Second virial coefficients of fuel-gas components: (carbon monoxide + nitrogen) and (carbon monoxide + ethene)

Second virial coefficients of fuel-gas components: (carbon monoxide + nitrogen) and (carbon monoxide + ethene)

M-3079 J. Chem. Thermodynamics 1995, 27, 755–761 Second virial coefficients of fuel-gas components: (carbon monoxide+nitrogen) and (carbon monoxide+e...

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M-3079 J. Chem. Thermodynamics 1995, 27, 755–761

Second virial coefficients of fuel-gas components: (carbon monoxide+nitrogen) and (carbon monoxide+ethene) P. J. McElroy a and S. Buchanan Chemical and Process Engineering Department, University of Canterbury, Christchurch, New Zealand

(Received 1 August 1994; in final form 6 December 1994) Excess and unlike-interaction second virial coefficients of (0.5CO+0.5N2 ) and of (0.5CO+ 0.5C2 H4 ) and reported at temperatures from 300 K to 348 K. The results are compared with the predictions of the Tsonopoulos and the Mak and Lielmezs equations. The excess molar enthalpies for both mixtures have been calculated. 7 1995 Academic Press Limited

1. Introduction This study extends earlier work on binary mixtures of components of natural gases.(1) The Groupe Europe´en de Recherches Gazie`res (GERG) has demonstrated(2) that the virial equation of state with second and third virial coefficients only is capable of predicting the compression factors of multi-component mixtures to within 0.1 per cent. Consequently accurate unlike-interaction second virial coefficients are required. The GERG group extended the scope of their correlation(3) to include ‘‘coke oven’’ (coal-derived) fuel gases and their mixtures with natural gases. The major change is an extension to include carbon monoxide, ethene, and hydrogen as significant compounds in the mixtures. The GERG maximum mole fraction of N2 of 0.055 in natural gas is also appropriate for ‘‘coke-oven gas’’. The pressure-change-of-mixing method to obtain excess second virial coefficient o using o=2RT ·Dp/p 2(1+Dp/p),


has been described on a number of occasions.(4, 5) The unlike-interaction second virial coefficient B12 is readily obtained from o and the pure-component B values using B12=o+(B11+B22 )/2. a


To whom correspondence should be addressed.

0021–9614/95/070755+07 $12.00/0

7 1995 Academic Press Limited


P. J. McElroy and S. Buchanan

When the excess second virial coefficient o as a function of temperature is determined, the excess molar enthalpy HmE can be obtained(6) using the relation: HmE =2y(1−y)p(o−T ·do/dT ),


where y denotes the mole fraction of component 2. Equations (1) and (3) have been derived using the pressure-series virial equation: pVm=RT+Bp+C'p 2+· · ·,



truncated by setting C'p and higher terms to zero. Equivalent equations using the volume-series virial equation: pVm=RT{1+(B/Vm )+(C/Vm2 )+· · · },


have been derived by Knobler. The equation for o is (7)

o=2RT ·Dp/p 2−{ 12 (B22−B11 )2−o(B11+B22 )+34 (F112+F122 )}p/RT,


F112=C112−13 (2C111+C222 ),


F122=C122−13 (C111+2C222 ).




The equation for HmE derived using the volume-series virial coefficient equation has been shown by Wormald(8) to be HmE =2y(1−y)p(o−T ·do/dT)−(p 2/RT)·{Bf−(1−y)B11 f11−yB22 f22 }+ (p 2/RT){c−(1−y)c111−yc222 },


where fii=Bii−T ·dBii /dT,


ciii=Ciii−T ·dCiii /dT.


Since C'=(C−B 2 )/RT, whether truncation of the pressure-series equation or truncation of the volume-series is preferable depends on the magnitudes of C and B 2. For this work for N2 and CO, the B values are small so that B 2 is small compared to C. Truncations of the volume or pressure series are essentially equivalent. For (0.5CO + 0.5C2 H4 ) the HmE calculated using the truncated pressure series is found to be approximately 0.015 J·mol−1 . The experimental uncertainty in HmE is estimated to be 20.1 J·mol−1 . Any correction to the HmE values is therefore not justified and so we have used the truncated pressure-series virial equation throughout.

