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Excess enthalpies and Gibbs free energies for nitrogen + methane at temperatures below the critical point of nitrogen
J. Chem.Thermodynamics1976,8,785-792
Excess enthalpies and Gibbs free energies for nitrogen + methane at temperatures below the critical point of nitrogen D. W. MCCLURE,” K. L. LEWIS,b R. C. MILLER,” L. A. K. STAVELEY b
and
Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, U.K. (Received 24 February 1976) Mixing calorimetry has been used to determine the excess enthalpy HE as a function of composition for liquid mixtures of nitrogen + methane at 91.5 and 105.0 K. By use of a separate static apparatus, total vapour pressure as a function of composition was determined for this same liquid system at 90.68 K. Barker’s method has been used to convert the results into excess Gibbs free energies GE as a function of mole fraction x. An intercomparison is ma& of available @ data for nitrogen + methane at temperatures below the critical point of nitrogen (126.2 K). GE/T at x = 0.5 is plotted as a function of reciprocal temperature with slopes taken from the experimental HE values. Good agreement is found between the present results and a number of other recent studies.
1. rntroduction Excess properties of liquid nitrogen + methane are of importance from two points of view. First, this is a system of some concern to the growing liquefied natural gas industry; and, second, it is of continuing interest to the scientific community in relation to the development of theories of simple liquid mixtures. Experimental HE values may be of direct use in analysis of heat-exchange equipment, but the most important industrial use stems from the fact that HE establishes the variation of GE with temperature. This provides a framework for intercomparing and correlating vapour-Iiquid phase equilibrium data needed for separation-equipment analysis. In the development of liquid mixture theories, experimental HE and GE values help to provide the basis for testing and improvement. Predicted HE values are particularly sensitive to the unlike-molecule parameters used in the models. A number of vapour-liquid phase equilibrium studies have been reported(‘) for nitrogen + methane between the triple-point temperature of methane (90.68 K) and the critical temperature of nitrogen, and a comparison of GE values derived from these studies has been recently published. (‘I The only important discrepancies a Department of Chemistry, Portland State University, Portland, Oregon 97207, U.S.A. b Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, U.K. c Department of Mineral Engineering, University of Wyoming, Laramie, Wyoming 82071, U.S.A.
786
D. W. MCCLURE ET AL.
appeared at the lowest temperatures. No published HE results appear to be available for this system; however, one of the present authors did make some liquid-phase measurementsjust below the critical temperature of nitrogen.t3’ The purpose of the current investigation was to make an independent determination of GE at the lowest possible temperature and to measure HE at temperatures where reasonably accurate results could be obtained.
2. Experimental Two independent experimental systems were used in this investigation. A static system for measurement of total vapour pressure was employed to determine GE values. Determination of HE values was accomplished by means of a mixing calorimeter. The basic experiment for the measurement of total vapour pressuresabove binary liquid mixtures at low temperatures has been described in earlier publications.(4) Since these publications, sufficient modifications and recalibrations have been made to justify some discussion of the experiments on nitrogen + methane. The glass vapour-pressure cell and surrounding cryostat assemblywere exactly as reported in 1967.‘4’ Commercially obtained research methane of 99.99 moles per cent stated minimum purity was used as the cryostatting medium by maintaining it at its triplepoint temperature (90.68 K). The value obtained for the triple-point pressure (11.74 kPa compared with 11.71 kPa in the previous workc4)) and its constancy with melting were considered to be sufficient checks on the purity of the methane. Methane of the samepurity as the cryostat material and then commercial nitrogen of 99.9995 moles per cent stated minimum purity were separately condensed into the vapour-pressure cell from large glass storage globes thermostatted near room temperature. The volumes of these globes were determined by weighing, with water as the calibration fluid. All connecting lines were glass, and the appropriate volumes were determined by gas-expansion techniques. The amounts of each pure component added to the cell were calculated from pressuresmeasured in the glass storage globes before and after condensation. The liquefied components were mixed in the cell by a magnetic stirrer. With the cell held at the equilibrium temperature, the gas phase was slowly enlarged to twice the normal volume, mixed, and recompressed, using the equipment described in 1967.