steel gauze throttle:( ) ( ) ( )2 1 2 1 2 1/ /{ }p H H p p P f p p (1.18)since p = (H/p)T at the mean pressure, pav = (p1 + p2)/2 as (p2 p1) 0. For vapour densities, the virialequation of state can be terminated after the third virial coefficient term, which leads to the result;( ) ( )( )( )2 1 2 1 2 1 2 1(d / d ) 0.5 ' d '/ d H H p p B T B T p p p p C C T + + (1.19)Tp1Tp2porous plug(stainless steel gauze) heater1.2 Experimental Methods 11Landolt-BrnsteinNew Series IV/21Awhere C'/RT is equal to the third virial coefficient in the pressure virial series. The isothermal Joule-Thomson coefficient can then be written as( ) 0 av av1 2 / 2 0.5 (d / d ) /p p B RT p C T C T RT + (1.20)where the zero-pressure isothermal Joule-Thomson coefficient, 0 , which is equal to (B - TdB/dT), can beobtained from the intercept of a plot of p versus pav. Since 0 depends on B and its temperaturederivative, values for 0 are required over a wide temperature range for the reliable determination ofsecond virial coefficients.1.2.4 Refractive Index and Relative Permittivity MeasurementsThe dependence of the relative permittivity of a gas, , on the molar volume can be expressed by theClausius-Mosotti equation:( )( )m2m m1.....2V B CAV V + + ++(1.21)where the coefficients are dielectric virial coefficients. By introduction of the virial equation of stateterminated after the second term, this becomes:( )( ) ( )1.....2RT pA B A Bp RT + ++(1.22)Values for (B A B ) at any given temperature can be determined from measurements of the dielectricconstant at different pressures. Since the second dielectric virial coefficient is very much smaller than theproduct A B, values for B can be determined by taking an approximate value for B .It was shown by Koschine and Lehrmann [92-kos/leh] that a better procedure was to use a system oftwo cells of matching volumes, each containing a capacitor - they had a parallel-plate type. Gas pressureand capacity were measured in one cell. The gas was then expanded into the other previously-evacuatedcell, and a second set of measurements made. Finally, the first cell was evacuated and the measurementsrepeated after expansion into this volume. Their scheme for data analysis gives values for both the densityand dielectric virial coefficients.Measurements of the refractive index, n, of a gas at different pressures also provide information on thesecond virial coefficient since similar equations are obtained to the above, but with n2 replacing . TheLorentz-Lorenz function is given by:( )( )2m12 2m m11 .....2 n nn V B CAV V n + + + + (1.23)where A1 is related to the polarisability : A1 = 4NA/3 and Bn and Cn are optical, or refractivity, virialcoefficients. Combination with the virial equation of state leads to the result( )( ) ( )21211 ..... .2 nn RT pA B BRT n p + + + (1.24)The second refractivity virial coefficient is usually small compared with the second density virialcoefficient, and so estimates can be made for Bn. Details of the experimental method of refractive indexmeasurement using a Michelson interferometer at temperatures from 250 K to 340 K and at pressures upto 3 MPa are given by Husler and Kerl [88-hau/ker], who also derive values for third density virialcoefficients from their results.12 1.3 Correlation, Prediction and Estimation of Virial CoefficientsLandolt-BrnsteinNew Series IV/21A1.2.5 Vapour Pressure and Enthalpy of Vaporization MeasurementsSecond virial coefficients for a large number of organic compounds have been calculated from enthalpiesof vaporization and vapour pressure data [81-hos/sco] at the former U.S. Bureau of Mines ResearchCenter, Bartlesville by J.P. McCullough, D.W. Scott and G. Waddington. The exact Clapeyron equationcan be rearranged to give( ) ( ) vapm L m1 ...1 / dln / d 1/HBZV R V V p T + + (1.25)where VL is the liquid molar volume, vapH is the enthalpy of vaporization and p is the vapour pressure.This group has used heat capacity measurements to check the consistency of their results from therelationship( )2 20lim d d .p T p C p T B T (1.26)There is a large uncertainty in the derived virial coefficients but this method can be used for compoundswhere direct p-V-T methods are unsuitable.1.3 Correlation, Prediction and Estimation of Virial CoefficientsThe most satisfactory methods of data correlation are based on sound theory. In the case of the secondvirial coefficient, this depends on accurate knowledge of the intermolecular pair potential energyfunction, U(R, 1, 2) which, in general, depends on the orientations, 1 and 2, as well as the separation,R, of the molecules:12 1 22( ) d d2 ANB T fV (1.27)where f12 = exp{-U(R, 1, 2)/kT} - 1. For a linear molecule:d d sin d d and 4i i i i ir where i and i are the usual angles necessary to specify the orientation. For a three-dimensional rigidrotator,2d d sin d d d and 8i i i i i ir where i , i , and i are the Euler angles.For hydrogen and helium, quantum-mechanical expressions for the second virial coefficient must beused [69-mas/spu], and even for gases with a higher relative molar mass quantum-mechanical correctionsmust be applied at low temperatures.In practice, it is only for the simplest of substances that ab initio calculations of the pair interactionpotential energy have been possible with sufficient accuracy. For helium, for example, the pair potentialwas determined [97-kor/wil] using infinite order symmetry adapted perturbation theory with very largeorbital basis sets for intermediate separations, accurate dispersion coefficients at long range and quantummechanical Monte Carlo calculations at short range. The results were fitted to a modified Tang-Toennies[84-tan/toe] form of potential, with no experimental input. This potential energy function was shown [97-jan/azi] to give excellent agreement with experimental second virial coefficient data.It is more usual with closed-shell atoms to consider potential models such as the exchange-Coulomband Hartree-Fock dispersion potentials and to determine the parameters from dilute gas properties such asthe second virial coefficient and the transport properties, viscosity and thermal conductivity, together with1.3 Correlation, Prediction and Estimation of Virial Coefficients 13Landolt-BrnsteinNew Series IV/21Amolecular beam data and visible-UV spectroscopic results. This approach has been most successful