- Email: [email protected]
A model for enthalpy of vaporization using a new one parameter equation of state for fluids
Fluid Phase Equilibria,
18 (1984)
237
231-243
Elsevier Science Publishers B.V.. Amsterdam
- Printed in The Netherlands
A MODEL FOR ENTHALPY OF VAPORI2AlION USING A NEW ONE PARAMETER EQUATION OF STATE FOR FLUIDS G. NATARAJAN and D. S. VISWANATH Chemical Engineering Department, University of Missouri-Columbia, Columbia, MO
65211
(Received January, 1984)
ABSTRACT Natarajan, G. and Viswanarh, D.S., 1984. A model for enthalpy of vaporization using a new one parameter equation of state for fluids. Fluid Phase Equilibria, 18: 237-243. An equation of state for a real fluid is presented and compared with the existing models such as the Carnahan-Starling equation of state.
The proposed
equatfon Is used in computing enthalples of vaporizatfon of benzene from boiling point to a temperature of 0.95 T,. several hydrocarbons at 298.15K.
It
has also been used to compute
The present model for calculating
AH" for AH" has been
compared wfth other models due to Yosfm-Owens, Wilhelm-Battino, Reiss and co-workers, Camahan-Starling,
and Muller-Prausnitt.
INTRODUCTION Molecular theory of fluids and the theoretical development of equations of state for real fluids have not developed to a stage of application to real flufds due to the severe mathematical difficulties.
However, the recent advances fn
computing capabflftles have enabled successful computer experiments through molecular dynamfcs and Monte Carlo calculations.
The results of such experiments
have made significant contrlbutions in the theoretical understanding of dense fluids.
In this work utillzlng the perturbation technique and the recent Monte
Carlo results an equation of state in closed form Is derived and tested exhaustively to check Its abflity to predict compressibility and enthalpies of vaporization. Usfng different approaches Thiele (1963) and Werthefm (1963) arrived at a closed form solution for the Percus-Yevick equatfon and showed ZHS - Pv/Nkt - (l+y+y2)/(I-y)3
y = b/4v = (l/6) (~4
0378-3812/84/$03.00
(vo/v); b = (2/3)x
(1)
No3
0 1984 Elsevier Science Publishers B.V.
238 for the compressibility of non-attracting hard spheres.
The same result was
obtained using scaled-particle theory by Reiss, et al. (1959).
Carnahan and
Starling (1969) studying the different virial expansions slightly modified the Ree-Hoover expansion to arrive at the relation
zcs for
= Pv/NkT = (l+y+y2-y3)/(1-y)3
non-attracting
hard
spheres.
(2) Equation (2) is regarded as one of the best
analytical forms of equation of state for hard spheres. NEW EQUATION OF STATE The Percus-Yevick solution represents the hard sphere fluid with good success. However the agreement is poor when tested for real fluids and therefore more realistic potentials such as the Lennard-Jones 12-6 potential are required for better representation.
Since the rigid sphere approximation holds good at high
temperatures, a perturbation technique can be employed for real fluids with hard sphere potential as the reference.
The perturbations due to density and temperature
can be estimated from the repulsive part of the potential function.
This scheme was
originated by Zwanzig (1954) and later used by several workers' (Smith and Alder, 1959; Frisch, et al., 1966; Mcquarrie and Katz, 1966; Barker and Henderson, 1967 1. Following this technique Levesque and Vet-let (1969) showed that P/pkT = (P/pkT)Hs +BodJ
fI(pd=) + BL (pd")' f2(pd=)
(3)
where 3 fI(pd ) = c i-I b i (pd3)i ; f2( d3) = C j-l cj(pd3)j
(4)
The numerical value of the constants in equation (3) evaluated by the Monte Carlo method (Levesque and Verlet, 1969) are bI = - 5.851, b2 = - 5.757 and b7 = - 5.966. As most of the b values are of the same order of magnitude, we take hi's are equal and consider only the first order correction. Substftuting the compactness factor y for pd3, the series in y is seen to be -y ln(l-y).
With these substitutions
equation (3) becomes P/pkT = P/(pkT)HS + 2.071116 y In (l-y)
(5)
The constant 2.071116 in equation (5) is obtained using an average value of b = -5.858 and notfng that the b, values estimated by Levesque and Verlet (1969) are based on the virial volume b,/4 where as the volume used in compactness factor y is the hard sphere close packing volume No3/K
The value of B is taken as unity as
239
the attractive part is strongly dependent on y and is a weak function of temperature.