(4) This was done to ensure homogeneity and near-equilibrium composition for the gas phase. Equilibrium pressureswere measured directly with a quartz spiral pressure gauge calibrated in situ against a gas-operated dead-weight gauge.(4) Barker’s method was used to convert the p, x measurementsinto GEvalues and gas-phase compositions. The liquid mole fractions were initially calculated from the gross amounts of pure components added to the cell. They were subsequently corrected in an iterative procedure using the calculated gas-phase amount and composition. Excessenthalpy measurementswere performed at 91.5 and 105.0K using a recently described mixing calorimeter. (5) This system has been used previously to determine HE for some simple liquid mixtures’5’ and liquid mixtures of light hydrocarbons.@)
HE AND
G@FOR LIQUID
787
Nz + CH,
The same nitrogen and methane were used as in one of the previous studies:(“) N,, 99.9 moles per cent minimum purity; CH4, 99.0 moles per cent minimum purity. To check the influence of the impurities, one test experiment was made at 91.5 K using the gasesemployed in the total-pressure measurements. The two pure liquids were initially separated in upper and lower calorimeter compartments by a large-orifice valve, which, on opening, allowed the liquids to mix. Endothermic mixing was compensated by supplying a measured quantity of electrical energy. HE values were calculated from the enthalpies of mixing as previously reported.‘@ 3. Results
Experimental total vapour pressures as a function of the mole fraction of methane in the liquid phase at 90.68 K are listed in table 1. The liquid mole fractions and pressuresare believed accurate to &-0.0003and +0.3 kPa respectively. TABLE 1. Total vapour-pressures for Na + CH4 at 90.68 K, where x(CH,) is the liquid-phase mole fraction of methane, p the measured total vapour pressure, pcalo.and y(CHI) the total pressure and vapour-phase mole fraction of methane from a Barker-method analysis, and GE the excess Gibbs free energy at zero pressure
x(‘3-L)
&Pa
0 0.12484 0.21782 0.32279 0.42551 0.51473 0.62049 0.70187 0.81128 1
381.42 337.63 309.66 282.14 255.87 233.48 203.22 175.67 131.24 11.74
GE/J mol - 1
YOU
337.56 309.94 282.03 256.05 233.12 203.12 176.12 131.02 -
0.0103 0.0168 0.0234 0.0299 0.0360 0.0453 0.0556 0.0801 -
0 74.4 115.9 148.5 166.0 169.5 159.7 141.9 103.8 0
Also presented in table 1 are the results of the Barker-method calculation”) for total vapour pressures, gas-phase mole fractions for methane, and values of GE at zero pressure. In this calculation the gas phase was assumed to obey the pressure virial equation truncated after the second virial coefficient term, and the liquid-phase GE was assumed to be given by a three-term Redlich-Kister equation. The second virial coefficients were taken to be - 192 cm3 mol-’ for nitrogen, - 581 cm3 mol-’ for methane, and -279 cm3 mol- ’ for the cross coefficient. Pure-component molar volumes were taken as 35.53 cm3 mol- ’ for methane and 37.75 cm3 mol-’ for nitrogen. The resulting GE equation is (component 1, methane): GE= RT~~x~(0.9001 -0.0026(x1-xz)+0.0018(xl which yields 169.6 J mol-’ for xl = x2 = 0.5.
-x,)“},
(1)
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D. W. MCCLURE ET AL.
The results of the enthalpy of mixing experiments at 91.5 and 105.0 K are presented in table 2. Liquid mole fractions of methane, total amounts of liquid mixture, corrected energy inputs & per mole of liquid mixture, and excessenthalpies at both the mixture saturation pressure, HE(p’), and corrected to zero pressure, HE(O), are tabulated. The energy inputs have been corrected for the effect of valve opening and uncompensated mixing (arising from the fact that the mixing process could be electrically compensated only in discrete stages). TABLE 2. Excessenthalpiesfor Nz + CH, at 91.5 and 105.0 K, where T is the thermodynamic temperature, x(CH*) is the liquid-phase mole fraction of methane, n the total amount of liquid mixture, Q is the corrected electrical energy input (see text) required to compensate for the mixing process, HE(pS) the molar excess enthalpy at the mixture total vapour pressure, and HE(O) the molar excess enthalpy at zero pressure T/K 91.5
105.0
x(CH,)
n/m01
Q/J mol-1
P(p’)/J
mole1 ZfE(0)/J mol-1
0.286 0.486 0.521 a 0.589 0.753 0.883
0.1956 0.2317 0.1969 a 0.2356 0.2332 0.2277
123.2 125.9 172.1 a 150.6 103.0 36.3
106.8 136.7 139.8 a 136.9 109.9 60.8
106.6 136.6 139.8 a 136.9 109.9 60.8
0.337 0.433 0.514 0.580 0.622 0.714
0.1743 0.2081 0.1801 0.2292 0.2081 0.1814
132.1 117.7 149.5 128.2 113.9 74.6
86.2 101.2 105.3 109.0 105.6 96.9
80.1 95.3 100.0 104.3 101.3 93.9
a Results for experiment using 99.99 moles per cent methane and 99.9995 moles per cent nitrogen.