withmonatomic gases for which U(R) is now well-defined [89-azi/sla, 90-azi/sla, 94-boy, 89-dha/all, 90-dha/mea]. Analysis of the second virial coefficient data alone does not lead to a unique form for theintermolecular potential energy function, although information on parts of the curve can be obtained byinversion methods [81-mai/rig]. Once the full curve is known by inclusion of other dilute-gas properties,then the second virial coefficient values calculated from this potential function can be consideredreliable. A comparison is shown in Table 1 between the present recommendations for B for argon, whichwere based entirely on experimental second virial coefficients, and values calculated from the potentialenergy function of Aziz and Slaman [90-azi/sla], for which experimental virial coefficients attemperatures above 200 K were used, with other data, to determine the potential parameters.Table 2. Comparison of second virial coefficients for argonT/K B(T)/cm3mol-1T/K B(T)/cm3mol-1This work 90-azi/sla This work 90-azi/sla80 -275.1 4.0 -277.2 200 -47.9 0.3 -48.085 -246.1 3.0 -247.1 250 -27.7 0.3 -27.890 -221.7 2.0 -221.8 300 -15.4 0.3 -15.395 -200.9 1.5 -200.7 400 -1.2 0.3 -1.0100 -183.0 1.0 -182.5 500 6.8 0.5 6.8110 -153.8 1.0 -153.3 600 11.8 0.5 11.7125 -121.7 0.5 -121.3 700 15.3 0.5 14.9150 -86.3 0.3 -86.3 800 17.8 0.5 17.2For diatomic (and higher polyatomic) molecules, the angle-dependence of the pair intermolecularpotential energy function makes the determination of U(R, 1, 2) very difficult. For this reason, it hasbeen customary to correlate second virial coefficient data on the basis of a function which is dependentjust on intermolecular separation. Furthermore, although the form of the interaction energy curve willdiffer from substance to substance, lack of knowledge of the detailed form has led to the wide-spread useof generalised forms of intermolecular potential functions. Specific molecular parameters are then derivedfrom fitting second virial coefficient data.The simplest potential form which exhibits the necessary properties of a core repulsion and anattractive interaction energy at larger separations is the square-well (SW) potential energy function,illustrated in Figure 10.Fig. 10. Square-well potential energy function.For SW molecules with core diameter , attractive energy - and well-width (-1), the second virialcoefficient is given by [81-mai/rig]U(R)R0- 14 1.3 Correlation, Prediction and Estimation of Virial CoefficientsLandolt-BrnsteinNew Series IV/21A( ) ( ) 30( ) 1 1 exp / 1 B T b kT , ] ](1.28)where b0 = 2NA3/3.This three-parameter equation gives a very reasonable fit to the recommended data for mostcompounds except alcohols. The agreement is generally within experimental uncertainty over the wholetemperature range although for some compounds the calculated B - T plots show a slightly differentcurvature to the experimental results. Different sets of parameters often give equally satisfactory fits,which means that no physical significance should be given to the results. The SW potential energyfunction is unsatisfactory in not giving the maximum at high reduced temperature which is foundexperimentally for gases such as helium.A more realistic form of U(R) will have a soft repulsive part and a longer range attractive part to thecurve, with the theoretical R-6 dependence at large separations. The repulsive interaction is theoreticallygiven by an exponential term, but inverse-power forms give a similar degree of softness. Takentogether, these results give the (n-6) potentials:6( ) / /nU R a R b R (1.29)of which the most widely-used is the Lennard-Jones (12-6) potential (24-len):( ) ( ) 12 6( ) 4 / / U R R R (1.30)where is the molecular separation at zero potential energy, and - is the maximum attractive energy.Second virial coefficients are given for this potential by analytical integration which gives( ) 2 1/ 400( ) / / .jjjB T b a T+

(1.31)Expressions were given [24-len] for the coefficients aj and tabulations of the reduced second virialcoefficient B T b ( ) /0 at a series of reduced temperatures kT/ from 0.3 to 100 are available [81-mai/rig),together with molecular parameters for a number of substances. Laesecke [2000-lae] has investigated thesignificance of the individual terms in a series with temperature exponents (1 - i)/4 where i = 1 to 80 andfound by structural optimization methods that the B(T) values were best fitted by an eight term series withi = 1 to 8. This corresponds to the first four terms of the theoretical infinite series, plus an additional fourterms to account for all the remaining contributions. Where experimental data are available over a widetemperature range, it is found that they cannot be satisfactorily correlated within the estimated uncertaintyon the basis of this potential.Other, more complex forms of U(R) have been proposed [81-mai/rig] which have proved verysatisfactory for the representation of specific rare gas interactions, for example. However, for thecorrelation and prediction of second virial coefficient data, empirical methods are generally used. Thosemethods which are based on the corresponding states principle usually represent the second virialcoefficient by a series of terms in inverse powers of temperature, as suggested by results for the (n-6)potentials, but usually with integer powers.For non-polar molecules, Tsonopoulos [74-tso] modified the Pitzer and Curl [57-pit/cur] relationshipfor the reduced second virial coefficient in terms of Tr, the temperature reduced by the criticaltemperature, and a third parameter, the acentric factor , which had been introduced to extend theapplication to non-spherical non-polar molecules, to give:c2 3 8c r r r r2 3 8r r r0.330 0.1385 0.0121 0.0006070.14450.331 0.423 0.0080.0637 .BpRT T T T TT T T + + (1.32)1.3 Correlation, Prediction and Estimation of Virial Coefficients 15Landolt-BrnsteinNew Series IV/21AThis gave a very reasonable fit to the second virial coefficient data then available, but more recent,accurate values from Burnett and speed of sound measurements indicate that the coefficients need to bere-determined. Even so, this method is very valuable for estimating second virial coefficients where dataare lacking.For polar molecules, the temperature dependence of B(T) is different. One way to account for this [74-tso] .is to add