Utilfzfng equation (l), equation (5) becomes
ZhV = (l+y+y*)/(l-y)3 + 2.071116 y In (l-y)
(6)
In arriving at equatfon (6), equation (1) rather than equation (2) is utilized as our results fn calculating enthalpies of vaporization of varfous substances at 198.16 K (Table 2) showed equation (1) to be better.
Further it has been found
that the Carnahan-Starling equation is very inaccurate for a mixture of hard spheres whereas equation (1) gives accurate results. mathematical sense, - Q/(1-y)13
Also, in a strfct
in equatfon (2) is by itself a correction term to
the exact hard sphere equation (1). RESULTS A comparison of the compressibility values predicted by different models with the exact calculations of Alder and Wainwright (1960) is shown in Table 1.
All the
models perform to the same degree of accuracy with the present model slightly better than the other two models.
However a better criteria to test the
theoretical models is to calculate other thermodynamic properties which involve differentfatfon and/or integration of the model equation.
Estimation of a property
like enthalpy of vaporization requires an equation of state and properties of liquid and vapor states.
Equation (6) combfned with the relation hHV = /pdv gives
AH, = RT Iln{(v9/ve)/(l-y)I + {3y(2-~1/2(1-~)*1 + 2.071116 {(l-y)
In (l-y) + ~11
(7)
The results of equation (7) have been compared with the values of Yosfm and Owens (1970) based on equation (1) and the values of Wflhelm and Battino (1973) based on equation (2) are shown In Table 2. experimental values of ve
AHv was estimated usfng equation (7) and
and molecular diameters reported by Wilhelm and Battino
TABLE 1 Comparison of Compressfbilfty Equations
v/v0 :s
zNv
zcs
'HS
'AW
10.20 12.54
10.16 12.43
10.80 13.18
10.17 12.50
1:7
8.50 5.86
8.56 5.83
9.01 6.03
8.59 5.89
ro:o 5.:
2.93 1.36
3.03 1.36
3.06 1.36
3.05 1.36
240
TABLE 2 Comparison of AHv (kJ/mole) at 298.15 K for Hydrocarbons Hydrocarbon
Expt.
AH, NV
% Dev.
AHV HS
% Dev.
AH, C5
% Dev.
n-Hexane n-Heptane n-Octane n-Nonane n-Oecane n-Dodecane n-Tetradecane 3-Methylheptane 2.3-Oimethylhexane 2,4-Dimethylhexane 2,2,4-Trimethylpentane Cyclohexane Methylcyclohexane Benzene To1 uene m-xylene
31.551 36.551 41.488 46.442 51.367 61.287 71.170 39.836 38.794 37.769
30.407 34.807 39.007 43.461 47.389 56.439 64.513 37.794 37.536 36.436
3.63 4.77 5.98 6.42 7.74 7.91 9.35 5.12 3.24 3.53
29.630 33.943 38.069 42.444 46.321 55.235 63.234 36.676 36.609 35.529
6.09 7.14 a.24 8.61 9.82 9.87 11.15 7.43 5.63 5.93
29.166 33.348 37.346 41.566 45.327 53.880 61.632 36.189 35.908 34.863
7.56 8.76 9.98 10.50 11.76 12.09 13.40 9.15
35.133 33.037 35.359 33.849 37.991 42.656
34.798 33.537 33.592 33.711 37.497 41.461
-1.51 -0.66 0.41 1.30 2.80
0.95
33.911 32.679 34.705 32.873 36.598 40.502
3.48 1.08 1.85 2.88 3.67 5.05
33.278
5.28
X5 32:320 35.945 39.741
5*$ 4:52 5.38 6.83
,
,
s
;:z
TABLE 3 Comparison of Experimental AH" (kJ/mole) of Benzene with Values Obtained from the Models Temp. K 351.74 360.46 365.66 371.61 375.35 376.95 385.45 393.99 399.25 406.25 419.75 439.47 455.25 459.07 477.75
Expt. Data
Present
Yosfm-Owens
30.831 30.495 30.205 29.868 29.489 29.465 28.851 28.552 27.898 27.514 26.521 25.071 23.846 23.436 21.766
30.524 30.017 29.713 29.365 29.145 29.051 28.550 38.043 27.728 27.307 26.482 25.237 24.191 23.929 21.572
29.727 29.229 28.931 28.590 28.375 28.283 27.794 27.299 26.993 26.583 25.781 24.573 23.561 23.307 21.998
1.29
3.09
Average absolute per cent dev.