In the analysis of the experiments, the necessary phase-equilibrium calculations were made using GE values from Parrish and Hiza(‘) and second virial coefficients from McGIashan et a1.,@,9, with a geometric-mean rule deviation parameter of 0.03. Vapour pressures, energies of vaporization, and other relevant properties for nitrogen were taken from the compilation of Strobridge,“” with similar properties of methane from Goodwin.(“) For this system, the difference between the corrected molar enthalpy of mixing Q and the excess enthalpy HE(@) was found to be predominantly the vaporization correction for nitrogen at 91.5 K. At 105 K, significant corrections were needed for vaporization of methane and energy changes for the pure liquids in going from their respective vapour pressuresto the mixture saturation pressure. Small corrections were also made for liquid-phase VE and gas-phase enthalpy of mixing. Higher temperatures could not be studied because the calorimeter could not withstand higher nitrogen vapour pressures,and the uncertainties in the calorimeter corrections were found to increase rapidly with temperature above 105 K. In the conversion from HE(@) to HE(O) estimates of the mixture excesscoefficient of thermal expansion(’ ‘) and excess isothermal compressibility(‘3) were utilized in
HE AND GE FOR LIQUID
789
Nz + CH<
the calculation, which has been outlined by Lewis, Saville, and Staveley.(r4’ These excess properties are large for nitrogen + methane at temperatures above 100 K. In both casesthe composition dependence was taken to be of the form Ax,xz. At 105 K, A was estimated to be -0.007 K-’ for the excess coefficient of thermal expansion and -0.000013 kPa-’ for the excessisothermal compressibility. The result for the one experiment at 91.5 K using the high-purity nitrogen and methane (indicated in table 2) is in excellent agreement with the other results. A similar experiment was not performed at 105 K. Any more volatile impurities in the 99.0 moles per cent methane would have a greater effect on HE derived from experiments at the higher temperature. Thus, the results at 105 K must be considered to have slightly larger uncertainty than those at 91.5 K, where the estimated maximum experimental error is &-3 J mol - l. The liquid-phase mole fractions should be accurate to kO.003. Nitrogen + methane HE(O) results were fit by the least squares method to twoterm Redlich-Kister equations (component 1, methane) : HE(91.5 K) = x,x,(552.6+67.5(x, HE(105.0 K) = x,x,(402.2+131.5(x,
--x2)) J mol-‘, -x2)} J mol-‘.
12) (3)
Equation (2) represents the 91.5 K results with a standard deviation of 1.2 J mol-‘, while equation (3) represents the 105.0 K results with a standard deviation of 1.1 Jmol- ‘. Curves from these equations and the experimental results are plotted against x(CH,) in figure 1.
120
20 0 0
0.2
0.4 0.6 x(CM,)
0.8
1
FIGURE 1. Excess enthalpy of nitrogen + methane at 91.5 and 105.0 K, where HE is the excess enthaipy at zero pressure, and x(CH,) is the liquid-phase mole fraction of methane. 0, 91.5 K, this work; 0, 105.0 K, this work; --, equations (2) and (3).