another term, a/Tr6 - b/Tr8, where a is related to the reduced dipole moment. b is zero formolecules such as aldehydes, ethers, ketones and nitriles which do not hydrogen-bond. Values for a and bhave been given [74-tso, 75-tso] for a number of polar substances, but where these parameters are notavailable it is not possible to predict the second virial coefficient.An alternative approach [75-hay/oco, 77-tar/dan] is to use the mean radius of gyration instead of theacentric factor as the third parameter. Hayden and OConnell [75-hay/oco], for example, use the radius ofgyration to determine an effective non-polar acentric factor, in terms of which the molecular energyparameter and size parameter are expressed. An equation is given for the second virial coefficient fornon-polar substances in terms of these three parameters; for polar non-associating substances additionalterms involving the reduced dipole moment are given, and for polar-associating substances theassociation contribution is added. This approach gives a better fit than the Tsonopoulos method for somehalogenated and oxygenated compounds, and for some compounds containing nitrogen or sulphur.However, for associating compounds, the additional parameter is determined specifically for thecompound considered and there is no procedure for estimating it for other compounds.More recently, a method has been described [84-mcc/dan], based on group-additivity, which does notdepend on a knowledge of molecular properties or on empirical parameters. Each group contribution wasderived by analysis of available second virial coefficient data, and represented by the equation3 7 9.r r r r/ / / /i i i i i iB a b T c T d T e T + + + + (1.33)For most groups, only the first four terms were required. Second virial coefficients for any organiccompound (except acids for which the contributions are not available) can be calculated from these groupcontributions, and critical temperatures, for reduced tempeatures from 0.5 to 5, by summing up theproducts of the group contribution and their respective number of occurrences. The method comparesfavourably with other estimation methods, and is more generally applicable.The third virial coefficient is given [69-mas/spu] by the sum of a pairwise additive term plus a termarising from departure from pairwise additivity:add non-add( ) C T C C + (1.34)where2add 12 23 31 1 2 3 33 ANC f f f d d dV (1.35)( ) ( ) 2non-add 12 23 31 1 2 3 3exp / 1 exp / .3 ANC U kT U U U kT d d dV , ] + + ] (1.36)The non-additive contribution to the total energy, U, is given by U123 - Uij. For the square-wellpotential with well width < , Cadd is given in reduced form by( ) ( ) 6 4 3add5/ 8 18 32 15 exp / 1 C kT + ( ) ( ) 26 4 3 22 36 32 18 16 exp / 1 kT + + ( ) ( ) 36 4 2. 6 18 18 6 exp / 1 kT + (1.37)The square-well expressions for B(T) and C(T) have been used [96-gil/mol) to represent the temperaturedependence of these virial coefficients for real gases in the analysis of speed of sound measurements to16 1.4 Properties of Gases in Terms of Virial CoefficientsLandolt-BrnsteinNew Series IV/21Aobtain gas densities. However, it is found that separate triads of parameters are required for each of thesevirial coefficients, indicating that no physical significance should be given to these values. It is not to beexpected that Cadd alone can represent the third virial coefficient.For the most satisfactory correlation of third virial coefficients it is best to turn to empirical methodsof which the method of Orbey and Vera [83-orb/ver] is particularly simple and effective. The third virialcoefficient in reduced form is given by( )2c2.8 2 10.5rrc0.02432 0.003130.01407CpT TRT + 2.8 3.0 6.0 10.5r r r r0.01770 0.040 0.003 0.002280.02676 .T T T T + + + (1.38)In this volume, third virial coefficients are not correlated but simply tabulated, with a note given of thesets which are considered the most reliable.1.4 Properties of Gases in Terms of Virial CoefficientsThe thermodynamic properties of gases may readily be calculated from a knowledge of the virialcoefficients and their dependence on temperature. For calculations at pressures not much greater than 1bar, a knowledge of the second virial coefficient is usually sufficient. At higher pressures, thecontribution of the third virial coefficient becomes more significant.In the following paragraphs, expressions for the thermodynamic properties are given first in a generalform for use with actual p-V-T data or any equation of state, and then specifically in terms of virialcoefficients. Internal energy, enthalpy, heat capacity at constant volume and at constant pressure, entropy,the Helmholtz energy, and Gibbs energy for a real gas at temperature T and pressure p are expressed asdeparture functions, relative to the value for that property for the ideal-gas state at the reference pressurepo. Expressions are also given for the fugacity-pressure ratio and the Joule-Thomson coefficient.1.4.1 Internal energy, UmThe departure of the molar internal energy from the ideal-gas value may be written( ) mom m mmT .VVU U p T p dV + (1.39)Using the virial equation of state, this becomes( )2m m 1 m 1 m2 ......oU U RT B V C V + + (1.40)where ( ) ( )1 1d d and d d . B T B T C T C T 1.4.2 Enthalpy, HmThe difference between the enthalpy of a real gas and that of an ideal gas under the same conditions issimply related to the corresponding difference in internal energyo om m m m. H H U U pV RT + (1.41)Thus, using the virial equation of state1.4 Properties of Gases in Terms of Virial Coefficients 17Landolt-BrnsteinNew Series IV/21Ao 1 1m m 2mm2...... .2B B C CH H RTV Vj \ + +, (, (( , (1.42)1.4.3 Heat capacity at constant volume, CV, mThis property for a real gas is given in terms of the ideal gas value by the expression( )mmo 2 2,m ,m md .VV VVC C T p T V (1.43)In terms of the virial equation of state, this becomes1 2 1 2 o, m , m2mm2 2......2V V B B C CC C RV Vj \+ + + + , (, (( ,(1.44)where ( ) ( )2 2 2 2 2 22 2d d and d d . B T B T C T C T 1.4.4 Heat capacity at constant pressure, Cp, mThis property for a real gas is given in terms of the ideal gas value by the expression( )( ) ( )mmm2o 2 2,m ,m mm// d ./ Vp pVV Tp TC C R T T p T Vp V (1.45)In terms of the virial equation of state , this becomes( ) ( )21 1 2 o 2,m ,m2m m/ 2..... .p p B B C C C BC C RV V + (1.46)1.4.5 Entropy, SmThe departure of this function from the ideal-gas values is given by( ) mom m m m m mln ln / ( / ) / dVS S R p R pV RT p T V R V V + (1.47)which leads to the following result in terms of virial coefficients( ) o 2 2m m 1 m 1 mln / 2 ...... . S S R p B V B C C V + + + + (1.48)1.4.6 Helmholtz energy, AmRelative to the reference ideal-gas state, this function for a real gas is given by the expression:( ) ( )mom m m m m- / d ln / lnVA A p RT V V RT pV RT RT p +(1.49)which, in terms of virial coefficients, gives the following result:18 1.5 Data EvaluationLandolt-BrnsteinNew Series IV/21Ao 2 2m m m{ln ( / 2 )......