A new equation of state (hsft) based on fractal theory

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A new equation of state (hsft)based on fractal theoryHua Zhao a & Pingli Pei-Shengma ba Department of Chemical Engineering, Chemistryand Environmental Science , NewJersey Institute ofTechnology , Newark, NJb Department of Chemical Engineering , TianjinUniversity , Tianjin, P. R. ChinaPublished online: 09 Sep 2010.

To cite this article: Hua Zhao & Pingli Pei-Shengma (2002) A new equation ofstate (hsft) based on fractal theory, Chemical Engineering Communications, 189:9,1155-1195, DOI: 10.1080/00986440213880

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ANEWEQUATIONOFSTATE (HSFT) BASEDONFRACTALTHEORY

HUA ZHAO

Department of Chemical Engineering,Chemistry and Environmental Science,NewJersey Institute ofTechnology,Newark, NJ

PINGLIPEI-SHENGMA

Department of Chemical Engineering,Tianjin University,Tianjin, P. R. China

This paper describes the molecular distribution of fluids by some fractal

characteristics based on the current understandings of microstructures in

fluids. The coordination relation was derived according to this fractal model,

and the molecular mean potential function for simple square-well fluids was

proposed. By applying this new mean potential function, a new equation of

state (EOS) named HSFT was derived from statistical mechanics. Vapor

pressures and saturated liquid densities of about 200 pure substances were

correlated by the proposed model. Resulting equation parameters were fur-

ther generalized by acentric factor o and critical compressibility factor Zc.

Saturated properties for 180 substances and enthalpies of vaporization for 115

substances, including compounds with strong polarity, were calculated by the

generalized HSFT equation. Compared with several other equations of state,

satisfactory results computed by HSFT equation imply that the generalized

HSFT equation possesses better adaptability and reliability.

Keywords: Fractal; Occupation number; Mean potential; Equation of state

(EOS)

Received 17 February 2000; in final form 20 March 2001.

Address correspondence to Hua Zhao, E-mail: [email protected] (contact for

current mailing address).

Chem. Eng. Comm.,189: 1155�1195, 2002Copyright# 2002 Taylor & Francis

0098-6445/02 $12.00+ .00

DOI: 10.1080=00986440290012564

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INTRODUCTION

Thermodynamic properties of real fluids can be calculated by combiningmolecular interactions and their microscopic structures. Although X-rayscattering data (Marcus, 1977) can determine the pair distribution functionof the fluid directly, the results are usually limited to simple fluids (such asargon, mercury, etc.) due to the complicated nonlinear behaviors of fluidmolecules. Statistical mechanics (Prausnitz, et al., 1986) is also quitehelpful in comprehending the molecular space distribution in fluids.However, it is very difficult to arrive at accurate formulas of thecoordination relation of molecules due to the complicated mathematicalcalculations. In the past four decades, various physical models have takenour understanding of the fluid phase to a relatively sophisticated level. Dueto the fact that short range structure in fluids is similar to the solid state,many famous physical models were developed based on this characteristic,such as quasi-lattice theory (Guggenheim, 1952), free volume theory(Prigogine, 1957) and Flory’s theory (Flory, 1965). Advanced physicalmodel theories of the liquid state require complicated combinatorialmathematics to achieve realistic models of liquid structure (Baker, 1963).Recently, local structure models of polymer solutions analyzed by fractaltheory have been reported (Witten, 1998). Several types of fractal struc-tures that impart special properties to liquids have been built: random-walkand rigid-linear polymers (Elias, 1984), branched polymers (Daoud, 1995),and colloidal aggregates (Witten and Gates, 1986). In this paper, based onthe knowledge of microstructures in fluids, an assumption of fractal dis-tribution will be proposed for simple fluids as a new physical model.

Fractal theory, as a newly developing branch of nonlinear science,has become a very powerful tool in describing those extremely compli-cated behaviors in nature and engineering. This awareness is largely dueto the activities of B. B. Mandelbrot (1977, 1982, 1988), who called at-tention to particular geometrical properties of such objects as the shoresof continents, the branches of trees, or the surface of clouds. He coinedthe name fractal for these complex shapes to express that they can becharacterized by noninteger (fractal) dimensionality. The basic idea offractal sets is their self-similarity in some manner. A fractal is a shapemade of parts similar to the whole in some way, as indicated by Man-delbrot (Feder, 1988). The relevance of fractals to physics and manyother fields was also pointed out by Mandelbrot, who demonstrated therichness of fractal geometry and presented further important results in hisbooks on the subject (1982, 1988). Based on the idea of nonlinearbehaviors of molecular distribution in fluids, the fractal characteristics offluids will be explored in our work. Further, a new thermodynamic modelwill be developed based on this fractal structure, and the calculations ofthermodynamic properties will be used to support our assumptions.

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FRACTALMODEL ANDOCCUPATIONNUMBER

In this paper, we use ‘‘fluids’’ to indicate dense gases and liquids whosemolecules have some kinds of local structures, not a random distribution.Further, a fluid is an equilibrium state of matter and, therefore, is distinctfrom an amorphous solid. Local structure in the fluid may be char-acterized by a pair distribution function g(r) that is related to the prob-ability of finding pairs of molecules separated by distance r. At liquiddensities, the fluid exhibits short-range structure similar to the solidand long-range disorder characteristic of the gas phase (Hailer andMansoori, 1983). This suggests that a local structure exists in the fluid ina range limit. It is also commonly acknowledged that there are multi-coordination rings in the fluid and usually the first coordination ringcontributes most to the macroscopic thermodynamic properties. The firstcoordination ring is assumed to be simply represented by Figure 1, wherethe coordination ring is composed of a central molecule and itscoordination molecules.

Based on the analysis of the microstructure in the fluid phase above,it is reasonable to assume that a fractal structure can be generated in thefluid by using the coordination ring (Figure 1) as a fractal generator.Such a fractal distribution has infinite elaborate structures within thescale limits (the range of the scale: from the size of a molecule to themacro-size of the fluid). In each level of structure, the basic property ofself-similarity always exists. The pair distribution function of this fractalstructure also indicates that there are multicoordination rings in the fluidthat are consistent with the experimental data discussed above.

Figure 1. Schema of the first coordination ring.

A NEW EQUATION OF STATE (HSFT) BASED ON FRACTAL THEORY 1157

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This type of fractal structure can easily be described by the self-similar dimension Ds, whose definition is:

Ds ¼lnNc

lnL0ð1Þ

where Nc is the number of molecules within the range of a centralmolecule that is usually defined as occupation number; L0, called theself-similar ratio in fractal which is the ratio of the diameter of the co-ordination ring to the diameter of a molecule.

In order to quantitatively analyze this fractal behavior, assume thediameter of a molecule (effective diameter for a nonspherical molecule) isd and the distance between two adjacent molecules is D. Then the ratio L0

is given by

L0 ¼2Dþ d

dð2Þ

The local reduced density of the coordination ring (Figure 1) can beexpressed by

z ¼ Ncv1v2

ð3Þ

where v1 ¼ pd3=6 is the volume of a molecule and v2 ¼ pðL0dÞ3=6 is thevolume of the coordination ring. Substituting these volume formulas intoEquation (3), we have

z ¼Ncðp6 d3Þp6 ðL0dÞ3

¼ Nc

L30

ð4Þ

As is well known, the fluid reduced density Z is given by

Z ¼ b0

v¼ b

4vð5Þ

where v is the molar volume of the fluid, and b0 ¼ b=4 is the molar volumeof hard spheres.

Also

b0 ¼ NApd3

6

� �ð6Þ

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where NA is Avogadro’s constant.For the fluid system with fractal structure, because of the self-simi-

larity of fractal distribution in each level, the fluid reduced density Z isequal to the local reduced density z. Thus, combining Equations (4) and(5) gives

Nc ¼ L30Z ð7Þ

In order to build the relationship between the ratio L0 and some fluidstate parameter, assume every molecule is in the center of a fictitioussphere (Figure 2). Meanwhile, the neighboring fictitious spheres aretangent with each other.

The volume of fictitious spheres v0 can be calculated in two differentways:

v0 ¼ p6D3 ¼ r0

v

NA

� �ð8Þ

where r0 is a constant for the volume of fictitious spheres per volume ofthe fluid. r0 is the function of molecular arrangement styles in space, so itis related to a certain substance. Solving Equation (8) for D

Figure 2. Microdistribution of fictitious spheres.


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D ¼ 6r0vpNA

� �1=3

ð9Þ

Putting Equation (9) into Equation (2) and then combining Equa-tions (5) and (6) gives

L0 ¼ 2r0Z

� �1=3

þ 1 ð10Þ

In order to determine the occupation number in Equation (7), thespecific property of r0 should be studied. Using Equations (5) and (6) inEquation (9) yields

D

d

� �3

¼ r0Z

� 1 ð11Þ

In addition, according to the physical meaning, if Z ! 0, thenr0 ! 0; if Z ! 1, then r0 ! 1. To satisfy those mathematical require-ments, r0 is assumed to be the function of Z, and in the format ofr0 ¼ Zc ðc 1Þ. Parameter c, named as the fractal structure exponent, isa characteristic constant related to certain substances (explained later).The exponent c demonstrates the space arrangement styles of the mole-cules.

Using the above assumption into Equation (10), we have

L0 ¼ 2Zðc�1Þ3 þ 1 ð12Þ

Then substituting Equation (12) into (7), the formula of the occu-pation number can be obtained:

Nc ¼ Zþ 6Zðcþ2Þ3 þ 12Z

ð2cþ1Þ3 þ 8Zc ð13Þ

Figure 3 indicates that the relation of Nc and Z is nonlinear if c 6¼ 1.0.Meanwhile, Nc is related to different substances by parameter c. Ifc¼ 1.0, Equation (13) is the van der Waals’ basic assumption: Nc is linearin density at low densities (Sandler, 1985).

Fractal dimension, as a characteristic measure of fractal structure,can be understood as the occupation ability of fractal objects in spacein some way. Fractal dimension may be expressed in various formsfor different objects, such as Hausdorff dimension, self-similar dimen-sion, and cluster fractal dimension (Feder, 1988). In this situation, the

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self-similar dimension which has been defined by Equation (1), is moresuitable. Substituting Equation (12) and (13) into Equation (1), we havethe expression of self-similar dimension for the fluid

Ds ¼lnðZ þ 6Z

ðcþ2Þ3 þ 12Z

ð2cþ1Þ3 þ 8ZcÞ

lnð2Zðc�1Þ3 þ 1Þ

ð14Þ

Obviously, the self-similar dimension exists mathematically onlywhen the occupation number Nc � 1, or there is a critical value of Z ¼ Z0that satisfies the following equation:

Z0 þ 6Zðcþ2Þ3

0 þ 12Zð2cþ1Þ

3

0 þ 8Zc0 ¼ 1 ð15Þ

If Z � Z0, the molecular distribution is considered as a fractalstructure. Otherwise, it is a random distribution since the molecules moverandomly in gases with low densities. It can be proved in mathematicsthat Equation (15) always has a solution when parameter c is greater thanzero. This conclusion is consistent with the pair distribution function forliquids and gases as discussed above: liquids have short-range structures,but gases with low densities essentially have no local structure.