2. Experimental The apparatus and experimental procedure have been fully described(4) and were unchanged for this work. The carbon monoxide was supplied by Matheson Gas Products (Ultra-High-Purity grade) specified as better than 99.8 moles per cent of CO

Second virial coefficients of {0.5CO+0.5(N2 or C2 H4 )}


with N2 as the major impurity. The nitrogen used was Research-Grade supplied by New Zealand Industrial Gases and specified as 99.99 moles per cent of N2 . The ethene used was supplied by Matheson Gas Products Co. and was analysed by gas chromotography as 99.9 moles per cent of C2H4 with C2 H2 (0.04 mole per cent) as the major impurity. All gases were passed through a silica-gel drying train but otherwise were not further treated. To determine unlike-interaction second virial coefficients using equation (2), pure-component B values must be selected from previously published values. For N2 Jaeschke et al.(2) having carried out a detailed analysis of the available values in this temperature range concluded that those of Roe(9) and of Michels et al.(10) were consistent with a number of other studies and were the best measurements available. Brugge et al.(11) also compared their two measurements with published values and found agreement with the work of Roe and of Michels et al. The fitted equation by Jaeschke et al.(2) is B(N2 )/(cm3 ·mol−1 )=−144.6+0.74091·(T/K)−9.1195·10−4 ·(T/K)2,


and this relation has been used here in deriving B12 for (0.5N2 + 0.5CO). The second virial coefficients of CO have been discussed recently(12) with the conclusion that the equation due to Goodwin:(13) B/(cm3 ·mol−1 )=55.956−201.67·102 ·(K/T )+66.55·104 ·(K/T )2− 109.77·106 ·(K/T )3,


is a good representation of the measured values. Second virial coefficients for C2 H4 have been reported by McElroy and Ji(14) and compared with previous studies. The equation: B/(cm3 ·mol−1 )=53.6535−27398.0·(K/T )−9.03445·106 ·(K/T )2,


derived by Levelt-Sengers and Hastings(15) was shown to be an excellent representation of the measurements and has been used in this work. The values of all the pure-component virial coefficients used for determining B12 are listed in table 1.

3. Results and discussion The measured values of pressure, pressure change, and temperature are recorded in table 2. Also tabulated are the excess second virial coefficient o derived using equation TABLE 1. Pure-component virial coefficient used to generate B12 T/K CO 300.05 303.15 313.16 318.15

−8.3 −7.6 −5.6 −4.6

B/(cm3 ·mol−1 ) C2 H4

T/K N2

−138.0 −3.8 −126.0 −1.2

CO 328.16 333.15 343.16 348.16

−2.8 −1.9 −0.2 +0.5

B/(cm3 ·mol−1 ) C 2 H4


−113.7 1.0 −102.9 2.8


P. J. McElroy and S. Buchanan TABLE 2. Excess and unlike-interaction second virial coefficients of (0.5N2+ 0.5CO) and of (0.5C+0.5C2 H4 ) Dp/Pa



303.16 303.15 318.15 318.14 333.15 333.15 348.15 348.17

103.053 101.392 100.557 104.063 102.535 103.017 102.691 100.365

300.06 300.04 313.16 313.15 328.16 328.16 343.15 343.15

99.0315 101.819 99.836 101.535 101.596 97.884 100.042 100.315

o/(cm3 ·mol−1 )

B12 /(cm3 ·mol−1 )

(0.5CO+0.5N2 ) −1.28 −0.61 −1.76 −0.86 −1.74 −0.91 −1.67 −0.82 −1.42 −0.75 −1.52 −0.79 −1.75 −0.96 −1.69 −0.97

−6.3 −6.6 −3.8 −3.7 −1.2 −1.2 0.7 0.7

(0.5CO+0.5C2 H4 ) 54.84 59.01 50.34 50.73 45.64 43.46 39.87 40.07

27.9 28.4 26.3 25.6 24.1 24.7 22.7 22.7

−45.2 −44.8 −39.5 −40.2 −34.1 −33.6 −28.8 −28.8

(1) and the unlike-interaction second virial coefficient B12 derived from equation (2) and the pure B values listed in table 1. The measured B12 values may be compared with predictive correlations which have been developed such as the Tsonopoulos equation(16) which has the form: Bpc /RTc=f (0)(TR )+v ·f (1)(TR )+f (2)(TR ),


where TR and v are reduced temperature T/Tc and acentric factor. This may be applied to unlike-interaction B values using Tc, 12=(Tc, 1 Tc, 2 )(1−k12 ),