}. A A RT p B C V + (1.50)1.4.7 Gibbs energy, GmThe departure function for Gibbs energy may be writteno om m m m mG G A A pV RT + (1.51)which, on application of the virial equation, becomes( ) o 2 2m m m mln / / 2 .... . G G RT p B V B C V + + + + (1.52)1.4.8 Fugacity-pressure ratio, f / pFugacity f may be defined in terms of the molar Gibbs energy by the relation( )oo om m mln / d .ppG G RT f f V p (1.53)From this, the following expression may be derived:( )m0ln / / d .pRT f p RT p V p (1.54)Expressing the molar volume of the real gas in terms of the virial coefficients leads to the equation:( )2 2m mln / / / 2 ....... f p B V C B V + + + (1.55)1.4.9 Joule-Thomson coefficient, JTThe Joule-Thomson coefficient is given by the relation:( ) JT m m ,m/ ppT V T V C (1.56)which takes the following form in terms of virial coefficients:2o 1 1 2 1J 1 ,mom m , m2 2 2 ( )( ) .........T ppB B B C C R B B BB B CV V C , ] + + + +, ] , ] ](1.57)1.5 Data Evaluation1.5.1 Data Storage and ProcessingThe values of virial coefficients presented in this review were obtained through the following steps.(a) Search of the world's scientific literature,1.5 Data Evaluation 19Landolt-BrnsteinNew Series IV/21A(b) Collection in a computer readable database,(c) Extraction from the database and selection of the "best" values, and(d) Fitting to a function of temperature.Virial coefficients are constants in the virial equation of state of gases. They are not measured directly butare derived from a variety of observed properties. They are functions of temperature. Only those valuesbased on some observation are reported here. The numerical values were extracted from the originalpublications or from those collected by the Polish Academy of Science [96-dym/mar]. The latter sourcefurnished about one-third of the total set. All values were then checked against the original documentsafter they were entered into the database to insure integrity. Literature through the end of 1998 is coveredin the collection.The numerical values of virial coefficients presented in this review were inserted into the SOURCEdatabase maintained by the Thermodynamics Research Center. The database contains experimentalvalues of thermodynamic, thermochemical, and transport properties of pure compounds and binary andternary mixtures [2001-fre/don, 99-wil, 99-wil/mar]. Each property value is linked to the compound orcomponents of a mixture by use of a registry number assigned by Chemical Abstracts Service or by theThermodynamics Research Center. Each value is also linked to a document that reports it. A keyconsisting of the year of publication, the first three letters of the last name of the first author and the firstthree letters of the last name of the second author identifies literature references, if any. An additionalinteger starting with 0 is included to form a unique key. As new data are published they are added to theSOURCE database thus maintaining a complete set which can serve as the basis for future compilations.Each property value in the SOURCE database is accompanied by an estimate of uncertainty. This takesthe form of a bias, which defines a range of values below and above the property value. It is expected thatthe true value of the property lies in this range with a high probability. See references [2001-fre/don, 99-wil, 99-wil/mar] for additional explanation of uncertainties. Uncertainties are assigned by the personresponsible for adding the value to the database or by a later evaluation. They are based on an assessmentof the information in the original report, including uncertainties reported by the author. When authorshave reported uncertainties, these values are normally given in the tables. In cases where the authorsassessments are clearly unrealistic, the data are either not used in the fit or the uncertainty value isincreased during the analysis. These are annotated in the tables. The assignment generally reflects allrecognized sources of experimental error. All errors, irrespective of what variable is directly affected, arepropagated to the listed virial coefficient.1.5.2 Selection of ValuesData values were extracted from the SOURCE database by suitable software and then screened to identifythe "best" (most accurate) values. The selection was based on a comparison of the estimated uncertaintiesof values for the same substance. The selection also took into account the distribution of virialcoefficients with temperature. An appropriate algorithm has been developed at the ThermodynamicsResearch Center and has been used for several compilations. Briefly, the uncertainty for each data valuein a set was compared to a weighted mean of the uncertainties of all the other values. The weightingfactor was an inverse exponential function of the absolute value of the difference between the temperatureof the value being evaluated and the temperatures of the other values. The screening level, the size of thedata set and range of temperatures it covered determined the parameters used in the comparison.Additional details are given in [96-wil/mar]. Selected values are marked with various symbol in the tablesof data.1.5.3 Fitting to Smoothing FunctionsThe selected values of virial coefficients for each compound were fitted to a smoothing function oftemperature by the least-squares criterion, whenever there were three or more data values over anappreciable temperature range. The squares of the deviation between calculated and observed values wereweighted in proportion to the reciprocal of the square of the estimated uncertainties. The data were thenscaled by subtracting the means of each term in the polynomial from the given values. This eliminated theconstant term. The singular