Figure 4 shows that the self-similar dimension Ds varies with re-duced density Z and fractal structure exponent c. Ds increases with Z,which indicates the increasing of occupation ability of molecules. It isinteresting that at low Z, Ds decreases with c, but at high Z, Ds increases

Figure 3. Occupation number varies with the reduced density.


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with c. This can be explained as follows: although a higher value of cmeans more regular arrangements of molecules, at low Z, molecules withhigher c strongly tend to be in irregular distribution because of more freevolume among the fluid. Therefore, the total effect is the decreasing of theregularity in molecular distribution with increasing of c at low density.With the increasing of Z, the total effect is to have more regular ar-rangements in space that increases the value of Ds.

MEANPOTENTIAL ANDHSFT EQUATION

Statistical mechanics provide a golden connection between moleculardistribution and macro-scale thermodynamic properties. Especially, wenote that for the hard-sphere potential, occupation number Nc is in-dependent of temperature at all densities (Sandler, 1985). Therefore, byassuming that the interaction energy of the fluid molecules can be de-scribed by the square-well potential, the mean potential can be derived byapplying the appropriate functions from statistical mechanics.

f ¼ �Nce ð16Þ

Substituting Equation (13) into Equation (16) gives the mean po-tential based on the fractal model:

f ¼ �eðZþ 6Zðcþ2Þ3 þ 12Z

ð2cþ1Þ3 þ 8ZcÞ ð17Þ

Figure 4. Self-similar dimension varies with the reduced density and parameter c.

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where f decreasing with Z if 0 c 1 indicates fewer interactions in lessdense fluids (Figure 5), which is consistent with the van der Waals sup-position (Anderson and Prausnitz, 1980).

Van der Walls proposed the molecular mean potential f (Andersonand Prausnitz, 1980) as:

f ¼ � 2aN

VN2A

¼ � 8a

bNAZ ð18Þ

where constant a depends on temperature. Clearly, f of van der Waals islinear with the reduced density. But f given by Equation (17) is nonlinearin reduced density, and f is also related to a specific substance. For vander Waals’ equation of state, a¼ 27b2pc, b¼RTc=(8pc), e¼RTc=NA;substituting these equations into Equation (18) yields f¼ 727eZ, whichis a special case of Equation (17) when c¼ 1.0. So, the proposed meanpotential will probably be more consistent with the molecular interac-tions of real fluids and express the molecular potential more accuratelythan van der Waals’.

An engineering-oriented discussion of van der Waals’ theory waspresented by Vera and Prausnitz (1972). For a pure fluid, the generalizedcanonical van der Waals partition function Q is

Q ¼ 1

N!

V

L3

� �NVf

V

� �Nexp

�f2kT

� �� Nqr;v;e� �N ð19Þ

Figure 5. Mean potential varies with the reduced density.


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where the thermal de Broglie wavelength is L ¼ h=ð2pmkTÞ1=2. Addi-tional h is Plank’s constant, m is the mass, k is Boltzmann’s constant, andT is the absolute temperature. For non-long-chain molecules and non-electrolytes, qr;v;e is only the function of temperature.

Equation (19) refers to N molecules occupying a total volume V. Thefree volume Vf represents the volume available to the finite-sized mole-cules; since real molecules occupy space, Vf < V. As discussed by Veraand Prausnitz (1972), the free-volume term in Equation (19) is most ac-curately represented by the closed-form, hard-sphere equation ofCarnahan and Starling (1969), which can be written in the form

Vf

V¼ exp

Zð3Z� 4Þ1� Zð Þ2

" #ð20Þ

From statistical mechanics, the equation of state can be given by

p ¼ kT@ lnQ

@V

� �T;N

ð21Þ

Combining Equations (17) and (19)�(21) yields a new molecularthermodynamic model based on fractal theory:

p ¼ RT

v

1þ Zþ Z2 � Z3

1� Zð Þ3

" #

� e0

2vZþ 2ðcþ 2ÞZ

ðcþ2Þ3 þ 4ð2cþ 1ÞZ

ð2cþ1Þ3 þ 8cZc

h i ð22Þ

where Z¼ b=(4v), b=4 is the volume of one mole of hard-sphere mole-cules, v is the molar volume, e

0 ¼ NAe, NA is Avogadro’s number, and e isthe square-well energy parameter.

In Equation (22), there are three parameters, the molar hard-spherevolume b=4, the square-well energy parameter e

0, and the fractal structure

exponent c. So, we call Equation (22) Hard-Sphere Three-ParameterEquation of State Based on Fractal Theory, abbreviated HSFT.

We notice that the three parameters in the HSFT equation havedistinct physical significance, and they can express the characteristics ofthe molecules themselves. Defining b ¼ b0 RTc=Pc, e

0 ¼ e0RTc, and ac-cording to the critical conditions:

ð@p=@vÞTc ¼ 0 ð23Þ

ð@2p=@v2ÞTc ¼ 0 ð24Þ

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pcvc=RTc ¼ Zc ð25Þ

The values of b0; e0, and c can easily be calculated by solving these threeequations simultaneously if the critical parameters are known for a cer-tain compound. Appendix A lists the calculated values of b0; e0, and c forabout 200 commonly used organic and inorganic compounds.

Figure 6 shows that the fractal structure exponent c decreases as thenumber of carbons in n-alkanes increases. The larger the number ofcarbons, the lower the spherical symmetry of the molecule, which meansthe space occupation ability of molecules decreases and the irregularity ofthe molecular arrangements in fluids increases. In most cases, the criticalcompressibility factor Zc is larger for simple, small spherical, and non-polar molecules, and is smaller for complex, nonspherical, and polarmolecules. The fractal structure exponent c increases with the increase ofthe critical compressibility factor as shown in Figure 7. Therefore, thefractal structure exponent c is a characteristic of the fractal distributionof molecules in fluids.

CORRELATIONCALCULATIONBYHSFT EQUATION

In order to calculate the phase equilibria of mixtures accurately, EOSshave to describe the vapor pressure of pure substance precisely. For hard-sphere molecules, parameter b has no relation to temperature. While themolecules of real fluid are elastic (soft), b is in relation to temperature.For the molecules of real fluid, we assume:

b� ¼ abðTrÞb ð26Þ

Figure 6. Parameter c varies with the number of carbon in n-alkanes.


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where abðTrÞ is the temperature rectified coefficient of parameter b:

abðTrÞ ¼ exp½A1ð1� TrÞ1=3 þ A2ð1� TrÞ þ A3ð1� TrÞ4=3 ð27Þ

Many experimental results indicate that the interaction of moleculesrelates to temperature. Thus, the energy parameter e

0is considered to be

the function of temperature. This article also gives the temperature re-lation formula of parameter e

0:

e� ¼ aeðTrÞe0 ð28Þ

where aeðTrÞ is the temperature rectified coefficient of parameter e0:

aeðTrÞ ¼ 1þ A4ð1� TrÞ2=3 þ A5ð1� TrÞ þ A6ð1� TrÞ4=3 ð29Þ

Using Equations (26)�(29) in Equation (22) yields the HSFT equa-tion of real fluids:

p ¼ RT

v

1þ Zþ Z2 � Z3

1� Zð Þ3

" #

� e�

2vZþ 2ðcþ 2ÞZ

ðcþ2Þ3 þ 4ð2cþ 1ÞZ

ð2cþ1Þ3 þ 8cZc

h i ð30Þ

where Z ¼ b�=ð4vÞ.

Figure 7. Parameters e0; b0; c varies with Zc.

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Based on the equilibrium condition of equal fugacity for vapor andliquid phases, for each temperature ab and ae were calculated by Equation(22) from the experimental saturated liquid density (experimental datafrom Smith and Srivastava (1986)). The equation parameters A1�A6

were therefore correlated using this calculated ab�T and ae � T data.Using the calculated parameters A1�A6 for each compound, saturatedliquid densities and saturated vapor pressures of 188 pure substances forpolar and nonpolar fluids (experimental data from Smith and Srivastava(1986)) were computed by the HSFT Equation (30). The calculated resultsare presented in Appendix B. From this table, the total average relativeerror of saturated liquid densities and saturated vapor pressures calcu-lated from Equation (30) are 0.10% and 0.34% respectively, which showsthat the calculated and experimental results are in good agreement overwide ranges of temperature. Meanwhile, Appendix B gives the values ofparameters A1�A6 for each substance. Moreover, the HSFT equationdemonstrates good precision for the calculation on the saturated liquiddensities of associating acetic acid and some metals (Table I).

Diagrams of pVT prediction of methane and ammonia by the HSFTequation in three different temperature conditions (below the criticalpoint, critical area, and supercritical state) are shown in Figure 8 andFigure 9, respectively. These figures indicate the calculated data from theHSFT equation are very consistent with the experimental data (Angus etal., 1978; Haar and Gallagher, 1978). Satisfactory results were also ob-tained in predicting thermodynamic properties of supercritical fluids ofmethane and ammonia. That will be a good basis in predicting mixturephase equilibria, including supercritical components.

GENERALIZATIONOFHSFT EQUATION

In the previous calculations using the HSFT equation, each substance hasa set of HSFT equation parameters A1, A2, A3, A4, A5, and A6 that were

Table I Variations for Saturated Properties of Acetic Acid and Some Metals

No. Compounds Tr N

AADv

(%)

AADp

(%) References

1 acetic acid .493� .997 28 .201 .905 Smith and Srivastava (1986)

2 lithium .211� .526 25 .118 .961 Volyok (1969)

3 sodium .200� .580 20 .141 1.443 Volyok (1969)

4 potassium .222� .622 19 .168 1.285 Volyok (1969)

5 rubidium .214� .619 18 .193 .604 Volyok (1969)

6 cesium .220� .634 18 .064 .808 Volyok (1969)

Total 128 0.15 1.00


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correlated by experimental data. In order to calculate other thermo-dynamic properties by the HSFT equation and widen the application ofthe HSFT equation for more substances, it is necessary to generalize theHSFT equation parameters A1, A2, A3, A4, A5, and A6 with certain

Figure 8. pVT diagram of methane.

Figure 9. pVT diagram of ammonia.