WilhelmBattino
Refss, et. al.
MullerPrausnftt
29.301 28.826 28.541 28.214 28.008 27.919 27.449 26.974 26.679 26.284 25.509 24.340 23.355 23.108 21.832
33.951 33.738 33.600 33.431 33.319 33.270 32.996 32.697 32.505 32.233 31.663 30.712 29.826 28,291
30.207 30.256 30.259 30.238 30.253 30.201 30.106 29.970 29.866 29.706 29.328 28.533 27.835 27.643 26.662
4.10
17.04
7.67
29.592
241
(1973) as a function of temperature.
Vg employed was the ideal gas volume as the
introduction of second virial did not improve mdels
coatpared in this paper.
(AH,,) prediction for any of the Table 3 shows the predfcted AH, values as a
function of temperature for benzene.
The experimental data are those collected in
our laboratory (Natarajan and Viswanath, 1983) and these values agreed with the published data of Todd and co-workers (1978) within f 0.5 percent.
In this
coatparison we have also fncluded the values predicted by models due to Reiss, et al. (1959) and Muller-Prausnftz (1979).
The method of Rdss.
et al. uses a
TABLE 4 Statistical Analysis of Enthalpy of Vaporization: Compound
A Comparison
Present
Wilhelm Battino
YosimOwens
Reiss et al.
MullerPrausnitz
Temp. Range (n)
Benzene
3 a
1.29 1.56
4.10 1.71
3.09 1.54
17.04 6.05
7.67 7.21
351.79 to 477.75 (15)
Toluene
5 a
2.86 1.14
6.14 1.74
5.18 1.58
8.24 5.48
11.02 5.37
379.63 to 521.13 (16)
p-xylene a a
6.06 2.33
9.26 2.52
a.40 2.35
4.90 5.76
10.40 5.53
411.49 to 557.25 (14)
a: average absolute percent deviation from experimental data obtained in our laboratory; a: standard deviation; n: number of data points considered in the temperature range.
TABLE 5 AH~ For Hfgh Molecular Weight Compounds
Colnpound Quinoline
Anthracene
Phenanthrene
Tep.
Lit. Da.ta
510.75 553.15 593.15 633.15 653.15 613.47 622.97 639.97 652.97 652.00
z-2 a 42:5 40.0 39.Ob 56.6 55.8 54.3 53.1 5a.2*c
Present 45.3 42.9 40.4 37.7 36.1 53.3 52.5 51.2 50.2 51.8
MullerPrausnitz 41.0 38.6 36.2 33.5 32.1 43.8 43.0 41.9 41.1 42.3
a: Viswanath (1979); b: Kudchadker. et al. (1979); c: Muller-Prausnftz (1979). *This value appears to be higher as a value of 53.0 kJ/mole is quoted by Kudchadker, et al. (1979) which is in better agreement with the present model.
242
temperature dependent thermal expansfon coefficient and the semi-empirfcal method of Muller and Prausnitt employs several adjustable parameters.
Table 3 Is extended
into Table 4 to show a statistical analysis for benzene, toluene and p-xylene.
A
detailed analysis for toluene, p-xylene and other compounds will be published elsewhere.
This model is tested further for Its ability in predicting @Iv values
for high molecular weight, two or more ring compounds.
The results are compared
with the Muller-Prausnitz method developed for high molecular weight compounds. The results presented in Table 5 show the superiority of the present model compared to the Muller-Prausnitt method.