value decomposition technique [88-pre/fla] was used for the remaining20 1.6 Glossary of SymbolsLandolt-BrnsteinNew Series IV/21Acoefficients. The constant was then regenerated from the means. The smoothing function used for thesecond virial coefficient was the polynomial in reciprocal temperature..iiB a T (1.58)The number of terms used in these polynomials was sufficient to generate a random deviationbetween calculated and the selected observed values. This number usually depended on the range oftemperature covered by the data set. The maximum order of the polynomials was usually three.Additional terms seldom improved the fit significantly. The following metrics are given for each fitted setas a measure of fit to the data. The degree of freedom: this is the number of distinct values in the selectedset minus the order of the polynomial. The number of distinct values is the number separated by at least1.5 K. Root mean square deviation (unweighted) is given by:2exp calc( )RMS B Bn

(1.59)where n is the total number of values in the data set.Root mean square deviation (weighted) is given by:2exp calc( )RMS iiw B Bw

(1.60)where 21 .i iw u These functions have no theoretical basis. They furnish means of calculating tables of smoothedvalues of the second virial coefficients and their derivatives and of visualising the scatter of experimentalvalues. These functions did not fit some data sets adequately. In this case it was necessary to split the datafor a substance into two regions of temperature, and fit the two sets independently. The virial coefficientvalues merged at the boundary.1.6 Glossary of Symbolsa radius of spherea coefficients of B(T)A defined by equations (1.7) and (1.21)A Helmholtz energyb hard sphere second virial coefficientB second virial coefficientC heat capacity (with subscript p or V)C third virial coefficientD fourth virial coefficientf flow rate: equation (1.18)f frequency: equation (1.15)f fugacity: equation (1.53)f Meyer function: equation (1.27)F forceg acceleration due to gravityG Gibbs energyH enthalpyk Boltzmann constantM relative molecular massn refractive indexN cell constant in Burnett methodNA Avogadro constantp pressureP electric power: section 1.2.3R intermolecular separationR gas constantS entropyT temperatureu speed of soundU intermolecular potential energyfunctionV volumew weight applied to individual datapointsReferences 21Landolt-BrnsteinNew Series IV/21AZ compressibility factor, orcompression factor second acoustic virial coefficient relative permittivity intermolecular attractive well-depth position of the outer wall in asquare-well potential Joule Thomson coefficient ratio of heat capacities third acoustic virial coefficient defined in equation (1.18) eigenvalue, , Euler angles density molecular diameter 82 (three dimensional) defined by equation (1.27) orientation acentric factorSubscriptsa acousticadd pairwise additiveav averagec criticalm molarL liquidn optical, or refractivity(virial coefficient)n amount of substanceo mean (radius)p constant pressurer reduceds sphereT constant temperatureV constant volumevap vaporization polarisability dielectric (virial coefficient)Superscripts* virial coefficients in the pressureseriespg perfect gasReferences24-len Lennard-Jones, J. E.; Proc. Roy. Soc. A106 (1924) 463.36-bur Burnett, E. S.; J. Appl. Mech. 3 (1936), 136.57-pit/cur Pitzer, K. S.; Curl, Jr., R. F.; J. Am. Chem. Soc. 79 (1957), 2369.61-dou/har Douslin, D. R.; Harrison, R. H.; Moore, R. T.; McCullough, J. P.; Chem. Phys. 35(1961) 1357.66-tra/was Trappeniers, N. J.; Wassenaar, T.; Wolkers, G. J.; Physica (Amsterdam) 32 (1966)1503.69-mas/spu Mason, E. A.; Spurling, T. H.; The Virial Equation of State, The InternationalEncyclopaedia of Physical Chemistry and Chemical Physics, Pergamon Press, Oxford,(1969).74-tso Tsonopoulos, C.; AIChE. J. 20 (1974) 263.75-hay/oco Hayden, J. G.; OConnell, J. P.; Ind. Eng. Chem., Process Des. Dev. 14 (1975) 209.75-tso Tsonopoulos, C.; AIChE. J., 21, (1975), 827-829.77-alb/wor Al-Bizreh, N.; Wormald, C. J.; J. Chem. Thermodyn. 9 (1977) 749.77-tar/dan Tarakad, R. R.; Danner, R. P.; AIChE. J. 23 (1977) 685.79-ewi/mar Ewing, M. B.; Marsh, K. N., J. Chem. Thermodyn. 11 (1979) 793.81-hos/sco Hossenlopp, I. A.; Scott, D. W.; J. Chem. Thermodyn. 13 (1981) 423.81-mai/rig Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A.; Intermolecular forces; theirorigin and determination. Oxford University Press, Oxford (1981).81-meh/mol Mehl, J. B.; Moldover, M. R.; J. Chem. Phys. 74 (1981) 4062.82-sch/mue Schramm, B.; Mueller, W.; Ber. Bunsen-Ges. Phys. Chem. 86 (1982) 110.82-zam/ste Zamojski, W.; Stecki, J.; Pol. J. Chem. 56 (1982) 563.22 1.6 Glossary of SymbolsLandolt-BrnsteinNew Series IV/21A83-mar/lin Marcos, D. H.; Lindley, D. D.; Wilson, K. S.; Kay, W. B.; Hershey, H. C.; J. Chem.Thermodyn. 15 (1983) 1003.83-orb/ver Orbey, H.; Vera, J. H.; AIChE. J. 29 (1983) 107.84-mcc/dan McCann, D. W.; Danner, R. P.; Ind. Eng. Chem., Process Des. Dev. 23 (1984) 529.84-tan/toe Tang, K. T.; Toennies, J. P.; J. Chem. Phys. 80 (1984) 3726.86-kle/wag Kleinrahm, R.; Wagner, W.; J. Chem. Thermodyn. 18 (1986) 739.87-spi/gau Spiske, J.; Gaube, J.; Chem. Eng. Technol. 10 (1987) 143.88-hau/ker Husler, H.; Kerl, K.;. Int. J. Thermophys. 9 (1988) 117.88-pat/jof Patel, M. R.; Joffrion, L.; Eubank, P. T.; AIChE. J. 34 (1988) 1229.88-pre/fla Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterlling, W. T.; Numerical Recipesin C, New York; Cambridge Univ. Press (1988).89-azi/sla Aziz, R. A.; Slaman, M. J.; Chem. Phys. 130 (1989) 187.89-dha/all Dham, A. K.; Allnatt, A. R.; Meath, W. J.; Aziz, R. A.; Mol. Phys. 67 (1989) 1291.89-ewi/tru Ewing, M. B.; Trusler, J. P. M.; J. Chem. Phys. 90 (1989) 1106.90-azi/sla Aziz, R. A.; Slaman, M. J.; J. Chem. Phys. 92 (1990) 1030.90-dha/mea Dham, A. K.; Meath, W. J.; Allnatt, A. R.; Aziz, R. A.; Slaman, M. J.; Chem. Phys. 142(1990) 173.91-sch/web Schramm, B.; Weber, C.; J. Chem. Thermodyn. 23 (1991) 281.92-kos/leh Koschine, A.; Lehmann, J. K.; Meas. Sci. Technol. 3 (1992) 411.94-boy Boyes, S. J.; Chem. Phys. Lett. 221 (1994) 467.94-mil/hen Millat, J.; Hendl, H.; Bich, E.; Int. J. Thermophys. 15 (1994) 903.96-dym/mar Dymond, J. H.; Marsh K. N.; Maczynski, A.; Floppy Book for Virial Coefficients ofPure Gases and Gas Mixtures, TRC Databases for Chemistry and Engineering,Thermodynamics Research Center, Texas A&M University (1996).96-est/tru Estrada-Alexanders, A. F.; Trusler, J. P. M.; Int. J. Thermophys. 