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properties related to the substances themselves. In this paper, the acentricfactor o and critical compressibility factor Zc will be considered forgeneralizing the HSFT equation due to their availability for manycompounds.

For molecules with nonpolarity or weak polarity, the critical com-pressibility factor Zc and the acentric factor o have such approximaterelationship as (Reid et al., 1987):

Zc ¼ 0:291� 0:08o ð31Þ

Based on this, most equations of state were generalized only by usingacentric factor o to correlate equation parameters. So those generalizedequations can be used to predict the thermodynamic properties of non-polar or weakly polar molecules. However, for molecules with medium orstrong polarity, the relation between the critical compressibility factor Zcand the acentric factor o does not exist simply as shown in Equation (31).So, it is more reasonable to rectify such deviation by correlating equationparameters with both the acentric factor and the critical compressibilityfactor (Yan and Xu, 1988). However, such rectification is still limited forstrongly polar or strongly asymmetric substances. To solve such a pro-blem, we will divide compounds into two categories based on theirpolarity.

Category (I) includes compounds with non-, weak, or medium po-larity, such as alkanes, alkene, aromatic hydrocarbons, and someinorganic compounds. The dipole moments of those substances areusually less than 1.8� 1.9 D.

Category (II) includes compounds with strong polarity or strongasymmetry, such as (1) cycloalkanes; (2) alkenes and alkynes with cis-and trans- structures; and (3) inorganic compounds with strong polarity(such as ammonia and sulfur dioxide). The dipole moments of substancesin this category are usually greater than 1.8� 1.9 D.

By applying both the critical compressibility factor Zc and acentricfactor o (those data from (Reid et al., 1987)) as correlating factors, thefollowing generalized relations are obtained from the equation para-meters A1, A2, A3, A4, A5, and A6, which have been calculated previously(listed in Appendix B).

For compounds in Category (I):

A1 ¼ �0:111753þ 0:0553240o� 0:627530o2 þ 1:00942o3 ð32Þ

A2 ¼ �2:651913� 0:367162oþ 3:211241o2 þ 1:240563=Zc ð33Þ


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A3 ¼ 0:995455� 0:164491o� 3:718632o2 � 0:530949=Zc ð34Þ

A4 ¼ 0:216354þ 0:918071o� 0:404821o2 þ 0:0490255Zc ð35Þ

A5 ¼ 0:656121� 2:519939oþ 1:306044o2 � 0:454057=Zc ð36Þ

A6 ¼ �2:234184þ 2:518916o� 0:229030o2 þ 0:855387=Zc ð37Þ

For compounds in Category (II):

A1 ¼ �0:169761� 0:0948199oþ 0:0945103o2 þ 0:178597Zc ð38Þ

A2 ¼ �2:795534þ 1:327360o� 0:985656o2 þ 1:242604=Zc ð39Þ

A3 ¼ 3:686885� 0:526304oþ 0:331051expðoÞ � 1:420531=Zc ð40Þ

A4 ¼ �0:581897þ 1:113578oþ 0:772611o2 þ 2:53999Zc ð41Þ

A5 ¼ �0:8171352� 2:078932o� 3:084861o2 þ 1:615519o3 ð42Þ

A6 ¼ 2:501389þ 6:060817o� 1:463972expðoÞ � 0:160401=Zc ð43Þ

where the ranges of the acentric factor and critical compressibility factorare o ¼ �0:22 � 0:70 and Zc ¼ 0:2 � 0:3, respectively.

Calculating Saturated Liquid Densities by Generalized HSFT

Saturated liquid densities of 180 substances were calculated by the gen-eralized HSFT equation, as shown in Table II. The total average relativeerror of 180 substances with 5408 experimental data is just 2.38%, whichindicates the generalized HSFT equation can calculate saturated prop-erties for a wide range of substances.

Table III shows the total average relative error of saturated liquiddensities predicted by the other four equations of state, i.e., SRK (Soave,1972), PR (Peng and Robinson, 1976), PT (Patel and Teja, 1982), andCCOR (Lin et al., 1983; Guo et al., 1985a, 1985b), respectively. The re-sults from the generalized HSFT equation are also shown in this table.Comparison of those results shows that the HSFT equation has higherprecision than the other four equations in calculating saturated propertiesfor both polar and nonpolar substances.

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Table II Variations of Saturated Liquid Density by Generalized HSFT

No. Compounds Tr N AADv

1 methane .477� .997 45 1.823

2 ethane .298� .995 45 2.815

3 propane .262� .982 43 2.824

4 n-butane .510� .922 28 1.592

5 isobutane .522� .904 25 3.302

6 n-pentane .322� .967 42 1.068

7 2-methyl-butane .413� .971 35 .702

8 2,2-dimethyl-propane .602� .998 44 2.223

9 n-hexane .363� .970 42 2.311

10 2-methyl-pentane .581� .965 23 .680

11 3-methyl-pentane .561� .979 41 1.796

12 2,2-dimethyl-butane .561� .947 31 .179

13 2,3-dimethyl-butane .550� .978 40 .495

14 n-heptane .354� .968 42 1.661

15 2-methyl-hexane .515� .977 43 .554

16 3-methyl-hexane .538� .977 42 1.149

17 3-ethyl-pentane .555� .967 27 .442

18 2,2-dimethyl-pentane .550� .967 27 .274

19 2,3-dimethyl-pentane .553� .972 31 3.491



22 2,2,3-trimethyl-butane .546� .966 39 1.196

23 n-octane .394� .970 42 2.068

24 2-methyl-heptane .495� .972 37 1.240

25 3-methyl-heptane .488� .972 38 .974

26 4-methyl-heptane .486� .949 38 .489

27 3-ethyl-hexane .485� .975 40 1.387

28 2,2-dimethyl-hexane .504� .973 38 .590

29 2,3-dimethyl-hexane .493� .974 39 .220

30 2,4-dimethyl-hexane .493� .974 39 1.514

31 2,5-dimethyl-hexane .496� .964 38 .721

32 3,3-dimethyl-hexane .489� .961 38 2.110

33 3,4-dimethyl-hexane .491� .962 38 .190

34 2-methyl-3-ethyl-pentane .489� .974 39 2.578

35 3-methyl-3-ethyl-pentane .482� .973 39 .392

36 2,2,3-trimethyl-pentane .485� .973 39 3.075

37 2,2,4-trimethyl-pentane .364� .969 40 .773



40 n-nonane .579� .713 15 2.239

41 cyclopropane .495� .970 34 1.830

42 cyclobutane .433� .594 37 .901

43 cyclopentane .448� .983 39 1.175

44 cyclohexane .504� .978 43 .684


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Table II (Continued )


45 methyl-cyclopentane .514� .916 35 1.054

46 cycloheptane .492� .976 40 9.148

47 methylcyclohexane .482� .968 32 .919

48 ethylcyclopentane .537� .976 38 .797

49 1,1-dimethyl-cyclopentane .536� .556 8 4.065

50 ethylcyclohexane .450� .611 30 5.021

51 1,1-dimethyl-cyclohexane .464� .514 10 5.429

52 cis-1,2-dimethyl-cyclohexane .450� .616 31 4.210

53 trans-1,2-dimethyl-cyclohexane .461� .522 12 3.160





58 n-propyl-cyclopentane .537� .617 17 .914

59 ethylene .368� .995 45 1.773

60 propylene .241� .997 45 1.532

61 1-butene .512� .925 35 2.165

62 cis-2-butene .494� .693 27 3.018

63 trans-2-butene .499� .880 40 1.447

64 isobutylene .493� .838 35 2.591

65 1-pentene .417� .953 38 2.204

66 cis-2-pentene .590� .931 22 5.164

67 trans-2-pentene .455� .714 37 3.213

68 3-methyl-1-butene .640� .662 10 2.753

69 2-methyl-2-butene .438� .745 24 8.946

70 1-hexene .562� .663 33 .454

71 cis-2-hexene .573� .587 7 4.012

72 trans-2-hexene .568� .599 15 3.270

73 cis-3-hexene .567� .588 10 4.097

74 trans-3-hexene .564� .594 15 2.915

75 2-methyl-2-pentene .566� .587 11 1.498

76 3-methyl-cis-2-pentene .566� .587 11 2.442

77 3-methyl -trans-2-pentene .562� .582 9 3.009

78 4-methyl-cis-2-pentene .598� .620 12 4.475

79 4-methyl-trans-2-pentene .594� .617 12 4.740

80 2,3-dimethyl-1-butene .585� .607 12 3.257

81 3,3-dimethyl-1-butene .598� .641 19 1.599

82 1-heptene .527� .564 9 4.762

83 2,3,3-trimethyl-1-butene .542� .606 20 .177

84 1-octene .507� .694 19 .564

85 cyclopentene .541� .597 15 .231

86 cyclohexene .434� .651 28 2.028

87 propadiene .519� .618 12 3.116

88 1,3-butadiene .468� .856 29 2.019

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89 2-methyl-1,3-butadiene .452� .622 28 .675

90 1,5-hexadiene .538� .639 39 3.072

91 methyl-acetylene .539� .962 37 2.900

92 1-butyne .522� .608 21 5.651

93 2-butyne .559� .606 18 5.108

94 benzene .505� .978 42 2.086

95 toluene .333� .923 38 2.430

96 ethylbenzene .433� .789 23 2.818

97 o-xylene .440� .971 39 1.897

98 m-xylene .433� .943 37 2.618

99 p-xylene .467� .797 27 3.223

100 styrene .447� .646 34 5.922

101 n-propyl-benzene .425� .671 28 3.073

102 isopropyl-benzene .426� .675 30 1.378

103 1-methyl-2-ethyl-benzene .547� .670 25 7.992

104 1-methyl-4-ethyl-benzene .548� .681 27 8.523

105 1,2,3-trimethyl-benzene .417� .456 7 .195

106 1,2,4-trimethyl-benzene .428� .564 12 2.308


108 acetone .498� .970 33 1.015

109 methyl-ethyl-ketone .508� .596 7 .862

110 methyl-n-propyl-ketone .500� .626 11 .970

111 diethyl-ketone .508� .619 11 6.489

112 methyl-isopropyl-ketone .520� .576 6 2.138

113 methyl-isobutyl-ketone .501� .653 14 .604

114 cyclo-pentanone .436� .580 16 1.070

115 cyclo-hexanone .490� .556 7 4.442

116 methyl-phenyl-ketone .435� .678 42 .215

117 methyl-chloride .464� .956 40 1.776

118 methyl-iodide .479� .581 19 8.184

119 dibromo-methane .520� .638 31 1.686

120 dichloro-methane .416� .812 28 7.525

121 chloroform .403� .804 31 4.197

122 dichloromonofluro-methane .543� .972 36 .456

123 chlorodifluro-methane .550� .989 40 .801

124 carbon-tetra-chloride .455� .988 44 1.136

125 trichlorofluro-methane .480� .987 37 .782

126 dichloro-difluoro-methane .447� .982 40 .291

127 chloro-trifluoro-methane .480� .987 40 1.667

128 carbon-tetra-fluoride .404� .804 30 1.883

129 ethyl-bromide .433� .611 13 6.627

130 ethyl-chloride .530� .832 26 6.841

131 ethyl-fluoride .461� .624 14 4.604

132 1,1-dichloro-ethane .461� .625 13 .542


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133 1,1-difluoro-ethane .600� .998 38 2.279