790
D. W. MCCLURE ET AL.
4. Discussion Recently, Parrish and Hiza (2) have compared vapour-liquid equilibrium results of numerous investigations for N, + CH, by plotting the values of GE@= 0.5) against temperature. The relation between HE and GE at constant pressure can be written in the form: a(GE/T)/a(l/T) = HE. (4) Thus, if GE/T is plotted against l/T, the slope at any point is equal to HE. Figure 2 is such a plot for N, + CH,. Except for the GE(O)result from the present work,
1.9 90 t 1
95
loo
T/K 105 110 115 I --r-120
1.0
0.9
1.5 I 8 1.1
I
(NO/ T)/K-t FIGURE 2. Excess Gibbs free energy for mixtures of nitrogen + methane, where G” is the excess Gibbs free energy at zero pressure and x = 0.5, and T the thermodynamic temperature. +, this work; 0, reference 2; 0, reference 17; 0, reference 18; A, reference 19; A, reference 20; curve with slopes equal to P’s from this work. 0, reference 21; n , reference 22; -,
all necessary data were taken from reference 2 and GE was calculated from p, x results using Barker’s method with a consistent set of input parameters. The curve was drawn with slopes at 91.5 and 105.0K in accord with the HE results from the present investigation. The vertical position of the curve may be changed, but the slopes cannot change appreciably. The dashed portion of the curve extends upwards in temperature, under the assumption that HE is linear in temperature. At still higher temperatures, HE becomes strongly non-linear. No attempt has been made to extend the curve into this region. It can be concluded that a number of N2 + CH4 vapour-liquid equilibrium studies are in agreement among themselvesand in accord with the GEand HE values of this study. Previous values of GE(x = 0.5) near 91 K appear to be somewhat low. A modified hard-sphere model has been shown to predict quite closely the temperature dependence of both the excess voIume(‘5*‘6) and the excess Gibbs free energyc2’for N2 + CH.+. Using the model as presented in reference 16, the rnixingrule deviation parameters for determining unlike-molecule characteristic size and
HE AND G’ FOR LIQUID
Nz + CHI
791
energy were evaluated by simultaneous fit of VE(ps, x = 0.5) and HE(ps, x = 0.5) at 105 K. VE(p’) was taken from reference 15 and HE(@) from the present study. The resulting correction factor for the arithmetic-mean rule for size parameters is 1.0106, while the correction factor for the geometric-meanrule for energyparametersis 0.9791. These values are somewhat different from those reported in reference 16, where they were evaluated from GE and VE data. Simultaneous prediction of accurate values for all three excessproperties of Nz + CH, does not seemto be possible with this model in its present form. In figure 3 the model prediction for the temperature dependenceof HE(pS, x = 0.5) is presented. The two experimental points from the current study are also shown.
T/K FIGURE 3. Excess enthalpy for mixtures of nitrogen + methane, where HE is the excess enthalpy at the mixture saturation pressure and x = 0.5, and T the thermodynamic temperature. 0, this work; -, calculations based on model adapted from reference 16.
Calculated and experimental temperature dependencesare in good agreement. The model predicts highly non-linear behaviour for HE(@) as the temperature approaches the critical temperature of nitrogen. In particular, HE(@) is predicted to become negative at temperatures above 118 K. In a previous flow-calorimeter study,‘3’ a negative HE value was actually observed. HE = -28 J mol-’ was measured at 122.4 K and 3.25 MPa, with x(N,) = 0.519. This value is in reasonable agreement with the curve on figure 3. One author (R.C.M.) is grateful to the U.S. National Science Foundation and the University of Wyoming for financial support. Two of the authors (D.W.M. and R.C.M.) wish to thank New College for their kind hospitality. REFERENCES 1. Hiza, M. J. ; Kidnay, A. J. ; Miller, R. C. Eqrrilibrium Properties of Fluid Mixtures, A Bibliography of Data on Fluids of Cryogenic Interest. IFI/Plenum: New York. 1975. 2. Parrish, W. R.; Hiza, M. J. A&. Cryo. Z%gr. 1974, 19, 300. 54
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D. W. MCCLURE ET AL.