LIST OF SYMBOLS AW b bi
Alder-Wafnright hard sphere closed packed volume, m3 mol-I constants in eqn. (4)
C.
constants in eqn. (4)
d
Camahan-Starling
d fl f2 HS AHV
molecular diameter, m a functfon in eqn. (3) and (4) a function in eqn. (3) and (4) Hard Sphere enthalpy of vaporization, kJ mole-’
f
integer in eqn. (4)
j
integer in eqn. (4)
k
Boltzmann constant, J deg"
N P
Avogadro Number, mole-' -2 pressure, N m
R
gas-law constant, J deg"
T
temperature, k
V
volume, m3 mole
vO
volume at close packing, m3 mol -1 vapor volume, m3 mole
?I VR
-1 -1
lfquid volume, m3 mole-l
Y
compactness parameter (y = aNa3/ti Ye)
z
compressibility factor (2 = Pv/pkT)
f3
= l/kT
P
particle densfty (p = N/v)
u
collision dfameter, m
243
REFERENCES Alder, B.J. and T.E. Wainwright, 1960. Studies in Molecular Dynamics. II. Behavior of a Small Number of Elastic Spheres, J. Chem. Phys. 33:1439-1451. Barker, J.A. and D. Henderson, 1967. Perturbation Theory and Equation of State for Fluids. The Square-Well Potentfal. J. Chetn. Phys. 47:2856-2861. Carnahan, N.F. and K.E. Starling, 1969. Equation of State for Non-attracting Rigid Spheres. J. Chem. Phys. 51:635-636. Frfsch, H., J.L. Katz, E. Praestgaard and J.L. Lebowitz', 1966. High Temperature Equation of State-Argon. J. Phys. Chem. 70:2016-2020. Equations of State in Engineering and Research. Ed: K.C. Henderson, D., 1979. Advances in Chemistry Series 182, American Chao and R.L. Robinson. Jr. Chemical Socfety, Washington, D.C., pp. 1. Kudchadker. A.P., S.A. Kudchadker and R.C. Wflhoit. 1978. Naphthalene. API Publfcation 707, American Petroleum Institute, Washington, D.C., pp. 37. Kudchadker, A.P., S.A. Kudchadker and R.C. Wflhoit, 1979. Anthracene and Phenanthrene. API Monograph Series, API Publication 708, American Petroleum Institute, Washfngton, D.C., pp. 37. LevesF;;idi. and L. Verlet, 1969. Perturbation Theory and Equation of State for Phys. Rev. 182:307-316. High Temperature Equation of State. J. McQuarrfe, I?.A. and J.L. Katz, 1966. Chem. Phys. 44:2393-2397. Muller, 6. and J.M. Prausnitz. 1979. Residual Enthalpies of High Boflfng IEC Pmt. Desfgn Dev. 18:679-683. Hydrocarbons. Natarajan, G. and D.S. Vfswanath, 1983. High Temperature Calorimeter for the Measurement of Vapor Pressure and Enthalpy of Vaporization. Rev. Sci. Instrum. 54:1175-1179. Reiss, A., H.L. Frisch and J.L. Lebowftz, 1959. Statistical Mechanics of Rigid Spheres. J. Chem. Phys. 31:369-380. Smith, E.B. and B.J. Alder, 1959. Perturbation Calculation In Equilibrium Statistical Mechanics: Hard Sphere Basfs Potential. J. Chem. Phys. 30:1x90-1199. Thiele. E.W., 1963. Equation of State for Hard Spheres. J. Chem. Phys. 39:474-479. 1978. Vapor Flow Calorimetry of Todd, S-S., I.A. Hossenlopp and D.W. Scott, Benzene. J. Chem. lhermodyn. 10:641-648. Viswanath, D.S., 1979. Qufnolfne. API Monograph Series. API Publication 711, American Petroleum Institute, Washington. D.C., pp. 37. Exact Solution of the Percus-Yevick Integral Equatfon for Werthelm, N., 1963. Hard Spheres. Phys. Rev. Lett. 10:321-323. Wflhelm, E. and R. Battino, 1973. On the Calculation of Heats of Vaporization from Hard Sphere Equations of State. J. Chem. Phys. 58:3561-3564. Yosim, S.J. and B.B. Owens, 1963. Calculation of Heats of Vaporization and Fusion of Non-fonfc Liquids from the Rigid Sphere Equatfon of State. J. Chem. Phys. 39:2222-2226. Zwanzig. R.W., 1954. High Temperature Equation of State by a Perturbation Method. I:. Non-polar Gases. J. Chem. Phys. 22:1420-1426.