134 1,1,2-trichloro-ethane .538� .640 22 4.510

135 1,2-difluro-1,1,2,2-tetrachloro-

ethane

.550� .661 42 3.295

136 1,2,2-trichloro-1,1,2-trifluoroe .509� .989 43 4.864

137 1,2-dichloro-1,1, 2,2-tetrafluoroe .475� .986 43 2.583

138 chloropentafluro-ethane .566� .957 37 2.995

139 vinyl-chloride .612� .775 16 1.364

140 1,1-difluoro-ethene .766� .994 42 1.032

141 trichloro-ethylene .499� .618 35 3.174

142 perchloro-ethylene .502� .635 31 1.025

143 perfluoro-ethylene .470� .640 35 .545

144 methanol .414� .970 39 3.697

145 ethanol .448� .974 35 1.989

146 ethylene-glycol .581� .769 20 8.082

147 1-propanol .522� .963 29 1.990

148 isopropanol .549� .972 32 3.235

149 n-butanol .524� .974 31 1.688

150 2-butanol .524� .910 29 .666

151 isobutanol .548� .977 28 1.517

152 tertbutyl-alcohol .601� .875 35 2.107

153 1-pentanol .474� .867 29 1.679

154 2-methyl-1-butanol .513� .680 28 1.335

155 3-methyl-1-butanol .509� .619 21 1.919

156 2-methyl-2-butanol .552� .688 19 1.644

157 1-hexanol .508� .702 17 2.127

158 1-heptanol .542� .703 14 .311

159 1-octanol .450� .834 31 4.185

160 2-octanol .446� .582 21 .537

161 2-ethyl-1-hexanol .517� .582 11 1.474

162 1-decanol .430� .751 27 4.470

163 1-dodecanol .445� .716 33 3.072

164 cyclo-hexanol .488� .688 18 1.086

165 allyl-alcohol .525� .679 22 1.466

166 m-cresol .417� .609 18 2.376

167 benzyl-alcohol .440� .705 29 2.726

168 ammonia .498� 1.00 62 3.358

169 water .465� 1.00 77 3.617

170 carbon monoxide .513� .914 23 2.340

171 carbon dioxide .712� .996 43 .897

172 nitrogen .500� .990 64 1.280

173 oxygen .352� .996 101 1.027

174 sulfur dioxide .750� .994 19 1.908

175 fluorine .658� .988 20 1.341

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Saturated liquid densities of propylene and ethanol calculated by HSFT,SRK, PR, PT, and CCOR are compared in Figures 10 and 11, respec-tively, where Dv is relative error:

Dv ¼ ðVcal � VexpÞ=Vexp � 100

Obviously, in a wide range of temperatures, the generalized HSFTequation can calculate the saturated liquid densities more precisely thanthe other four equations. Especially when Tr < 0.55 or Tr > 0.95, thosefour equations usually cannot be used.

Calculating Enthalpies ofVaporization by Generalized HSFT

Enthalpy is one of the most important thermodynamic functions and isindispensable in chemical process design and control. This calculationuses information from both vapor and liquid phase, so it is a good indexto measure the stability and adaptability of an EOS. Enthalpies ofvaporization for 115 substances were yielded by the generalized HSFTequation (Table IV, where AADH is the average variation from experi-



176 chlorine .439� .985 23 2.400

177 neon .563� .968 19 1.958

178 argon .556� .988 68 .916

179 krypton .553� .993 47 1.279

180 xenon .557� .994 65 2.084

Average 2.38

Table III Calculated Variations of Saturated Liquid Densities for Five EOSs

Compounds Substance # SRK PR PT CCOR HSFT

Alkanes 40 13.85 4.25 3.02 2.70 1.33

Cycloalkanes 18 10.31 5.39 4.33 3.74 2.89

Alkenes 35 11.13 3.04 2.47 2.86 2.88

Aromatic hydrocarbons 14 18.32 6.39 4.76 3.44 3.39

Ketones 9 18.74 7.45 4.42 5.74 1.98

Halogenides 27 13.51 6.38 5.09 5.80 2.84

Alcohols 24 15.69 8.40 5.79 10.84 2.31

Total=Average 167 13.94 5.48 3.90 4.74 2.42


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mental data). Those 115 substances include 32 alkanes, 10 cycloalkanes,6 alkenes, 11 aromatic hydrocarbons, 12 alcohols, 5 ketones, 4 ethers,12 esters, 4 sulfides, 9 halogenides, 7 oxy heterocylic compounds, and7 nitrogen compounds. The total relative error of those 115 substanceswith 455 experimental data is 3.303%, which shows that the generalizedHSFT equation can calculate enthalpies of vaporization precisely fromnonpolar to strongly polar compounds.

Table V provides the total relative variations of enthalpies ofvaporization obtained from SRK, PR, PT, and CCOR equations of state.

Figure 11. Variations of saturated liquid densities of ethanol by five EOSs.

Figure 10. Variations of saturated liquid densities of propylene by five EOSs.

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Table IV Predicted Variations of Enthalpies of Vaporization for 115 Substances

No. Compounds Tr N AADH

1 methane .587� .634 2 3.811

2 n-pentane .553� .658 8 3.406

3 n-hexane .588� .617 4 4.209

4 n-heptane .552� .580 2 4.741

5 2-methyl-hexane .562� .591 2 4.015

6 3-methyl-hexane .557� .660 4 2.571

7 3-ethyl-pentane .552� .552 1 5.924




11 2,2,3-trimethyl-butane .561� .561 1 4.650

12 n-octane .524� .605 7 3.992

13 2-methyl-heptane .533� .560 2 3.473

14 3-methyl-heptane .529� .529 1 .288

15 4-methyl-heptane .531� .629 4 4.065

16 3-ethyl-hexane .527� .692 2 2.953

17 2,2-dimethyl-hexane .542� .542 1 5.101

18 2,3-dimethyl-hexane .529� .529 1 3.646

19 2,4-dimethyl-hexane .539� .539 1 4.035

20 2,5-dimethyl-hexane .542� .542 1 4.453

21 3,3-dimethyl-hexane .531� .531 1 1.615

22 3,4-dimethyl-hexane .524� .524 1 4.646








30 n-decane .483� .719 8 1.425

31 n-dodecane .453� .453 1 3.173

32 n-tri-decane .441� .515 4 4.237

33 cyclo-propane .604� .604 1 2.993

34 cyclo-butane .621� .621 1 4.862

35 methyl-cyclo-pentane .560� .648 4 1.066

36 cyclo-hexane .528� .662 17 4.437

37 ethyl-cyclo-hexane .550� .647 5 .924

38 methyl-cyclo-hexane .521� .617 4 3.585

39 n-propyl-cyclo-pentane .495� .495 1 .173

40 ethyl-cyclo-hexane .490� .605 6 5.384

41 1,1-dimethyl-cyclo-hexane .505� .505 1 2.271

42 trans-1,2-dimethyl-cyclo-hexane .500� .626 2 4.755

43 propylene .618� .618 1 5.726

44 1,2-butadiene .616� .616 1 2.622


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Table IV (Continued )


45 1,3-butadiene .581� .581 1 4.738

46 2-methyl-1-butene .598� .654 3 5.565

47 2-methyl-2-butene .617� .663 3 4.011

48 1-octene .526� .650 6 4.115

49 toluene .504� .504 1 2.974

50 ethyl-benzene .478� .627 11 4.327

51 o-xylene .473� .473 1 1.146

52 m-xylene .483� .483 1 .097

53 p-xylene .484� .713 8 3.682

54 n-propyl-benzene .467� .467 1 3.492

55 iso-propyl-benzene .473� .473 1 1.873



58 1,3,5-trimethyl-benzene .468� .468 1 .124

59 n-butyl-benzene .451� .557 4 2.629

60 methanol .582� .670 13 2.176

61 ethanol .578� .909 13 2.762

62 1-propanol .556� .930 24 4.718

63 iso-propanol .587� .939 24 6.339

64 n-butanol .530� .890 16 6.104

65 iso-butanol .911� .911 1 1.123

66 tertbutyl-alcohol .816� .870 2 1.107

67 3-methyl-1-butanol .515� .515 1 5.078

68 2-methyl-1-butanol .522� .522 1 1.625

69 2-methyl-2-butanol .630� .815 5 3.591

70 1-hexanol .489� .604 5 1.025

71 1-octanol .453� .453 1 3.952

72 methyl-ethyl-ketone .557� .658 8 3.928

73 methyl-n-propyl-ketone .529� .700 10 3.551

74 methyl-isopropyl-ketone .539� .664 6 1.657

75 diethyl-ketone .532� .669 8 2.178

76 methyl-isobutyl-ketone .522� .681 8 3.018

77 methyl-formate .602� .643 3 1.863

78 ethyl-formate .598� .675 4 5.220

79 methyl-acetate .583� .677 9 2.609

80 ethyl-acetate .570� .695 11 3.148

81 methyl-propionate .562� .648 5 3.551

82 n-propyl-acetate .543� .682 13 3.089

83 ethyl-propionate .546� .616 3 3.412

84 methyl-butyrate .538� .538 1 3.059

85 methyl-iso-butyrate .551� .551 1 3.133

86 n-butyl-acetate .515� .515 1 3.761

87 ethyl-butyrate .527� .527 1 .453

88 methyl-benzoate .431� .431 1 3.647

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Results from the generalized HSFT equation are better or approximateto those from the other four equations, which indicates the generalizedHSFT equation can yield predictions satisfactory in thermodynamicproperties, such as enthalpies of vaporization.

CONCLUSIONS

1. Based on the characteristics of molecular distribution in fluids, afractal structure was proposed for describing the nonlinear behaviorof fluids. The occupation number and the mean potential were derivedfrom the fractal distribution by statistical mechanics. A molecularthermodynamic model based on fractal theory—the HSFT equation—was further derived from statistical mechanics.