3. Lewis, K. L. Ph.D. Thesis, Bristol University. 1972. 4. Mathot, V.; Staveley, L. A, K.; Young, J. A.; Parsonage, N. G. Trans. Fuaday Sot. 1956, 52, 1488. Davies, R. H.; Duncan, A. G.; Saville, G.; Staveley, L. A. K. ibid. 1%7, 63, 855. 5. Lewis, K. L.; Staveley, L. A. K. J. Chem. Thermoaynamics 1975, 7, 855. 6. Miller, R. C.; Staveley, L. A. K. Adv. Cryo. Engr. 1976, 21, to be published. 7. Barker, J. A. Aust. J. Chem. 1953, 6, 207. 8. McGlashan, M. L.; Potter, D. J. B. Proc. Roy. Sot. 1962, A267,478, 9. McGlashan, M. L.; Wormafd, C. J. Trans. Furaday Sot. 1964,60,646. 10. Strobridge, T. R. The Thermodynamic Properties of Nitrogen from 64 to 300 K Between 0.1 and 200 Atmospheres, NBS Tech. Note 129, 1962. 11. Goodwin, R. D. The Thermophysical Properties of Methane, from 90 to 500 K at Pressures to 700 Bar, NBS Tech. Note 653,1974. 12. Liu, Y. P.; Miller, R. C. J. Chem. Thermodynamics lQ72, 4, 85, 13. Miller, R. C. Accurate Density Correlations for LNG. Annual Report to the Amer. Gas Assoc. 1973. 14. Lewis, K. L.; Saville, G. ; Staveley, L. A. K. J. Chem. Thermodynamics 1975, 7, 389. 15. Massengill, D. R.; Miller, R. C. J. Chem. Thermodynamics 1973, 5, 207. 16. Rodosevich, J. B.; Miller, R. C. Adv. Cryo. Engr. 1974, 19, 339. 17. Chang, S.-D. ; Lu, B. C.-Y. Chem. Engr. Progr. Symp. Series 1%7, 63, 18. 18. Cines, M. R.; Roach, J. T. ; Hogan, R. J. ; Roland, C. H. Chem. Engr. Progr. Symp. Series 1%3,49, 1. 19. Sprow, F. B.; Prausnitz, J. M. AIChE J. 1966, 12, 780. 20. Fuks, S.; Bellemans, A. Bull. Sac. Chim. Belg. 1967, 76, 290. 21. Miller, R. C.; Kidnay, A. J.; Hiza, M. J. AZChE J. 1973, 19, 145. 22. Stryjek, R.; Chappelear, P. S.; Kobayashi, R. J. Chem. Eng. Data 1974, 19, 334.
Excess enthalpies and Gibbs free energies for nitrogen + methane at temperatures below the critical point of nitrogen D. W. MCCLURE,” K. L. LEWIS,b R. C. MILLER,” L. A. K. STAVELEY b
and
Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, U.K. (Received 24 February 1976) Mixing calorimetry has been used to determine the excess enthalpy HE as a function of composition for liquid mixtures of nitrogen + methane at 91.5 and 105.0 K. By use of a separate static apparatus, total vapour pressure as a function of composition was determined for this same liquid system at 90.68 K. Barker’s method has been used to convert the results into excess Gibbs free energies GE as a function of mole fraction x. An intercomparison is ma& of available @ data for nitrogen + methane at temperatures below the critical point of nitrogen (126.2 K). GE/T at x = 0.5 is plotted as a function of reciprocal temperature with slopes taken from the experimental HE values. Good agreement is found between the present results and a number of other recent studies.
1. rntroduction Excess properties of liquid nitrogen + methane are of importance from two points of view. First, this is a system of some concern to the growing liquefied natural gas industry; and, second, it is of continuing interest to the scientific community in relation to the development of theories of simple liquid mixtures. Experimental HE values may be of direct use in analysis of heat-exchange equipment, but the most important industrial use stems from the fact that HE establishes the variation of GE with temperature. This provides a framework for intercomparing and correlating vapour-Iiquid phase equilibrium data needed for separation-equipment analysis. In the development of liquid mixture theories, experimental HE and GE values help to provide the basis for testing and improvement. Predicted HE values are particularly sensitive to the unlike-molecule parameters used in the models. A number of vapour-liquid phase equilibrium studies have been reported(‘) for nitrogen + methane between the triple-point temperature of methane (90.68 K) and the critical temperature of nitrogen, and a comparison of GE values derived from these studies has been recently published. (‘I The only important discrepancies a Department of Chemistry, Portland State University, Portland, Oregon 97207, U.S.A. b Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, U.K. c Department of Mineral Engineering, University of Wyoming, Laramie, Wyoming 82071, U.S.A.
786
D. W. MCCLURE ET AL.
appeared at the lowest temperatures. No published HE results appear to be available for this system; however, one of the present authors did make some liquid-phase measurementsjust below the critical temperature of nitrogen.t3’ The purpose of the current investigation was to make an independent determination of GE at the lowest possible temperature and to measure HE at temperatures where reasonably accurate results could be obtained.