18 (1984)
237
231-243
Elsevier Science Publishers B.V.. Amsterdam
- Printed in The Netherlands
A MODEL FOR ENTHALPY OF VAPORI2AlION USING A NEW ONE PARAMETER EQUATION OF STATE FOR FLUIDS G. NATARAJAN and D. S. VISWANATH Chemical Engineering Department, University of Missouri-Columbia, Columbia, MO
65211
(Received January, 1984)
ABSTRACT Natarajan, G. and Viswanarh, D.S., 1984. A model for enthalpy of vaporization using a new one parameter equation of state for fluids. Fluid Phase Equilibria, 18: 237-243. An equation of state for a real fluid is presented and compared with the existing models such as the Carnahan-Starling equation of state.
The proposed
equatfon Is used in computing enthalples of vaporizatfon of benzene from boiling point to a temperature of 0.95 T,. several hydrocarbons at 298.15K.
It
has also been used to compute
The present model for calculating
AH" for AH" has been
compared wfth other models due to Yosfm-Owens, Wilhelm-Battino, Reiss and co-workers, Camahan-Starling,
and Muller-Prausnitt.
INTRODUCTION Molecular theory of fluids and the theoretical development of equations of state for real fluids have not developed to a stage of application to real flufds due to the severe mathematical difficulties.
However, the recent advances fn
computing capabflftles have enabled successful computer experiments through molecular dynamfcs and Monte Carlo calculations.
The results of such experiments
have made significant contrlbutions in the theoretical understanding of dense fluids.
In this work utillzlng the perturbation technique and the recent Monte
Carlo results an equation of state in closed form Is derived and tested exhaustively to check Its abflity to predict compressibility and enthalpies of vaporization. Usfng different approaches Thiele (1963) and Werthefm (1963) arrived at a closed form solution for the Percus-Yevick equatfon and showed ZHS - Pv/Nkt - (l+y+y2)/(I-y)3
y = b/4v = (l/6) (~4
0378-3812/84/$03.00
(vo/v); b = (2/3)x
(1)
No3
0 1984 Elsevier Science Publishers B.V.
238 for the compressibility of non-attracting hard spheres.
The same result was
obtained using scaled-particle theory by Reiss, et al. (1959).
Carnahan and
Starling (1969) studying the different virial expansions slightly modified the Ree-Hoover expansion to arrive at the relation
zcs for
= Pv/NkT = (l+y+y2-y3)/(1-y)3
non-attracting
hard
spheres.
(2) Equation (2) is regarded as one of the best
analytical forms of equation of state for hard spheres. NEW EQUATION OF STATE The Percus-Yevick solution represents the hard sphere fluid with good success. However the agreement is poor when tested for real fluids and therefore more realistic potentials such as the Lennard-Jones 12-6 potential are required for better representation.
Since the rigid sphere approximation holds good at high
temperatures, a perturbation technique can be employed for real fluids with hard sphere potential as the reference.
The perturbations due to density and temperature
can be estimated from the repulsive part of the potential function.
This scheme was
originated by Zwanzig (1954) and later used by several workers' (Smith and Alder, 1959; Frisch, et al., 1966; Mcquarrie and Katz, 1966; Barker and Henderson, 1967 1. Following this technique Levesque and Vet-let (1969) showed that P/pkT = (P/pkT)Hs +BodJ
fI(pd=) + BL (pd")' f2(pd=)
(3)
where 3 fI(pd ) = c i-I b i (pd3)i ; f2( d3) = C j-l cj(pd3)j
(4)
The numerical value of the constants in equation (3) evaluated by the Monte Carlo method (Levesque and Verlet, 1969) are bI = - 5.851, b2 = - 5.757 and b7 = - 5.966. As most of the b values are of the same order of magnitude, we take hi's are equal and consider only the first order correction. Substftuting the compactness factor y for pd3, the series in y is seen to be -y ln(l-y).
With these substitutions
equation (3) becomes P/pkT = P/(pkT)HS + 2.071116 y In (l-y)
(5)
The constant 2.071116 in equation (5) is obtained using an average value of b = -5.858 and notfng that the b, values estimated by Levesque and Verlet (1969) are based on the virial volume b,/4 where as the volume used in compactness factor y is the hard sphere close packing volume No3/K
The value of B is taken as unity as
239
the attractive part is strongly dependent on y and is a weak function of temperature.
Utilfzfng equation (l), equation (5) becomes
ZhV = (l+y+y*)/(l-y)3 + 2.071116 y In (l-y)
(6)
In arriving at equatfon (6), equation (1) rather than equation (2) is utilized as our results fn calculating enthalpies of vaporization of varfous substances at 198.16 K (Table 2) showed equation (1) to be better.