Table IV (Continued )


89 methyl-ether .621� .621 1 .778

90 ethyl-ether .601� .671 7 4.623

91 butyl-ether .514� .618 5 .788

92 diethyl-ether .454� .454 1 .630

93 carbon disulfide .511� .511 1 5.956

94 methyl-thioether .549� .617 4 3.509

95 ethyl-thioether .535� .535 1 5.126

96 thiophene .550� .617 3 .783

97 tetra-chloromethane .527� .590 6 4.565

98 trichloromethane .547� .640 5 4.827

99 tetra-chloro-ethylene .481� .578 5 2.707

100 trichloroethylene .522� .575 3 3.830

101 1,1,2-trichloro-ethane .495� .596 8 2.112

102 1,1-dichloro-ethane .560� .570 2 4.280

103 1,2-dichloro-ethane .523� .612 5 3.352

104 chloro-benzene .472� .640 2 3.373

105 bromo-benzene .445� .445 1 1.201

106 oxirane .605� .605 1 .287

107 furan .570� .621 3 1.896

108 tetrahydrofuran .552� .628 4 2.641

109 methyl-amine .613� .613 1 5.368

110 dimethyl-amine .637� .637 1 3.580

111 trimethyl-amine .577� .637 2 .577

112 n-butyl-amine .569� .684 5 5.833

113 dibutyl-amine .500� .601 3 3.207

114 pyridine .481� .626 9 .564

115 4-methyl-pyridine .462� .578 9 4.287

Total=average 455 3.303


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2. The temperature relationship for parameters b and e0 in the HSFTequationwere presented. Correlation calculations of the saturated liquiddensities and vapor pressures provide values of equation parameters.

3. By dividing compounds into two categories, the HSFT equationparameters A1, A2, A3, A4, A5, and A6 were generalized by the acentricfactor o and the critical compressibility factor Zc. Satisfactory resultswere achieved in calculating saturated liquid densities of 118 sub-stances and enthalpies of vaporization of 115 substances by the gen-eralized HSFT equation, which shows the generalized HSFT equationis adaptable and reliable in calculating thermodynamic properties.

Table V Calculated Variations of Enthalpies of Vaporization for Five EOSs

Compounds Substance # SRK PR PT CCOR HSFT

Alkanes 32 1.17 1.16 1.12 1.22 3.73

Cycloalkanes 10 3.80 3.95 4.22 3.70 3.05

Alkenes 6 3.71 3.46 3.61 3.61 4.46

Aromatic hydrocarbons 11 3.14 2.06 1.76 2.88 2.26

Alcohols 12 9.29 9.28 7.61 7.65 3.30

Ketones 5 3.41 1.83 2.93 3.73 2.87

Ethers 12 2.26 1.13 2.35 1.91 3.41

Esters 12 1.83 1.94 2.14 2.10 3.08

Sulfides 4 2.09 1.60 2.24 1.46 3.85

Halogenides 9 2.99 3.05 3.79 2.98 3.61

Oxy heterocylic compounds 3 1.45 1.09 2.70 1.33 1.07

Nitrogen compounds 7 5.14 4.75 4.64 5.29 3.35

Total=Average 115 3.75 3.49 3.53 3.65 3.30

APPENDIX A

Values of e0, b0, and c for 194 Substances

No. Compounds e0 b0 c

1 methane .7115624 .1178985 .6875446

2 ethane .7093328 .1153672 .6749656

3 propane .7064857 .1120469 .6582553

4 n-butane .7018541 .1063438 .6291332

5 isobutane .7078784 .1136876 .6665267

6 n-pentane .6950701 .0969844 .5798712

7 2-methyl-butane .7000176 .1039532 .6167402

8 2,2-dimethyl-propane .6988418 .1023828 .6084880

9 n-hexane .6940936 .0954844 .5717760

10 2-methyl-pentane .6977180 .1008203 .6003342

11 3-methyl-pentane .7012342 .1055469 .6250122

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Appendix A (Continued )


12 2,2-dimethyl-butane .7006109 .1047344 .6208066

13 2,3-dimethyl-butane .6994304 .1031719 .6126524

14 n-heptane .6955798 .0977500 .5839678

15 2-methyl-hexane .6945679 .0962188 .5757506

16 3-methyl-hexane .6922611 .0925078 .5555263

17 3-ethyl-pentane .6977180 .1008203 .6003342

18 2,2-dimethyl-pentane .6977180 .1008203 .6003342




22 2,2,3-trimethyl-butane .6977180 .1008203 .6003342

23 n-octane .6936191 .0947344 .5677112

24 2-methyl-heptane .6940936 .0954844 .5717760

25 3-methyl-heptane .6906167 .0895781 .5393741

26 4-methyl-heptane .6936191 .0947344 .5677112

27 3-ethyl-hexane .6906167 .0895781 .5393741

28 2,2-dimethyl-hexane .6960933 .0983203 .5880053

29 2,3-dimethyl-hexane .6950701 .0969844 .5798712

30 2,4-dimethyl-hexane .6950701 .0969844 .5798712

31 2,5-dimethyl-hexane .6950701 .0969844 .5798712

32 3,3-dimethyl-hexane .6906167 .0895781 .5393741

33 3,4-dimethyl-hexane .6966270 .9927346 .5921366

34 2-methyl-3-ethyl-pentane .6914226 .0910391 .5475127

35 3-methyl-3-ethyl-pentane .6977180 .1008203 .6003342

36 2,2,3-trimethyl-pentane .6914226 .0910391 .5475127




40 n-nonane .6940936 .0954844 .5717760

41 cyclopropane .7071732 .1128672 .6623632

42 cyclobutane .7018541 .1063438 .6291332

43 cyclopentane .7031270 .1079532 .6374159

44 cyclohexane .7012342 .1055469 .6250122

45 methyl-cyclopentane .7012342 .1055469 .6250122

46 cycloheptane .7212912 .1283751 .7384614

47 methylcyclohexane .6988418 .1023828 .6084880

48 ethylcyclopentane .6988418 .1023828 .6084880

49 1,1-dimethyl-cyclopentane .6994304 .1031719 .6126524

50 ethylcyclohexane .6994304 .1031719 .6126524

51 1,1-dimethyl-cyclohexane .6898677 .0881406 .5313390

52 cis-1,2-dimethyl-cyclohexane .6960933 .0983203 .5880053

53 trans-1,2-dimethyl-cyclohexane .6982809 .1016016 .6044533





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58 n-propyl-cyclopentane .6898677 .0881406 .5313390

59 ethylene .7031270 .1079532 .6374159

60 propylene .7024822 .1071407 .6332499

61 1-butene .7037803 .1087657 .6415778

62 cis-2-butene .7006109 .1047344 .6208066

63 trans-2-butene .7018541 .1063438 .6291332

64 isobutylene .7024822 .1071407 .6332499

65 1-pentene .7303261 .1375001 .7815268

66 cis-2-pentene .7057815 .1112110 .6539956

67 trans-2-pentene .7057815 .1112110 .6539956

68 3-methyl-1-butene .7071732 .1128672 .6623632

69 2-methyl-2-butene .7057815 .1112110 .6539956

70 1-hexene .6940936 .0954844 .5717760

71 cis-2-hexene .6994304 .1031719 .6126524

72 trans-2-hexene .6994304 .1031719 .6126524

73 cis-3-hexene .6994304 .1031719 .6126524

74 trans-3-hexene .6940936 .0954844 .5717760

75 2-methyl-2-pentene .6994304 .1031719 .6126524

76 3-methyl-cis-2-pentene .6994304 .1031719 .6126524

77 3-methyl-trans-2-pentene .6994304 .1031719 .6126524

78 4-methyl-cis-2-pentene .6994304 .1031719 .6126524

79 4-methyl-trans-2-pentene .6994304 .1031719 .6126524

80 2,3-dimethyl-1-butene .6994304 .1031719 .6126524

81 3,3-dimethyl-1-butene .6994304 .1031719 .6126524

82 1-heptene .7057815 .1112110 .6539956

83 2,3,3-trimethyl-1-butene .6940936 .0954844 .5717760

84 1-octene .6940936 .0954844 .5717760

85 cyclopentene .7000176 .1039532 .6167402

86 cyclohexene .6994304 .1031719 .6126524

87 propadiene .7000176 .1039532 .6167402

88 1,3-butadiene .6994304 .1031719 .6126524

89 2-methyl-1,3-butadiene .6960933 .0983203 .5880053

90 1,5-hexadiene .6940936 .0954844 .5717760

91 methylacetylene .7031270 .1079532 .6374159

92 1-butyne .6994304 .1031719 .6126524

93 2-butyne .7037803 .1087657 .6415778

94 benzene .7000176 .1039532 .6167402

95 toluene .6960933 .0983203 .5880053

96 ethylbenzene .6955798 .0977500 .5839678

97 o-xylene .6955798 .0977500 .5839678

98 m-xylene .6940936 .0954843 .5717760

99 p-xylene .6940936 .0954843 .5717760

100 styrene .7018541 .1063438 .6291332

101 n-propylbenzene .6966270 .0992735 .5921366

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102 isopropylbenzene .6940936 .0954844 .5717760

103 1-methyl-2-ethyl-benzene .6940936 .0954844 .5717760

104 1-methyl-4-ethyl-benzene .6940936 .0954844 .5717760

105 1,2,3-trimethylbenzene .6994304 .1031719 .6126524



108 acetone .6854765 .0758281 .4597345

109 methyl-ethyl-ketone .6895090 .0874297 .5273000

110 methyl-n-propyl-ketone .6898677 .0881406 .5313390

111 diethyl-ketone .6988418 .1023828 .6084880

112 methyl-isopropyl-ketone .6936191 .0947344 .5677112

113 methyl-isobutyl-ketone .6940936 .0954844 .5717760

114 cyclopentanone .7057815 .1112110 .6539956

115 cyclohexanone .6852748 .0745312 .4518596

116 methyl-phenyl-ketone .6898677 .0881406 .5313390

117 methyl-chloride .6982809 .1016016 .6044533

118 methyl-fluoride .7024822 .1071407 .6332499

119 methyl-iodide .7093328 .1153672 .6749656

120 dibromomethane .7727615 .1764846 .9545738

121 dichloromethane .7037803 .1087657 .6415778

122 chloroform .7154640 .1222032 .7086610

123 dichloromonofluro-methane .7006109 .1047344 .6208066

124 chlorodifluro-methane .6977180 .1008203 .6003342

125 carbon-tetrachloride .7006109 .1047344 .6208066

126 trichlorofluro-methane .7051069 .1103907 .6498624

127 dichlorodifluoro-methane .7057815 .1112110 .6539956

128 chlorotrifluoro-methane .7071732 .1128672 .6623632

129 carbon-tetrafluoride .7037803 .1087657 .6415778

130 ethyl-bromide .7401388 .1469767 .8250853

131 ethyl-chloride .7018541 .1063438 .6291332

132 ethyl-fluoride .7006109 .1047344 .6208066

133 1,1-dichloroethane .7057815 .1112110 .6539956

134 1,1-difluoroethane .6910066 .0902969 .5433701

135 1,1,2-trichloroethane .6868787 .0811562 .4913786

136 1,1,1-trifluroethane .7123189 .1187579 .6917237

137 1,2-difluro-1,1,2,2- tetrachloroethane .7093328 .1153672 .6749656

138 1,2,2-trichloro-1,1,2-trifluoroe .6922611 .0925078 .5555263

139 1,2,2,2-tetrafluoro dichloroethane .7051069 .1103907 .6498624

140 1,2-dichloro-1,1, 2,2-tetrafluoroe .7024822 .1071407 .6332499

141 chloropentafluro- ethane .7000176 .1039532 .6167402

142 vinyl-chloride .6966270 .0992735 .5921366

143 1,1-difluoroethene .7012342 .1055469 .6250122

144 trichloroethylene .6966270 .0992735 .5921366

145 perchloroethylene .6898677 .0881406 .5313390

146 perfluoroethylene .7000176 .1039532 .6167402

147 methanol .6850548 .0707109 .4282603


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148 ethanol .6891685 .0867266 .5233313