(2) the usual rule for pc, 12 ,(15) and the rule for f (2)(TR ) which sets f 12 =0 unless both components have a dipole moment. For the mixtures studied here only CO has a dipole (2) is zero. The forms of functions f (0) and f (1) are available.(17) moment and so f 12 Another correlation which may be applied to B12 is that due to Mak and Lielmezs(18) which is of the form:

Bpc /RTc=0.0778−0.45724·A/Tc ,


where A(TR , v)=A0 (TR )+vA1 (TR ). The functional forms of A0 and A1 are well established(18) and the extension of this equation to B12 using the same combining rules as for the Tsonopoulos equation has been demonstrated previously.(14)

Second virial coefficients of {0.5CO+0.5(N2 or C2 H4 )}


The measured B12 values for (0.5N2 + 0.5CO) are plotted in figure 1 along with two values from the published literature at lower temperatures.(19, 20) Also plotted are the Tsonopoulos equation and the Mak and Lielmezs equation both with k12=0. This seems reasonable for compounds as similar as these. Evidently the Mak and Lielmezs equation provides an excellent fit to the measurements and is significantly better than the Tsonopoulos equation. However, since the uncertainties in the values used are dB(CO) = 21 cm3 ·mol−1 , dB(N2 ) = 21 cm3 ·mol−1 , and do=21.5 cm3 ·mol−1 , the Tsonopoulos equation result is at the limit of the expected experimental error. In the GERG Technical Monograph No. 2(2) measurements of B12 for (0.5N2+ 0.5CO) were critically assessed and the equation: B12 /(cm3 ·mol−1 )=−122.189+0.52124·(T/K)−4.37181·10−4 ·(T/K)2,


was presented to represent the B12 behaviour. This equation, also plotted in figure 1, is evidently not a good representation of the experimental results. The values of B12 reported by Brewer(20) and by Menon,(19) also plotted in figure 1, are evidently in good agreement with the values measured in this work. The B12 results for (0.5CO + 0.5C2 H4 ) are plotted in figure 2. The equation due to Tsonopoulos and to Mak and Lielmezs are also plotted with k12=0.02. Evidently the predictions of the two equations are effectively indistinguishable and both give an improved fit when k12 is set to 0.02. However, an uncertainty of 23 cm3 ·mol−1 in

FIGURE 1. Unlike-interaction second virial coefficients for (0.5CO+0.5N2 ). e, This work; q, Menon;(19) r, Brewer;(18) – – –, GERG correlation;(2) — —, Tsonopoulos (k12=0);(14) — –, Mak and Lielmezs (k12=0).(16)


P. J. McElroy and S. Buchanan

FIGURE 2. Unlike-interaction second virial coefficients for (0.5CO+0.5N2 ). e, This work; w, Mason and Eakin;(19) ——, Tsonopoulos(14) and Mak and Lielmezs(16) both with k12=0; — –, Tsonopoulos(14) and Mak and Lielmezs(16) both with k12=0.02.

B(C2 H4 ) and 27.5 cm3 ·mol−1 in o gives 24 cm3 ·mol−1 as the estimated uncertainty in B12 so that the fit is still within experimental error when k12=0. Using equation (3) the excess molar enthalpy can be estimated and the values obtained are listed in table 3. For (0.5CO + 0.5C2 H4 ) the HmE values range from 3 J·mol−1 to 4 J·mol−1 and for (0.5CO + 0.5N2 ) HmE is close to zero. Martin et al. reported HmE values for a number of simple gas mixtures with values ranging from zero for (0.5O2 + 0.5N2 ) to 6.7 J·mol−1 for (0.5CO2 + 0.5CH4 ) and so magnitudes of results are consistent with their work. Also plotted in figure 2 is the only previously