17 (1996) 1325.96-gil/mol Gillis, K. A.; Moldover, M. R.; Int. J. Thermophys. 17 (1996) 1305.96-wag/der Wagner, W.; de Reuck, K. M.; Methane, International Thermodynamic Tables of theFluid State - 13, Blackwell Science (1996).96-wil/mar Wilhoit R. C.; Marsh, K. N.; Hong, X.; Gadalla, N.; Frenkel, M.; ThermodynamicProperties of Organic Compounds and Their Mixtures, Subvolume B. Densities ofAliphatic Hydrocarbons Alkanes, Landolt-Brnstein, Group IV. Physical Chemistry,Vol. 8, Berlin; Springer-Verlag, (1996). Also Subvolumes C-F.97-jan/azi Janzen, A. R.; Aziz, R. A.; J. Chem. Phys. 107 (1997) 914.97-kor/wil Korona, T.; Williams, H. L.; Bukowski, R.; Jeziorski, B.; Szalewicz, K; J. Chem. Phys.106 (1997) 5109.99-wil Wilhoit, R. C.; Documentation for the TRC Source Database, ThermodynamicsResearch Center, College Station TX, 77843, Nov. (1999) 207.99-wil/mar Wilhoit R. C.; Marsh, K. N.; Int. J. Thermophys. 10 (1999) 247.2000-lae Laesecke, A.; Reference correlations for the virial coefficients of the Lennard-Jonesfluid, private communication.2001-fre/don Frenkel, M.; Dong, Q.; Wihoit, R.C.; Hall, K.R.; Int. J. Thermophys. 22 (2001) 215.2. Inorganic Compounds 23Landolt-BrnsteinNew Series IV/21A2 Tabulated Data on Second Virial Coefficients of InorganicCompoundsArgon [7440-37-1] Ar MW = 39.95 1Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 3.4162 10 1.2087 104/(T/K) 7.6702 105/(T/K)2 1.9600 107/(T/K)3T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-176 -302.3 5.0 110 -153.8 1.0 400 -1.2 0.380 -275.1 4.0 125 -121.7 0.5 500 6.8 0.585 -246.1 3.0 150 -86.3 0.3 600 11.8 0.590 -221.7 2.0 200 -47.9 0.3 700 15.3 0.595 -200.9 1.5 250 -27.7 0.3 800 17.8 0.5100 -183.0 1.0 300 -15.4 0.3 1000 21.3 0.5Table 2. Experimental values with uncertainties and deviation from calculated values.T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)75.00 -313.8 1.0 -4.092-ewi/tru-1(L)150.65 -85.6 1.0 0.0 58-mic/lev({)80.00 -276.7 1.0 -1.692-ewi/tru-1(L)150.65 -85.6 1.0 0.0 58-mic/lev({)90.00 -221.4 0.8 0.392-ewi/tru-1(L)150.70 -85.7 0.3 -0.1 94-gil/kle-1()100.00 -182.1 0.6 0.992-ewi/tru-1(L)153.00 -83.2 0.3 -0.1 94-gil/kle-1()110.00 -152.9 0.5 0.992-ewi/tru-1(L)153.15 -82.5 1.0 0.4 58-mic/lev({)110.00 -152.7 1.3 1.1 94-gil/kle-1() 153.15 -83.0 1.0 -0.1 58-mic/lev({)110.00 -153.6 0.5 0.2 96-est/tru(z) 155.00 -81.2 0.3 -0.1 94-gil/kle-1()120.00 -130.7 0.6 0.5 94-gil/kle-1() 155.00 -81.4 0.2 -0.4 96-est/tru(z)120.00 -130.9 0.4 0.3 96-est/tru(z) 157.00 -79.2 0.3 -0.1 94-gil/kle-1()125.00 -121.0 0.4 0.792-ewi/tru-1(L)160.00 -76.3 0.3 -0.2 94-gil/kle-1()130.00 -113.0 0.3 0.1 94-gil/kle-1() 160.00 -76.4 0.2 -0.3 96-est/tru(z)130.00 -112.9 0.4 0.2 96-est/tru(z) 163.15 -71.9 1.0 1.4 58-mic/lev({)133.15 -108.0 1.0 0.2 58-mic/lev({) 163.15 -73.3 1.0 0.0 58-mic/lev({)135.00 -105.4 0.3 0.0 94-gil/kle-1() 165.00 -71.8 0.3 -0.2 94-gil/kle-1()138.15 -100.9 1.0 0.1 58-mic/lev({) 170.00 -67.6 0.3 -0.2 94-gil/kle-1()140.00 -98.5 0.3 0.0 94-gil/kle-1() 173.15 -64.2 1.0 0.8 58-mic/lev({)140.00 -97.2 0.3 1.3 96-est/tru(z) 173.15 -65.2 1.0 -0.2 58-mic/lev({)143.00 -94.7 0.3 -0.1 94-gil/kle-1() 175.00 -63.8 0.3 -0.1 94-gil/kle-1()143.15 -94.4 1.0 0.0 58-mic/lev({) 175.00 -63.8 0.2 -0.2 96-est/tru(z)145.00 -92.2 0.3 -0.1 96-est/tru(z) 180.00 -60.2 0.3 -0.1 94-gil/kle-1()146.00 -91.0 0.3 -0.1 94-gil/kle-1() 188.15 -54.3 1.0 0.4 58-mic/lev({)148.00 -88.7 0.3 -0.1 94-gil/kle-1() 188.15 -54.8 1.0 -0.1 58-mic/lev({)148.15 -88.3 1.0 0.1 58-mic/lev({) 190.00 -53.7 0.3 -0.1 94-gil/kle-1()148.15 -88.5 1.0 -0.1 58-mic/lev({) 190.00 -53.7 0.2 -0.1 96-est/tru(z)150.00 -86.0 0.2 0.392-ewi/tru-1(L)200.00 -47.9 0.1 0.092-ewi/tru-1(L)150.00 -86.7 0.2 -0.4 96-est/tru(z) 200.00 -48.0 0.3 -0.1 94-gil/kle-1()cont.24 2. Inorganic CompoundsLandolt-BrnsteinNew Series IV/21AArgon (cont.)-6-4-2024650 150 250 350 450 550 650 750T/K( Bexp - Bcalc )/cm3 . mol-1Fig. 1. The symbols show the deviation of the calculated from the experimental values from Table 2. Thecurves above and below the zero line indicate the calculated error region of the recommended valuesgiven in Table 1. The error bars represent the experimental errors. (Error bars smaller than the symbolsare omitted for clarity of the figure.)Table 2. (cont.)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)203.15 -46.0 1.0 0.3 58-mic/lev({) 298.15 -15.5 1.0 0.3 49-mic/wij()203.15 -46.5 1.0 -0.3 58-mic/lev({) 298.15 -15.8 1.0 0.0 49-mic/wij()205.00 -45.5 0.2 -0.2 96-est/tru(z) 300.00 -15.2 0.1 0.292-ewi/tru-1(L)220.00 -38.5 0.3 -0.1 94-gil/kle-1() 303.15 -15.1 0.1 -0.3 67-kal/mil()220.00 -38.6 0.2 -0.1 96-est/tru(z) 303.15 -15.1 0.1 -0.3 67-kal/mil()223.15 -37.1 1.0 0.1 58-mic/lev({) 310.00 -13.3 0.3 0.1 94-gil/kle-1()223.15 -37.4 1.0 -0.3 58-mic/lev({) 323.15 -11.1 1.0 0.1 49-mic/wij()248.15 -28.3 1.0 0.0 58-mic/lev({) 323.15 -11.2 1.0 -0.1 49-mic/wij()248.15 -28.6 1.0 -0.3 58-mic/lev({) 325.00 -10.7 0.3 0.2 94-gil/kle-1()250.00 -27.7 0.1 0.092-ewi/tru-1(L)340.00 -8.3 0.3 0.2 94-gil/kle-1()250.00 -27.7 0.3 0.0 94-gil/kle-1() 348.15 -7.1 1.0 0.2 49-mic/wij()250.00 -27.9 0.1 -0.2 96-est/tru(z) 348.15 -7.3 1.0 0.1 49-mic/wij()265.00 -23.4 0.3 0.0 94-gil/kle-1() 355.00 -6.4 0.1 0.0 96-est/tru(z)273.15 -21.1 1.0 0.2 49-mic/wij() 373.15 -3.9 1.0 0.2 49-mic/wij()273.15 -21.5 1.0 -0.1 49-mic/wij() 373.15 -4.0 1.0 0.1 49-mic/wij()280.00 -19.6 0.3 0.1 94-gil/kle-1() 373.15 -4.1 0.1 0.0 67-kal/mil()295.00 -16.3 0.3 0.1 94-gil/kle-1() 373.15 -4.0 0.1 0.1 67-kal/mil()295.00 -16.4 0.1 0.0 96-est/tru(z) 398.15 -1.1 1.0 0.3 49-mic/wij()cont.2. Inorganic Compounds 25Landolt-BrnsteinNew Series IV/21AArgon (cont.)Table 2. (cont.)