149 ethyleneglycol .6994304 .1031719 .6126524

150 1-propanol .6910066 .0902969 .5433701

151 isopropanol .6891685 .0867266 .5233313

152 1,2,3-glycerol .7057815 .1112110 .6539956

153 n-butanol .6936191 .0947344 .5677112

154 2-butanol .6906167 .0895781 .5393741

155 isobutanol .6926987 .0932422 .5595496

156 tertbutyl-alcohol .6936191 .0947344 .5677112

157 1-pentanol .6940936 .0954844 .5717760

158 2-methyl-1-butanol .6940936 .0954844 .5717760

159 3-methyl-1-butanol .6940936 .0954844 .5717760

160 2-methyl-2-butanol .7057815 .1112110 .6539956

161 1-hexanol .7212912 .1283751 .7384614

162 1-heptanol .6898677 .0881406 .5313390

163 1-octanol .7303261 .1375001 .7815268

164 2-octanol .6940936 .0954844 .5717760

165 2-ethyl-1-hexanol .6906167 .0895781 .5393741

166 1-decanol .6955798 .0977500 .5839678

167 1-dodecanol .6854765 .0758281 .4597345

168 cyclohexanol .6868787 .0811562 .4913786

169 allyl-alcohol .6922611 .0925078 .5555263

170 phenol .6868787 .0811562 .4913786

171 m-cresol .6871198 .0818437 .4953844

172 p-cresol .7037803 .1087657 .6415778

173 benzyl-alcohol .7057815 .1112110 .6539956

174 ammonia .6873735 .0825391 .4993746

175 hydrogen .7257071 .1328907 .7599250

176 water .6851975 .0738828 .4479319

177 deuterium oxide .6850499 .0713515 .4321860

178 carbon monoxide .7170892 .1239532 .7171633

179 carbon dioxide .7018541 .1063438 .6291332

180 nitrogen .7130934 .1196173 .6959580

181 oxygen .7115624 .1178985 .6875446

182 sulfur dioxide .6982809 .1016016 .6044533

183 fluorine .7115624 .1178985 .6875446

184 chlorine .7024822 .1071407 .6332499

185 neon .7312791 .1384298 .7858881

186 argon .7138732 .1204688 .7001783

187 krypton .7115624 .1178985 .6875446

188 xenon .7100582 .1162032 .6791028

189 acetic acid .6911780 .0566797 .3341638

190 lithium .6863186 .0640390 .3851632

191 sodium .6850905 .0726093 .4400463

192 potassium .6873853 .0617187 .3694896

193 rubidium .6850548 .0707109 .4282603

194 cesium .6865548 .0634531 .3812082

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APPENDIXB

ParametersofHSFTEquationandResultsforSaturatedProperties

of188Compounds

No.Compounds

Tra

Nb

A1

A2

A3

A4

A5

A6

AADvc

(%)

AADpd

(%)

1methane

.477�.997

45

.103041

1.537011

.798486

.230212

.880413

.683643

.188

.072

2ethane

.298�.995

45

�.100157

1.511860

�.766383

.280008

�.988367

.884719

.283

.441

3propane

.262�.982

43

�.096631

1.504381

�.738171

.241545

�.893196

.909819

.585

2.159

4n-butane

.510�.922

28

�.113089

1.949002�1.187671

.429293

�1.516976

1.452628

.028

.281

5isobutane

.522�.904

25

�.130391

1.770149�1.030060

.478104

�1.592717

1.481261

.043

.259

6n-pentane

.322�.967

42

�.046676

1.867575�1.073112

.467561

�1.763102

1.747335

.159

.886

72-m

ethyl-butane

.413�.971

35

�.168638

2.389852�1.578448

.476263

�1.681465

1.620018

.105

.849

82,2-dimethyl-propane

.602�.998

44

�.092391

2.242193�1.510165

.303685

�1.245057

1.279097

.108

.163

9n-hexane

.363�.970

42

�.140765

2.237154�1.401241

.502846

�1.831772

1.851009

.134

.758

10

2-m

ethyl-pentane

.581�.965

23

�.146416

2.390564�1.632640

.379113

�1.380553

1.457897

.040

.261

11

3-m

ethyl-pentane

.561�.979

41

�.203740

2.414926�1.622690

.470001

�1.574822

1.558179

.688

2.552

12

2,2-dimethyl-butane

.561�.947

31

�.134619

2.235101�1.461898

.359854

�1.298376

1.324037

.044

.204

13

2,3-dimethyl-butane

.550�.978

40

�.153630

2.380634�1.609075

.368801

�1.333327

1.375049

.052

.336

14

n-heptane

.354�.968

42

�.095691

2.017763�1.238501

.597483

�2.042897

2.062805

.157

.787

15

2-m

ethyl-hexane

.515�.977

43

�.154502

2.692524�1.924180

.487474

�1.789100

1.869406

.145

.374

16

3-m

ethyl-hexane

.538�.977

42

�.133121

2.457808�1.557605

.449293

�1.697952

1.774812

.215

.372

17

3-ethyl-pentane

.555�.967

27

�.129401

2.366360�1.630082

.404309

�1.469751

1.586625

.044

.330

18

2,2-dimethyl-pentane

.550�.967

27

�.161443

2.490234�1.684197

.443594

�1.589452

1.635886

.125

.254

19


.553�.972

31

�.078327

2.439313�1.633861

.341418

�1.461524

1.603809

.058

.346

20


.556�.966

39

�.186118

2.768379�1.985821

.472489

�1.717994

1.774103

.075

.194

21


.554�.968

40

�.143171

2.627717�2.000978

.392793

�1.421012

1.496975

.060

.199

22

2,2,3-trimethyl-butane

.546�.966

39

�.106006

2.167590�1.345629

.388436

�1.449282

1.480663

.060

.291

(Continued)

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Appendix

B(C

ontinued)

No.Compounds

Tra

Nb

A1

A2

A3

A4

A5

A6

AADvc(%

)AADpd(%

)