TABLE 3. Excess molar enthalpy of (0.5CO+0.5C2 H4 ) and (0.5CO+0.5N2 ) T K

300.05 313.16 328.16 343.16

HmE /{2y(1−y)p} cm3 ·mol−1 (0.5CO+0.5C2 H4 ) 77.7 74.6 62.0 58.7

HmE /(J·mol−1 ) (at p=105 Pa)

3.9 3.7 3.1 2.9

(0.5CO+0.5N2 ) 303.15 318.15 333.15 348.16

−0.77 −0.40 −0.19 −0.26

−0.04 −0.02 −0.01 −0.01

Second virial coefficients of {0.5CO+0.5(N2 or C2 H4 )}


measured B12 value which could be found. This is the measurement of Mason and Eakin(21) which is considerably less negative than this work. The assistance of Mr S. Moser in making the measurements on (0.5CO + 0.5N2 ) is gratefully acknowledged. We would also like to thank the New Zealand Lotteries Grant Board for their assistance in purchasing equipment items. REFERENCES 1. McElroy, P. J. J. Chem. Thermodynamics 1994, 26, 663. 2. Jaeschke, M.; Audibert, S.; Canegham, P. van; Humphreys, A. E.; Janssen van Rosmalen, R.; Pellei, Q.; Michels, J. P. J.; Schouten, J. A.; Seldam, C. A. ten High Accuracy Compressibility Factor Calculation for Natural Gases and Similar Mixtures by Use of a Truncated Virial Equation. GERG Technical Monograph 2, 1988. 3. Jaeschke, M.; Humphreys, A. E. Standard GERG Virial Equation for Field Use. GERG Technical Monograph TM5, 1991. 4. McElroy, P. J. J. Chem. Thermodynamics 1994, 26, 663. 5. McElroy, P. J.; Shannon, T. W.; Williamson, A. G. J. Chem. Thermodynamics 1980, 12, 371. 6. Knoester, M.; Taconis, K. W.; Beenakker, J. J. M. Physica 1967, 33, 389. 7. Knobler, C. M. Rev. Sci. Instruments 1967, 38, 184. 8. Wormald, C. J. J. Chem. Thermodynamics 1977, 9, 901. 9. Roe, D. R. Ph.D Thesis, Imperial College, University of London. 1972. 10. Michels, A.; Wouters, H.; Boer, J. de Physica 1934, 1, 587. 11. Brugge, H. B.; Hwang, C. A.; Rogers, W. J.; Holste, J. C.; Hall, K. R.; Lemming, W.; Esper, G. J.; Marsh, K. N.; Gammon, B. E. Physica 1989, A156, 382. 12. McElroy, P. J.; Moser, J. J. Chem. Thermodynamics 1995, 27, 267. 13. Goodwin, R. D. Cryogenics 1983, 23, 403. 14. McElroy, P. J.; Ji, F. J. Chem. Eng. Data 1993, 38, 410. 15. Levelt-Senger, A.; Hastings, J. Ethylene. International Thermodynamic Tables of the Fluid State. de Reuck, K. M.; Angus, S.; Cole, W. A.; Craven, R. J. B.; Wakeham, W. A.: editors. Blackwell: Oxford. 1988. Vol. 10, 53. 16. Tsonopoulos, C. J. A.I.Ch.E. J. 1974, 20, 263. 17. McElroy, P. J.; Hashim, H.; Wong, L. T. A.I.Ch.E. J. 1983, 29, 1007. 18. Mak, P. C. N.; Lielmezs, J. J. Ind. Eng. Chem. Res. 1989, 28, 127. 19. Menon, P. G. Ind. J. Pure Appl. Phys. 1965, 3, 334. 20. Brewer, J. Contract No. AF49/638/-1620 AFOSR No. 67, 2795, Arlington Virginia, U.S.A. 22209. 1967. 21. Mason, D. McA.; Eakin, B. E. J. Chem. Eng. Data 1961, 6, 499.