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)398.15 -1.2 1.0 0.2 49-mic/wij() 573.15 10.8 0.1 0.1 67-kal/mil()400.00 -0.9 0.1 0.3 92-ewi/tru-1(L)573.15 10.6 0.1 0.0 67-kal/mil()400.00 -1.1 0.1 0.1 96-est/tru(z) 600.00 11.8 0.1 0.0 92-ewi/tru-1(L)423.15 1.4 1.0 0.4 49-mic/wij() 673.15 14.3 0.1 -0.2 67-kal/mil()423.15 1.4 1.0 0.3 49-mic/wij() 673.15 14.2 0.1 -0.3 67-kal/mil()450.00 3.3 0.1 0.0 96-est/tru(z) 700.00 15.1 0.1 -0.2 92-ewi/tru-1(L)473.15 5.1 0.1 0.1 67-kal/mil() 773.15 17.1 0.1 -0.1 67-kal/mil()473.15 5.2 0.1 0.2 67-kal/mil() 773.15 17.0 0.1 -0.2 67-kal/mil()500.00 7.0 0.1 0.2 92-ewi/tru-1(L)Further references: [10-onn/cro, 25-hol/ott, 30-tan/mas, 53-wha/lup, 56-cot/ham, 60-lec, 62-fen/hal, 62-poo/sav, 66-cra/son, 67-wei/wyn, 68-byr/jon, 69-lic/sch, 70-bla/hal, 70-bos/col, 71-pro/can, 72-osb, 73-pop/cha, 74-bel/rei, 74-hah/sch, 74-sch/heb, 76-san/uri, 77-ren/sch, 77-sch/sch, 79-ewi/mar, 79-sch/leu-1,80-per/sch, 80-sch/geh, 80-woo/kro, 82-ker, 84-ker/hae, 88-pat/jof, 89-ewi/owu, 91-lop/roz].Boron trifluoride [7637-07-2] BF3MW = 67.81 2Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 9.1039 10 5.9081 104/(T/K) + 1.0478 107/(T/K)2 3.0463 109/(T/K)3T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1275 -132 5 335 -73 4 435 -26 1295 -107 5 355 -60 2 475 -15 1315 -88 5 395 -41 2Table 2. Experimental values with uncertainties and deviation from calculated values.T Bexp B Bexp - Bcalc Ref. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1 in Fig. 1)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)273.15 -135.1 3.0 -0.8 66-vis({) 323.15 -83.0 5.0 -1.3 73-wax/hil()273.15 -135.0 5.0 -0.7 73-wax/hil() 323.20 -82.0 5.5 -0.3 61-raw()283.15 -117.9 3.0 3.2 66-vis({) 333.15 -65.0 3.0 9.3 66-vis({)283.16 -123.0 5.0 -1.9 73-wax/hil() 335.84 -75.0 5.0 -2.6 73-wax/hil()293.15 -110.7 3.0 -1.2 66-vis({) 343.20 -71.2 5.8 -3.7 61-raw()293.20 -105.1 5.4 4.3 61-raw() 348.15 -67.0 5.0 -2.6 73-wax/hil()298.15 -98.1 3.0 6.1 66-vis({) 373.15 -52.0 2.0 -1.3 73-wax/hil()298.15 -106.0 5.0 -1.8 73-wax/hil() 398.15 -40.0 2.0 -0.5 73-wax/hil()303.20 -98.0 6.1 1.1 61-raw() 423.15 -30.0 1.0 0.3 73-wax/hil()310.65 -94.0 5.0 -1.8 73-wax/hil() 448.15 -22.0 1.0 0.5 73-wax/hil()313.15 -97.5 3.0 -7.5 66-vis({) 473.16 -16.0 1.0 -0.2 73-wax/hil()313.20 -89.7 5.6 0.2 61-raw() 498.15 -10.0 1.0 0.0 73-wax/hil()323.15 -78.6 3.0 3.2 66-vis({)cont.26 2. Inorganic CompoundsLandolt-BrnsteinNew Series IV/21ABoron trifluoride (cont.)Fig. 1. The symbols show the deviation of the calculated from the experimental values from Table 2. Thecurves above and below the zero line indicate the calculated error region of the recommended valuesgiven in Table 1. The error bars represent the experimental errors. (Error bars smaller than the symbolsare omitted for clarity of the figure.)Diborane [19287-45-7] B2H6MW = 27.67 3Table 1. Experimental values with uncertainty.T Bexp B Ref._________ ______________________________________K cm3 mol-1275.15 -227.0 11.0 49-car/claHydrogen cyanide [74-90-8] CHN MW = 27.03 4Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 6.0611 103 + 4.6389 106/(T/K) 9.8352 108/(T/K)2T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1305 -1424 150 335 -977 140 365 -734 110315 -1246 150 345 -878 130 375 -685 100325 -1099 140 355 -798 120 380 -665 100cont.-15-10-5051015250 300 350 400 450 500T/K( Bexp - Bcalc )/cm3 mol-12. Inorganic Compounds 27Landolt-BrnsteinNew Series IV/21AHydrogen cyanide (cont.)Table 2. Experimental values with uncertainties and deviation from calculated values.T Bexp B Bexp - Bcalc Ref._________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1T Bexp B Bexp - BcalcRef._________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1303.15 -1602 300 -141 65-cot/mac 348.15 -940 200 -89 65-cot/mac303.15 -1564 250 -103 65-cot/mac 348.15 -765 75 86 65-cot/mac303.15 -1332 100 129 65-cot/mac 383.15 -507 150 147 65-cot/mac343.15 -811 200 84 65-cot/mac 383.15 -672 150 -19 65-cot/mac343.15 -989 200 -94 65-cot/macCarbon monoxide [630-08-0] CO MW = 28.01 5Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 4.8826 10 1.5614 104/(T/K) 2.7570 105/(T/K)2 4.7684 107/(T/K)3T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1125 -118.1 0.5 235 -26.3 0.5 435 10.9 1.0135 -101.3 0.5 265 -16.6 0.5 475 14.3 1.0145 -87.6 0.5 295 -9.1 0.5 515 17.1 1.0165 -66.5 0.5 325 -3.2 0.5 555 19.5 1.0185 -51.2 0.5 355 1.6 0.5 570 20.3 1.0205 -39.4 0.5 395 6.8 0.5Table 2. Experimental values with uncertainties and deviation from calculated values.T Bexp B Bexp - BcalcRef. (Symbol_________ _____________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)120.00 -127.8 0.4 0.2 83-goo-1({) 323.20 -3.7 0.4 -0.2 64-con()140.00 -94.7 0.5 -0.5 83-goo-1({) 330.00 -4.3 0.5 -2.0 83-goo-1({)160.00 -71.5 0.6 -0.4 83-goo-1({) 348.15 0.9 1.0 0.3 52-mic/lup()180.00 -54.8 0.7 -0.2 83-goo-1({) 348.15 1.1 1.0 0.5 52-mic/lup()200.00 -42.0 0.8 0.1 83-goo-1({) 373.15 4.5 1.0 0.4 52-mic/lup()220.00 -32.3 0.2 0.1 83-goo-1({) 373.15 4.6 1.0 0.5 52-mic/lup()240.00 -24.3 0.3 0.2 83-goo-1({) 398.15 7.5 1.0 0.4 52-mic/lup()260.00 -17.5 0.3 0.5 83-goo-1({) 398.15 7.7 1.0 0.6 52-mic/lup()273.15 -14.2 1.0 0.2 52-mic/lup() 400.00 5.0 0.6 -2.3 83-goo-1({)273.15 -13.7 1.0 0.7 52-mic/lup() 423.15 10.0 1.0 0.3 52-mic/lup()280.00 -12.0 0.4 0.6 83-goo-1({) 423.15 10.2 1.0 0.4 52-mic/lup()295.00 -9.0 0.4 0.1 83-goo-1({) 423.20 9.6 0.5 -0.2 64-con()298.15 -8.3 1.0 0.2 52-mic/lup() 450.00 9.6 0.6 -2.6 83-goo-1({)298.15 -8.0 1.0 0.5 52-mic/lup() 473.20 14.5 0.2 0.4 64-con()300.00 -7.2 0.4 0.9 83-goo-1({) 513.20 17.3 0.2 0.3 64-con()323.15 -3.4 1.0 0.2 52-mic/lup() 573.20 20.5 0.2 0.0 64-con()323.15 -3.3 1.0 0.3 52-mic/lup()cont.28 2. Inorganic CompoundsLandolt-BrnsteinNew Series IV/21ACarbon monoxide (cont.)Further references: [29-sco, 31-tow/bha, 56-mat/sta, 63-mul/kir-1, 80-sch/geh, 82-sch/mue, 83-goo-1(set-2, set-3), 86-eli/hoa, 87-bar/cal, 91-bou/moo, 91-sch/eli, 96-vat/sch].Fig. 1. The symbols show the deviation of the calculated from the experimental values from Table 2. Thecurves above and below the zero line indicate the calculated error region of the recommended valuesgiven in Table 1. The error bars represent the experimental errors. (Error bars smaller than the symbolsare omitted for clarity of the figure.)Carbonyl sulfide [463-58-1] COS MW = 60.08 6Table 1. Experimental values with uncertainty.T Bexp B Ref._________ ______________________________________K cm3 mol-1T Bexp B Ref._________ ______________________________________K cm3 mol-1290.00 -270.0 30.0 92-bel/big 310.00 -226.7 26.0 92-bel/big300.00 -250.0 30.0 92-bel/bigCarbon dioxide [124-38-9] CO2MW = 44.01 7Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 5.7400 10 3.8829 104/(T/K) + 4.2899 105/(T/K)2 1.4661 109/(T/K)3cont.