Further it has been found
that the Carnahan-Starling equation is very inaccurate for a mixture of hard spheres whereas equation (1) gives accurate results. mathematical sense, - Q/(1-y)13
Also, in a strfct
in equatfon (2) is by itself a correction term to
the exact hard sphere equation (1). RESULTS A comparison of the compressibility values predicted by different models with the exact calculations of Alder and Wainwright (1960) is shown in Table 1.
All the
models perform to the same degree of accuracy with the present model slightly better than the other two models.
However a better criteria to test the
theoretical models is to calculate other thermodynamic properties which involve differentfatfon and/or integration of the model equation.
Estimation of a property
like enthalpy of vaporization requires an equation of state and properties of liquid and vapor states.
Equation (6) combfned with the relation hHV = /pdv gives
AH, = RT Iln{(v9/ve)/(l-y)I + {3y(2-~1/2(1-~)*1 + 2.071116 {(l-y)
In (l-y) + ~11
(7)
The results of equation (7) have been compared with the values of Yosfm and Owens (1970) based on equation (1) and the values of Wflhelm and Battino (1973) based on equation (2) are shown In Table 2. experimental values of ve
AHv was estimated usfng equation (7) and
and molecular diameters reported by Wilhelm and Battino
TABLE 1 Comparison of Compressfbilfty Equations
v/v0 :s
zNv
zcs
'HS
'AW
10.20 12.54
10.16 12.43
10.80 13.18
10.17 12.50
1:7
8.50 5.86
8.56 5.83
9.01 6.03
8.59 5.89
ro:o 5.:
2.93 1.36
3.03 1.36
3.06 1.36
3.05 1.36
240
TABLE 2 Comparison of AHv (kJ/mole) at 298.15 K for Hydrocarbons Hydrocarbon
Expt.
AH, NV
% Dev.
AHV HS
% Dev.
AH, C5
% Dev.
n-Hexane n-Heptane n-Octane n-Nonane n-Oecane n-Dodecane n-Tetradecane 3-Methylheptane 2.3-Oimethylhexane 2,4-Dimethylhexane 2,2,4-Trimethylpentane Cyclohexane Methylcyclohexane Benzene To1 uene m-xylene
31.551 36.551 41.488 46.442 51.367 61.287 71.170 39.836 38.794 37.769
30.407 34.807 39.007 43.461 47.389 56.439 64.513 37.794 37.536 36.436
3.63 4.77 5.98 6.42 7.74 7.91 9.35 5.12 3.24 3.53
29.630 33.943 38.069 42.444 46.321 55.235 63.234 36.676 36.609 35.529
6.09 7.14 a.24 8.61 9.82 9.87 11.15 7.43 5.63 5.93
29.166 33.348 37.346 41.566 45.327 53.880 61.632 36.189 35.908 34.863
7.56 8.76 9.98 10.50 11.76 12.09 13.40 9.15
35.133 33.037 35.359 33.849 37.991 42.656
34.798 33.537 33.592 33.711 37.497 41.461
-1.51 -0.66 0.41 1.30 2.80
0.95
33.911 32.679 34.705 32.873 36.598 40.502
3.48 1.08 1.85 2.88 3.67 5.05
33.278
5.28
X5 32:320 35.945 39.741
5*$ 4:52 5.38 6.83
,
,
s
;:z
TABLE 3 Comparison of Experimental AH" (kJ/mole) of Benzene with Values Obtained from the Models Temp. K 351.74 360.46 365.66 371.61 375.35 376.95 385.45 393.99 399.25 406.25 419.75 439.47 455.25 459.07 477.75
Expt. Data
Present
Yosfm-Owens
30.831 30.495 30.205 29.868 29.489 29.465 28.851 28.552 27.898 27.514 26.521 25.071 23.846 23.436 21.766
30.524 30.017 29.713 29.365 29.145 29.051 28.550 38.043 27.728 27.307 26.482 25.237 24.191 23.929 21.572
29.727 29.229 28.931 28.590 28.375 28.283 27.794 27.299 26.993 26.583 25.781 24.573 23.561 23.307 21.998
1.29
3.09
Average absolute per cent dev.
WilhelmBattino
Refss, et. al.