23

n-octane

.394�.970

42

�.112178

2.188635�1.394222

.608304

�2.131695

2.225033

.156

.804

24

2-m

ethyl-heptane

.495�.972

37

�.135454

2.399294�1.606593

.504241

�1.797843

1.930778

.142

.567

25

3-m

ethyl-heptane

.488�.972

38

�.126067

2.626426�1.773616

.517155

�1.950392

2.054011

.166

.730

26

4-m

ethyl-heptane

.486�.949

38

�.108462

2.248812�1.424796

.512703

�1.849026

1.966765

.088

.713

27

3-ethyl-hexane

.485�.975

40

�.145774

2.737230�1.851840

.563065

�2.101206

2.157093

.234

.852

28

2,2-dimethyl-hexane

.504�.973

38

�.094999

2.214287�1.444970

.460355

�1.681067

1.803264

.116

.530

29

2,3-dimethyl-hexane

.493�.974

39

�.155527

2.581336�1.773441

.490710

�1.772512

1.873124

.172

.561

30

2,4-dimethyl-hexane

.493�.974

39

�.141247

2.776932�2.047708

.476169

�1.798648

1.927761

.115

.610

31

2,5-dimethyl-hexane

.496�.964

38

�.121253

2.330286�1.549720

.488696

�1.751251

1.868763

.090

.737

32

3,3-dimethyl-hexane

.489�.961

38

�.136721

2.625119�1.688814

.540307

�2.033998

2.038368

.188

.944

33

3,4-dimethyl-hexane

.491�.962

38

�.120327

2.272223�1.475966

.479744

�1.701527

1.798724

.069

.515

34

2-m

ethyl-3-ethyl-pentane

.489�.974

39

�.097638

2.473336�1.600622

.500787

�1.911951

1.970298

.149

.631

35

3-m

ethyl-3-ethyl-pentane

.482�.973

39

�.124571

2.230308�1.417274

.456438

�1.606863

1.660260

.114

.490

36

2,2,3-trimethyl-pentane

.485�.973

39

�.123348

2.656485�1.761989

.513001

�1.977824

1.981681

.215

.704

37


.364�.969

40

�.094335

2.119550�1.325084

.471138

�1.709906

1.769229

.142

.584

38


.481�.961

38

�.139470

2.354207�1.560632

.462869

�1.646344

1.688084

.078

.624

39


.487�.971

36

�.125705

2.198032�1.379111

.445881

�1.580662

1.666274

.108

.490

40

n-nonane

.579�.713

15

�.074912

2.094172�1.358668

.885205

�2.829335

2.739768

.007

.068

41

cyclopropane

.495�.970

34

�.187394

1.659505

�.789741

.450414

�1.457010

1.255637

.085

.472

42

cyclobutane

.433�.594

37

.294977

.436314

�.063469

.144522

�.784422

.937583

.008

.056

43

cyclopentane

.448�.983

39

�.113781

1.926900�1.164326

.391225

�1.415461

1.386559

.107

.295

44

cyclohexane

.504�.978

43

�.120397

2.114123�1.368434

.413332

�1.523416

1.510018

.077

.407

45

methyl-cyclopentane

.514�.916

35

�.105229

1.936783�1.181634

.431415

�1.508875

1.488027

.029

.155

46

cycloheptane

.492�.976

40

�.304417

2.300966�1.595389

1.082799

�2.674349

2.120284

.465

.641

47

methylcyclohexane

.482�.968

32

�.133240

2.195314�1.404330

.448780

�1.618241

1.595947

.116

.383

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48

ethylcyclopentane

.537�.976

38

�.109674

2.253322�1.551341

.285563

�1.089244

1.233802

.076

.461

49

1,1-dimethyl-cyclopentane

.536�.556

8.307758

.300131

.204343

�.174907

�.028929

.612969

.002

.071

50

ethylcyclohexane

.450�.611

30

�.171776

1.845903�1.045103

.698854

�2.348156

2.187662

.008

.126

51

1,1-dimethyl-cyclohexane

.464�.514

10

.035852

1.468918

�.686776

�.329475

�.016158

.773452

.007

.057

52

cis-1,2-dimethyl-cyclohexane

.450�.616

31

�.213778

1.949994�1.048910

1.319424

�4.005368

3.258523

.009

.068

53

trans-1,2-dimethyl-cyclohexane.461�.522

12

.383835

�.818566

1.242001

.398000

�1.589690

1.680432

.006

.077

54


.467�.528

12

�.118500

1.678322

�.915383

.244233

�1.099367

1.368767

.006

.069

55


13

�.036585

1.231850

�.477915

.516384

�2.063060

2.046132

.007

.048

56


.462�.522

12

�.780389

4.681412�3.368473

.184926

�1.093820

1.398488

.066

.051

57


13

�.019779

1.345903

�.647386

.133058

�.873796

1.198440

.006

.059

58

n-propyl-cyclopentane

.537�.617

17

�.016943

2.090670�1.323168

.765788

�2.854976

2.676346

.007

.047

59

ethylene

.368�.995

45

�.063254

1.618616

�.865797

.293792

�1.206119

1.098558

.213

.368

60

propylene

.241�.997

45

�.037344

1.532518

�.799368

.263046

�1.084207

1.081190

.325

1.242

61

1-butene

.512�.925

35

�.114725

1.974753�1.282652

.354496

�1.258383

1.237898

.070

.107

62

cis-2-butene

.494�.693

27

�.080489

1.721798

�.978866

.660607

�2.180977

1.928724

.010

.067

63

trans-2-butene

.499�.880

40

�.072722

1.776620�1.058923

.448671

�1.495212

1.408512

.019

.178

64

isobutylene

.493�.838

35

�.086750

1.721289

�.982836

.524727

�1.754087

1.597566

.016

.298

65

1-pentene

.417�.953

38

.110956

.664821

�.203208

.648227

�1.589988

1.370984

.037

.369

66

cis-2-pentene

.590�.931

22

�.237915

2.441241�1.719568

.511038

�1.612195

1.535822

.032

.251

67

trans-2-pentene

.455�.714

37

�.106536

1.697687

�.979230

�.064021

�.048528

.470519

.018

.438

68

3-m

ethyl-1-butene

.640�.662

10

.132959

.271176

.385958

�.004866

�.097777

.399552

.009

.076

69

2-m

ethyl-2-butene

.438�.745

24

�.110320

1.333932

�.670694

.361155

�1.014217

1.085025

.032

.176

70

1-hexene

.562�.663

33

�.114937

2.304268�1.493661

.859340

�2.813691

2.493442

.007

.068

71

cis-2-hexene

.573�.587

7.152529

.235684

.437560

�.315737

.068678

.759890

.011

.058

72

trans-2-hexene

.568�.599

15

�.105703

1.957540�1.209536

�.002808

�.524104

.988928

.008

.048

73

cis-3-hexene

.567�.588

10

.190532

.273204

.314964

�.176856

�.091189

.692911

.011

.054

74

trans-3-hexene

.564�.594

15

.097760

1.050477

�.370094

�.191597

�.273498

.900099

.009

.053

(Continued)

1187

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Poly

tech

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06:

54 1

3 O

ctob

er 2

014

Appendix

B(C

ontinued)

No.Compounds

Tra

Nb

A1

A2

A3

A4

A5

A6

AADvc(%

)AADpd(%

)

75

2-m

ethyl-2-pentene

.566�.587

11

.174948

.272428

.324565

�.243766

.068667

.609271

.009

.061

76

3-m

ethyl-cis-2-pentene

.566�.587

11

.152847

.261366

.344380

�.205295

.069938

.545658

.008

.071

77

3-m

ethyl-trans-2-pentene

.562�.582

9.168192

.265008

.330741

�.222771

.067962

.593414

.010

.062

78

4-m

ethyl-cis-2-pentene

.598�.620

12

.175256

.200446

.405018

�.121545

.074681

.455229

.007

.039

79

4-m

ethyl-trans-2-pentene

.594�.617

12

.191549

.139731

.442300

�.132064

.078251

.477031

.008

.045

80

2,3-dimethyl-1-butene

.585�.607

12

.102407

.691884

�.018891

�.199859

.051699

.522882

.008

.054

81

3,3-dimethyl-1-butene

.598�.641

19

�.300542

3.119084�2.214340

.288392

�1.492662

1.591629

.002

.054

82

1-heptene

.527�.564

9�.006844

1.126906

�.560248

.029679

�.333622

.842330

.006

.058

83

2,3,3-trimethyl-1-butene

.542�.606

20

�.269178

2.608757�1.647808

.659532

�2.473338

2.299634

.007

.051

84

1-octene

.507�.694

19

�.063231

2.098299�1.354224

.958223

�3.049722

2.795651

.009

.453

85

cyclopentene

.541�.597

15

.258278

.115527

.449541

.866574

�2.751856

2.300102

.013

.067

86

cyclohexene

.434�.651

28

�.142013

2.097034�1.276154

.572878

�1.981615

1.823532

.013

.109

87

propadiene

.519�.618

12

�.291671

2.718912�1.803989

�.115218

�.341707

.758384

.009

.069

88

1,3-butadiene

.468�.856

29

�.053749

1.667714

�.935967

.537639

�1.839262

1.666716

.020

.210

89

2-m

ethyl-1,3-butadiene

.452�.622

28

�.155704

1.879910�1.008258

.616318

�2.259461

2.051356

.009

.055

90

1,5-hexadiene

.538�.639

39

.416133

�.544386

1.083137

1.389821

�4.229552

3.366943

.009

.066

91

methylacetylene

.539�.962

37

�.118814

1.782481�1.030355

.401349

�1.383460

1.361467

.047

.359

92

1-butyne

.522�.608

21

�.306367

2.342486�1.361461

.275608

�1.716144

1.845349

.008

.073

93

2-butyne

.559�.606

18

�.189181

1.831267�1.032712

.092617

�.817489

1.084980

.007

.060

94

benzene

.505�.978

42

�.120416

1.986785�1.232142

.416091

�1.521447

1.499776

.128

.492

95

toluene

.333�.923

38

�.066106

1.798125�1.027095

.574549

�2.010326

1.924216

.125

1.076

96

ethylbenzene

.433�.789

23

�.070957

1.837080�1.076362

.722149

�2.399913

2.240892

.020

.202

97

o-xylene

.440�.971

39

�.130397

2.197443�1.401893

.483465

�1.694458

1.734920

.140

.587

98

m-xylene

.433�.943

37

�.125601

2.143370�1.332165

.504871

�1.750587

1.783903

.100

.579

99

p-xylene

.467�.797

27

�.053823

1.748021

�.990025

.660003

�2.182679

2.074388

.016

.111

1188

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3 O

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014

100styrene

.447�.646

34

�.233826

2.343853�1.558766

�.241729

.102166

.591746

.017

.925

101n-propylbenzene

.425�.671

28

�.058582

1.719129

�.986233

.828872

�2.622458

2.423273

.013

.100

102isopropylbenzene

.426�.675

30

�.006698

1.662878

�.925871

1.061472

�3.382326

2.970841

.009

.139

1031-m

ethyl-2-ethyl-benzene

.547�.670

25

.664541�2.578038

2.839704

.024912

�.619062

1.143822

.028

.055

1041-m

ethyl-4-ethyl-benzene

.548�.681

27

�.338606

2.575935�1.646565

.772309

�2.490042

2.342215

.009

.050

1051,2,3-trimethylbenzene

.417�.456

7.057028

1.179723

�.578330

�.039827

�.302458

.911329

.007

.062


.428�.564

12

�.037382

1.761525�1.011455

.071347

�.664066

1.170026

.009

.073


.439�.687

39

�.038260

1.730290

�.997246

.741362

�2.353762

2.277211

.010

.051

108acetone

.498�.970

33

�.106474

2.434947�1.592300

.425341

�1.706406

1.703615

.238

.696

109methyl-ethyl-ketone

.508�.596

7.004355

1.482680

�.749586

.790439

�2.611741

2.379144

.002

.059

110methyl-n-propyl-ketone

.500�.626

11

.165651

1.298799

�.656862

1.098362

�3.570890

3.118918

.012

.061

111diethyl-ketone

.508�.619

11

�.174302

1.978619�1.217012

.428712

�1.440617

1.598407

.005

.070

112methyl-isopropyl-ketone

.520�.576

6�.264257

2.735491�1.747255

1.390271

�4.154049

3.409692

.008

.044

113methyl-isobutyl-ketone

.501�.653

14

�.100481

2.091334�1.299201

.676604

�2.333899

2.334414

.008

.067

114cyclopentanone

.436�.580

16

.073289

1.150478

�.584854

1.200298

�3.204189

2.543010

.008

.089

115cyclohexanone

.490�.556

7.159090

1.302565

�.580088

2.355491

�6.583455

4.916997

.005

.053

116methyl-phenyl-ketone

.435�.678

42

.088339

1.043785

�.308987

3.419346

�9.688744

7.274916

.021

1.005

117methyl-chloride

.464�.956

40

�.125676

1.863869�1.113356

.337132

�1.271937

1.202535

.084

.309

118methyl-fluoride

.453�.906

35

�.152821

.962191

�.311624

.342766

�.920183

.853218

.254

.100

119methyl-iodide

.479�.581

19

�.210716

1.549586

�.786897

.547399

�1.594074

1.324681

.008

.057

120dibromomethane

.520�.638

31

�.129420

1.117501

�.685056

1.238700

�1.709257

.862387

.007

.110

121dichloromethane

.416�.812

28

�.258453

1.992012�1.167442

.753791

�2.389871

2.083305

.044

.223

122chloroform

.403�.804

31

�.158824

1.722287�1.026242

.543231

�1.614809

1.483600

.050

.651

123dichloromonofluro-m

ethane

.543�.972

36

�.135512

2.031641�1.256269

.406465

�1.505070

1.488306

.058

.242

124chlorodifluro-m

ethane

.550�.989

40

�.119906

2.098241�1.345831

.345029

�1.303566

1.329749

.141

.203

125carbon-tetrachloride

.455�.988

44

�.112897

1.990176�1.235832

.451812

�1.632305

1.554295

.151

.763

126trichlorofluro-m

ethane

.480�.987

37

�.146663

2.106736�1.370086

.363420

�1.306298

1.290352

.093

.357

127dichlorodifluoro-m

ethane

.447�.982

40

�.119462

1.830182�1.082814

.357331

�1.275523

1.249533

.060

.486

(Continued)