-4-2024100 200 300 400 500 600T/K( Bexp - Bcalc )/cm3 . mol-12. Inorganic Compounds 29Landolt-BrnsteinNew Series IV/21ACarbon dioxide (cont.)Table 1. (cont.)T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1220 -247.9 1.0 320 -104.5 0.5 530 -24.2 0.5230 -223.8 0.5 350 -84.2 0.5 590 -14.3 0.5250 -184.9 0.5 380 -68.5 0.5 650 -6.7 0.5270 -155.0 0.5 420 -52.4 0.5 710 -0.5 0.5290 -131.5 0.5 470 -37.4 0.5 770 4.5 0.5-3-2-10123200 300 400 500 600 700 800T/K( Bexp - Bcalc )/cm3 . mol-1Fig. 1. The symbols show the deviation of the calculated from the experimental values from Table 2. Thecurves above and below the zero line indicate the calculated error region of the recommended valuesgiven in Table 1. The error bars represent the experimental errors. (Error bars smaller than the symbolsare omitted for clarity of the figure.)Table 2. Experimental values with uncertainties and deviation from calculated values.T Bexp B Bexp - Bcalc Ref. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1 in Fig. 1)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)217.00 -255.4 1.0 0.5 87-hol/hal(z) 240.00 -202.1 0.8 0.9 90-dus/kle(N)220.00 -247.5 1.0 0.4 87-hol/hal(z) 250.00 -184.8 0.3 0.1 87-hol/hal(z)220.00 -247.5 1.0 0.4 90-dus/kle(N)260.00 -168.9 0.3 0.1 87-hol/hal(z)230.00 -223.7 0.5 0.1 87-hol/hal(z) 260.00 -168.3 0.7 0.7 90-dus/kle(N)240.00 -202.8 0.4 0.2 87-hol/hal(z) 270.00 -155.1 0.3 -0.1 87-hol/hal(z)cont.30 2. Inorganic CompoundsLandolt-BrnsteinNew Series IV/21ACarbon dioxide (cont.)Table 2. (cont.)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)T Bexp B Bexp - BcalcRef. (Symbol_________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1in Fig. 1)273.15 -151.2 1.0 -0.2 35-mic/mic() 348.15 -85.4 0.8 -0.1 90-glo(L)273.15 -150.1 0.3 0.9 73-wax/dav({) 348.41 -86.7 1.0 -1.5 35-mic/mic()273.20 -150.4 0.5 0.5 87-jae() 353.20 -83.1 0.5 -0.7 87-jae()280.00 -142.7 0.3 -0.1 87-hol/hal(z) 372.92 -73.7 1.0 -1.8 35-mic/mic()280.00 -142.1 0.6 0.5 90-dus/kle(N)373.15 -71.9 0.3 -0.1 73-wax/dav({)290.00 -131.6 0.3 -0.1 87-hol/hal(z) 373.15 -71.6 0.2 0.2 87-hol/hal(z)293.20 -128.0 0.5 0.2 87-jae() 373.15 -72.0 0.7 -0.2 90-glo(L)298.15 -123.2 0.2 0.2 87-hol/hal(z) 398.15 -60.7 0.3 -0.1 73-wax/dav({)298.20 -123.6 1.0 -0.3 35-mic/mic() 398.15 -60.5 0.1 0.2 87-hol/hal(z)300.00 -121.7 0.2 -0.1 87-hol/hal(z) 398.15 -60.6 0.7 0.0 90-glo(L)300.00 -121.4 0.5 0.2 90-dus/kle(N)398.16 -62.2 1.0 -1.6 35-mic/mic()303.05 -119.5 1.0 -0.7 35-mic/mic() 412.98 -55.8 1.0 -0.8 35-mic/mic()304.19 -118.4 1.0 -0.7 35-mic/mic() 418.20 -54.0 1.0 -1.0 35-mic/mic()304.19 -117.7 1.0 0.0 90-glo(L)423.15 -51.4 0.3 -0.1 73-wax/dav({)305.23 -117.3 1.0 -0.5 35-mic/mic() 423.15 -51.3 0.1 0.1 87-hol/hal(z)313.20 -109.8 0.5 0.1 87-jae() 423.15 -51.3 0.6 0.0 90-glo(L)313.25 -110.8 1.0 -1.0 35-mic/mic() 423.20 -52.4 3.1 -1.1 66-vuk/mas()320.00 -104.7 0.2 -0.2 87-hol/hal(z) 423.29 -52.2 1.0 -1.0 35-mic/mic()320.00 -104.5 0.4 0.0 90-dus/kle(N)448.15 -43.5 0.1 -0.1 87-hol/hal(z)322.86 -103.5 1.0 -1.2 35-mic/mic() 473.20 -36.7 2.3 -0.1 66-vuk/mas()323.15 -102.3 0.3 -0.2 73-wax/dav({) 523.20 -25.1 1.8 0.4 66-vuk/mas()323.15 -102.0 0.2 0.1 87-hol/hal(z) 573.20 -16.3 1.3 0.5 66-vuk/mas()323.15 -102.2 0.9 -0.1 90-glo(L)623.20 -9.4 1.0 0.5 66-vuk/mas()333.20 -95.0 0.5 -0.1 87-jae() 673.20 -3.7 0.7 0.4 66-vuk/mas()340.00 -90.6 0.3 -0.2 90-dus/kle(N)723.20 0.9 0.5 0.3 66-vuk/mas()348.15 -85.4 0.3 -0.1 73-wax/dav({) 773.20 4.8 0.3 0.1 66-vuk/mas()348.15 -85.2 0.2 0.1 87-hol/hal(z)Further references: [1897-led/sac, 05-ray, 33-caw/pat, 37-caw/pat, 37-sch, 50-bot/mas, 50-lam/sta, 50-mac/sch, 55-pfe/gof, 56-cot/ham, 56-cot/ham-1, 57-coo, 58-per/dia, 63-mul/kir-1, 64-but/dad, 67-dad/eva,67-ku /dod, 67-sas/dod, 69-lic/sch, 70-bos/col, 70-tim/kob, 80-hol/wat, 80-kat/ohg, 80-sch/geh, 81-ben/bie, 82-ohg/nak-1, 82-sch/mue, 84-ohg/sak, 86-eli/hoa, 87-mal/nat, 88-pat/jof, 91-lop/roz, 91-sch/eli92-web].Carbon disulfide [75-15-0] CS2MW = 76.14 8Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 2.8415 10 3 2.8985 106/(T/K) + 9.5830 108/(T/K)2 1.2515 1011/(T/K)3T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1285 -937 50 340 -578 50 430 -290 50295 -847 50 360 -498 50 470 -193 50310 -738 50 380 -430 50325 -650 50 400 -371 50cont.2. Inorganic Compounds 31Landolt-BrnsteinNew Series IV/21ACarbon disulfide (cont.)Table 2. Experimental values with uncertainties and deviation from calculated values.T Bexp B Bexp - BcalcRef._________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1T Bexp B Bexp - BcalcRef._________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1281.94 -923 60 44 62-wad/smi 330.22 -638 15 -15 64-bot/spu-1295.20 -659 200 186 52-cas/mas 337.14 -605 60 -15 69-haj/kay295.20 -849 3 -4 58-bot/ree 346.04 -583 15 -31 64-bot/spu-1295.20 -646 100 199 58-bot/rem 353.15 -480 45 44 69-haj/kay297.68 -793 15 32 64-bot/spu-1 368.15 -430 42 39 69-haj/kay298.15 -802 50 20 62-wad/smi 374.15 -492 15 -43 64-bot/spu-1308.20 -748 3 1 58-bot/ree 382.15 -380 36 44 69-haj/kay308.20 -582 100 167 58-bot/rem 398.15 -335 30 41 69-haj/kay313.15 -810 100 -93 69-haj/kay 413.15 -310 25 25 69-haj/kay319.37 -696 50 -15 62-wad/smi 426.15 -381 15 -81 64-bot/spu-1323.15 -671 15 -11 64-bot/spu-1 427.15 -270 20 28 69-haj/kay323.15 -700 80 -40 69-haj/kay 453.15 -230 18 3 69-haj/kay323.20 -661 3 -2 58-bot/ree 473.15 -195 16 -10 69-haj/kay325.28 -661 15 -13 64-bot/spu-1Chlorine trifluoride [7790-91-2] ClF3MW = 92.45 9Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 1.0754 103 + 9.3227 105/(T/K) 2.7872 108/(T/K)2T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1T/K (B 2est)/cm3 mol-1275 -1371 100 300 -1065 100 340 -745 80285 -1236 100 320 -884 100 355 -661 60Table 2. Experimental values with uncertainties and deviation from calculated values.T Bexp B Bexp - BcalcRef._________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1T Bexp B Bexp - BcalcRef._________ ______________________________________ _____________________________________K cm3 mol-1cm3 mol-1273.20 -1360 30 37 56-mag-11)313.20 -841 45 99 56-mag-11)293.20 -1162 70 -24 56-mag-11)334.40 -706 20 74 56-mag-11)307.20 -1146 20 -152 56-mag-11)356.30 -689 170 -35 56-mag-11) Weight was replaced by larger uncertainties in the fitting analysis.Hydrogen chloride [7647-01-0] ClH MW = 36.46 10Table 1. Recommended values given by the following equation whose coefficients were obtained by aweighted least square fit of the selected experimental values:B/cm3 mol-1 = 8.1566 10 9.7274 104/(T/K) + 2.7321 107/(T/K)2 5.3320 109/(T/K)3T/K (B 2est)/cm3 mol-1