MullerPrausnftt
29.301 28.826 28.541 28.214 28.008 27.919 27.449 26.974 26.679 26.284 25.509 24.340 23.355 23.108 21.832
33.951 33.738 33.600 33.431 33.319 33.270 32.996 32.697 32.505 32.233 31.663 30.712 29.826 28,291
30.207 30.256 30.259 30.238 30.253 30.201 30.106 29.970 29.866 29.706 29.328 28.533 27.835 27.643 26.662
4.10
17.04
7.67
29.592
241
(1973) as a function of temperature.
Vg employed was the ideal gas volume as the
introduction of second virial did not improve mdels
coatpared in this paper.
(AH,,) prediction for any of the Table 3 shows the predfcted AH, values as a
function of temperature for benzene.
The experimental data are those collected in
our laboratory (Natarajan and Viswanath, 1983) and these values agreed with the published data of Todd and co-workers (1978) within f 0.5 percent.
In this
coatparison we have also fncluded the values predicted by models due to Reiss, et al. (1959) and Muller-Prausnftz (1979).
The method of Rdss.
et al. uses a
TABLE 4 Statistical Analysis of Enthalpy of Vaporization: Compound
A Comparison
Present
Wilhelm Battino
YosimOwens
Reiss et al.
MullerPrausnitz
Temp. Range (n)
Benzene
3 a
1.29 1.56
4.10 1.71
3.09 1.54
17.04 6.05
7.67 7.21
351.79 to 477.75 (15)
Toluene
5 a
2.86 1.14
6.14 1.74
5.18 1.58
8.24 5.48
11.02 5.37
379.63 to 521.13 (16)
p-xylene a a
6.06 2.33
9.26 2.52
a.40 2.35
4.90 5.76
10.40 5.53
411.49 to 557.25 (14)
a: average absolute percent deviation from experimental data obtained in our laboratory; a: standard deviation; n: number of data points considered in the temperature range.
TABLE 5 AH~ For Hfgh Molecular Weight Compounds
Colnpound Quinoline
Anthracene
Phenanthrene
Tep.
Lit. Da.ta
510.75 553.15 593.15 633.15 653.15 613.47 622.97 639.97 652.97 652.00
z-2 a 42:5 40.0 39.Ob 56.6 55.8 54.3 53.1 5a.2*c
Present 45.3 42.9 40.4 37.7 36.1 53.3 52.5 51.2 50.2 51.8
MullerPrausnitz 41.0 38.6 36.2 33.5 32.1 43.8 43.0 41.9 41.1 42.3
a: Viswanath (1979); b: Kudchadker. et al. (1979); c: Muller-Prausnftz (1979). *This value appears to be higher as a value of 53.0 kJ/mole is quoted by Kudchadker, et al. (1979) which is in better agreement with the present model.
242
temperature dependent thermal expansfon coefficient and the semi-empirfcal method of Muller and Prausnitt employs several adjustable parameters.
Table 3 Is extended
into Table 4 to show a statistical analysis for benzene, toluene and p-xylene.
A
detailed analysis for toluene, p-xylene and other compounds will be published elsewhere.
This model is tested further for Its ability in predicting @Iv values
for high molecular weight, two or more ring compounds.
The results are compared
with the Muller-Prausnitz method developed for high molecular weight compounds. The results presented in Table 5 show the superiority of the present model compared to the Muller-Prausnitt method.
LIST OF SYMBOLS AW b bi
Alder-Wafnright hard sphere closed packed volume, m3 mol-I constants in eqn. (4)
C.
constants in eqn. (4)
d
Camahan-Starling
d fl f2 HS AHV
molecular diameter, m a functfon in eqn. (3) and (4) a function in eqn. (3) and (4) Hard Sphere enthalpy of vaporization, kJ mole-’
f
integer in eqn. (4)
j
integer in eqn. (4)
k
Boltzmann constant, J deg"
N P
Avogadro Number, mole-' -2 pressure, N m
R
gas-law constant, J deg"
T
temperature, k
V
volume, m3 mole
vO
volume at close packing, m3 mol -1 vapor volume, m3 mole
?I VR
-1 -1
lfquid volume, m3 mole-l
Y
compactness parameter (y = aNa3/ti Ye)
z
compressibility factor (2 = Pv/pkT)
f3
= l/kT
P
particle densfty (p = N/v)
u
collision dfameter, m
243
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