1189

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by [

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Poly

tech

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06:

54 1

3 O

ctob

er 2

014

Appendix

B(C

ontinued)

No.Compounds

Tra

Nb

A1

A2

A3

A4

A5

A6

AADvc(%

)AADpd(%

)

128chlorotrifluoro-m

ethane

.480�.987

40

�.106753

1.921225�1.210885

.340489

�1.198629

1.172677

.073

.215

129carbon-tetrafluoride

.404�.804

30

�.039768

1.685231

�.948287

.337397

�1.312039

1.303127

.033

.086

130ethyl-bromide

.433�.611

13

.018874

.797220

�.336087

.569918

�1.226115

.985857

.008

.106

131ethyl-chloride

.530�.832

26

�.184053

1.250382

�.267301

.444244

�1.302920

1.145957

1.725

.310

132ethyl-fluoride

.461�.624

14

�.413471

2.811281�1.812222

.156812

�.583335

.727051

.014

.075

1331,1-dichloroethane

.461�.625

13

�.110032

1.928768�1.228899

.479598

�1.570606

1.518044

.010

.158

1341,1-difluoroethane

.600�.978

36

�.189636

2.596163�1.881532

.052257

�.224719

.381833

.167

.294

1351,1,2-trichloroethane

.538�.640

22

�.403338

3.104757�1.986368

1.333260

�4.410876

3.668114

.006

.080

1361,1,1-trifluroethane

.578�.991

37

�.497143

2.775284�1.883840

.751913

�1.983634

1.687796

.230

.162

1371,2-difluro-1,1,2,2-tetra

chloroethane

.550�.661

42

�.723991

5.325678�4.282388�2.819293

7.430373�4.477381

.011

.392

1381,2,2-trichloro-1,1,2-trifluoroe

.509�.989

43

�.036971

2.306884�1.509500

.306130

�1.416646

1.540835

.244

.468

1391,2,2,2-tetrafluoro

dichloroethane

.669�.958

29

�.174966

2.624576�2.012089

.222498

�.779967

.926636

.118

.331

1401,2-dichloro-1,1,2,2-tetra

fluoroe

.475�.986

43

�.085269

1.866325�1.104003

.437658

�1.548140

1.569032

.106

.413

141chloropentafluro-ethane

.566�.957

37

�.106636

2.400544�1.656338

.366142

�1.430014

1.509213

.108

.227

142vinyl-chloride

.612�.775

16

�.075237

1.852409�1.078995

.371521

�1.600737

1.522954

.010

.055

1431,1-difluoroethene

.766�.994

42

�.134079

2.077142�1.472219

.177634

�.620056

.587614

.447

.081

144trichloroethylene

.499�.618

35

.146459

.991560

�.428200

.238773

�.874552

.921997

.008

.067

145perchloroethylene

.502�.635

31

.055861

1.592074

�.817193

.739660

�2.761045

2.497962

.007

.067

146perfluoroethylene

.470�.640

35

�.059475

1.892399�1.236000

.671467

�2.271313

2.072273

.009

.061

147methanol

.414�.970

39

�.216581

3.351723�2.369878

.378499

�1.373065

1.636437

.211

.672

148ethanol

.448�.974

35

�.186360

3.250586�2.324435

.360968

�1.362715

1.914080

.140

.970

149ethyleneglycol

.581�.769

20

.128745

1.130007

�.555695

2.582476

�5.593159

4.267896

.007

.093

1190

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06:

54 1

3 O

ctob

er 2

014

1501-propanol

.522�.963

29

�.178637

2.886260�1.908335

.623822

�2.390688

2.879207

.200

.453

151isopropanol

.549�.972

32

�.144009

2.792561�1.806840

.622568

�2.472324

3.038358

.215

.442

1521,2,3-glycerol

.409�.759

42

.264612

.630188

�.189804

2.625982

�4.858930

3.692912

.018

2.071

153n-butanol

.524�.974

31

�.172740

2.648951�1.680919

.784818

�2.996275

3.425146

.229

.739

1542-butanol

.524�.910

29

�.069924

2.191339�1.229519

.958454

�3.719197

4.040261

.067

.465

155isobutanol

.548�.977

28

�.146940

2.479195�1.471802

.799065

�3.096983

3.524365

.459

.647

156tertbutyl-alcohol

.601�.875

35

�.125965

2.387323�1.423648

1.059240

�3.941310

4.253302

.062

.167

1571-pentanol

.474�.867

29

�.121919

2.415934�1.502598

.992610

�3.582625

3.846901

.062

.845

1582-m

ethyl-1-butanol

.513�.680

28

�.365816

3.905176�2.849526

.356151

�1.911511

2.786176

.011

.104

1593-m

ethyl-1-butanol

.509�.619

21

�.631165

4.963821�3.672700

�.507103

.148172

1.512433

.009

.109

1602-m

ethyl-2-butanol

.552�.688

19

�.034879

1.658473

�.841792

2.074488

�6.725725

6.074114

.010

.171

1611-hexanol

.508�.702

17

�.040875

2.106019�1.445434

.976769

�3.058142

3.364341

.007

.434

1621-heptanol

.542�.703

14

�.104192

2.426794�1.445339

2.756374

�8.925561

7.765757

.014

.379

1631-octanol

.450�.834

31

.121901

1.079526

�.569380

1.928931

�5.716916

5.218761

.084

.297

1642-octanol

.446�.582

21

�.193971

2.625202�1.676717

�.278130

�.990696

2.567878

.009

.188

1652-ethyl-1-hexanol

.517�.582

11

1.279815�4.781889

4.874938

14.638600�40.421450

28.613190

.008

.271

1661-decanol

.438�.766

27

�.176975

2.358660�1.468793

2.859149

�8.868339

7.672968

.037

.297

1671-dodecanol

.420�.676

33

.334393

.983210

�.304202

4.955384�15.002350

11.972810

.057

1.014

168cyclohexanol

.488�.688

18

.005589

1.524361

�.593073

2.467344

�7.855563

6.724191

.020

.071

169allyl-alcohol

.525�.679

22

�.309262

3.455390�2.464326

�.208966

.150294

.895294

.015

.222

170phenol

.497�.647

33

.459642

.896849

�.256224

1.781911

�5.816881

4.950120

.011

.099

171m-cresol

.417�.609

18

�.197766

3.124645�2.055964

1.074439

�3.921431

3.778487

.011

.149

172p-cresol

.568�.616

10

.033077

1.707492

�.961114

1.791405

�5.242979

4.473004

.003

.059

173benzyl-alcohol

.440�.705

29

.003638

1.573229

�.909725

1.418957

�3.660300

3.316236

.020

1.401

174ammonia

.498�1.00

62

�.126637

2.059637�1.247767

.359464

�1.404895

1.397372

.265

.437

175hydrogen

.422�.964

19

�.165045

1.651678

�.889163

.009738

�.214989

�.182815

.464

.498

176water

.465�1.00

76

�.096462

1.419588

�.355519

.474725

�1.671805

1.610597

.655

.723

177deuterium

oxide

.432�.999

45

�.071673

1.335700

�.233579

.501311

�1.821147

1.774878

.514

1.368

(Continued)

1191

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by [

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tech

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Appendix

B(C

ontinued)

No.Compounds

Tra

Nb

A1

A2

A3

A4

A5

A6

AADvc(%

)AADpd(%

)

178carbonmonoxide

.513�.977

25

�.121416

1.581142

�.878251

.299580

�1.073652

.913662

.216

.179

179carbondioxide

.712�1.00

44

�.153959

2.404081�1.752278

.302646

�1.129558

1.198420

.492

.057

180nitrogen

.500�.990

64

�.143192

1.833576�1.092787

.268549

�.999257

.826836

.139

.106

181oxygen

.352�.990

100

�.050736

1.268816

�.532617

.198730

�.812988

.668438

.281

.458

182sulfurdioxide

.750�.994

19

�.143084

2.502639�1.957778

.157160

�.549116

.657694

.120

.062

183fluorine

.658�.988

20

�.177129

2.316948�1.663537

.203449

�.904266

.841432

.600

.255

184chlorine

.439�.999

24

�.102990

1.695030

�.958055

.352967

�1.355961

1.187531

.207

.589

185neon

.563�1.00

20

�.056248

1.337005

�.711620

.264975

�.818958

.516993

.323

.113

186argon

.556�.988

68

�.111983

1.678160

�.984519

.226859

�.894084

.695214

.100

.106

187krypton

.553�.984

46

�.112964

1.684530

�.981598

.231785

�.921147

.719796

.063

.138

188xenon

.557�.994

65

�.144008

1.851977�1.135344

.259914

�.997091

.774761

.181

.097

Total

5658

0.10

0.34

aReducedtemperature

range

bDatium

points

cAAD

v¼

1 N

P N i¼1

jVl exp;i�Vl cal;ij

Vl exp;i

�100%

dAAD

p¼

1 N

P N i¼1jpexp;i�pcal;ij

pexp;i

�100%

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NOMENCLATURE

A1 � A6 parameters of HSFT equation

a parameter in Equation (24)

b=4 volume of one mole of hard-sphere molecules, m3 �mol�1c fractal structure exponent

D adjacent molecules distribution

Ds self-similar dimension

d diameter of molecule, m

g pair correlation function

h Planck’s constant, 6.624� 10�27erg � sk Boltzmann’s constant, 1.380� 107 16erg �K�1

L0 self-similar ratio

m mass of molecules

N number of molecules

NA Avogadro’s constant, 6.023� 1023molecules �mol�1Nc occupation number

p pressure, Mpa

Q canonical partition function

qr;v;e contribution of rotational and vibrational degree

of freedom to partition function

R gas constant, 8.314 J mol�1 �K�1

r position

T temperature, K

u interaction energy

V volume occupied by N molecules, m3

Vf free volume, m3 �mol�1Vl volume of liquid, m3 �mol�1v molar volume, m3 �mol�1v1 volume of a molecule, m3

v2 volume of the considered spherical area, m3

Z compressibility factor

Greek letters

ab temperature rectification of b*

ae temperature rectification of e*e; e0 energy parameter, J �kmol�1Z reduced density

z partial reduced density

r density of fluid

r0 accumulation density

f mean potential

L thermal de Broglie wavelength

Subscripts

c critical state

r reduced state

exp experimental

cal calculated


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A new equation of state (hsft) based on fractal theory