2. Experimental Two independent experimental systems were used in this investigation. A static system for measurement of total vapour pressure was employed to determine GE values. Determination of HE values was accomplished by means of a mixing calorimeter. The basic experiment for the measurement of total vapour pressuresabove binary liquid mixtures at low temperatures has been described in earlier publications.(4) Since these publications, sufficient modifications and recalibrations have been made to justify some discussion of the experiments on nitrogen + methane. The glass vapour-pressure cell and surrounding cryostat assemblywere exactly as reported in 1967.‘4’ Commercially obtained research methane of 99.99 moles per cent stated minimum purity was used as the cryostatting medium by maintaining it at its triplepoint temperature (90.68 K). The value obtained for the triple-point pressure (11.74 kPa compared with 11.71 kPa in the previous workc4)) and its constancy with melting were considered to be sufficient checks on the purity of the methane. Methane of the samepurity as the cryostat material and then commercial nitrogen of 99.9995 moles per cent stated minimum purity were separately condensed into the vapour-pressure cell from large glass storage globes thermostatted near room temperature. The volumes of these globes were determined by weighing, with water as the calibration fluid. All connecting lines were glass, and the appropriate volumes were determined by gas-expansion techniques. The amounts of each pure component added to the cell were calculated from pressuresmeasured in the glass storage globes before and after condensation. The liquefied components were mixed in the cell by a magnetic stirrer. With the cell held at the equilibrium temperature, the gas phase was slowly enlarged to twice the normal volume, mixed, and recompressed, using the equipment described in 1967.(4) This was done to ensure homogeneity and near-equilibrium composition for the gas phase. Equilibrium pressureswere measured directly with a quartz spiral pressure gauge calibrated in situ against a gas-operated dead-weight gauge.(4) Barker’s method was used to convert the p, x measurementsinto GEvalues and gas-phase compositions. The liquid mole fractions were initially calculated from the gross amounts of pure components added to the cell. They were subsequently corrected in an iterative procedure using the calculated gas-phase amount and composition. Excessenthalpy measurementswere performed at 91.5 and 105.0K using a recently described mixing calorimeter. (5) This system has been used previously to determine HE for some simple liquid mixtures’5’ and liquid mixtures of light hydrocarbons.@)
HE AND
G@FOR LIQUID
787
Nz + CH,
The same nitrogen and methane were used as in one of the previous studies:(“) N,, 99.9 moles per cent minimum purity; CH4, 99.0 moles per cent minimum purity. To check the influence of the impurities, one test experiment was made at 91.5 K using the gasesemployed in the total-pressure measurements. The two pure liquids were initially separated in upper and lower calorimeter compartments by a large-orifice valve, which, on opening, allowed the liquids to mix. Endothermic mixing was compensated by supplying a measured quantity of electrical energy. HE values were calculated from the enthalpies of mixing as previously reported.‘@ 3. Results
Experimental total vapour pressures as a function of the mole fraction of methane in the liquid phase at 90.68 K are listed in table 1. The liquid mole fractions and pressuresare believed accurate to &-0.0003and +0.3 kPa respectively. TABLE 1. Total vapour-pressures for Na + CH4 at 90.68 K, where x(CH,) is the liquid-phase mole fraction of methane, p the measured total vapour pressure, pcalo.and y(CHI) the total pressure and vapour-phase mole fraction of methane from a Barker-method analysis, and GE the excess Gibbs free energy at zero pressure
x(‘3-L)
&Pa
0 0.12484 0.21782 0.32279 0.42551 0.51473 0.62049 0.70187 0.81128 1
381.42 337.63 309.66 282.14 255.87 233.48 203.22 175.67 131.24 11.74
GE/J mol - 1
YOU
337.56 309.94 282.03 256.05 233.12 203.12 176.12 131.02 -
0.0103 0.0168 0.0234 0.0299 0.0360 0.0453 0.0556 0.0801 -
0 74.4 115.9 148.5 166.0 169.5 159.7 141.9 103.8 0
Also presented in table 1 are the results of the Barker-method calculation”) for total vapour pressures, gas-phase mole fractions for methane, and values of GE at zero pressure. In this calculation the gas phase was assumed to obey the pressure virial equation truncated after the second virial coefficient term, and the liquid-phase GE was assumed to be given by a three-term Redlich-Kister equation. The second virial coefficients were taken to be - 192 cm3 mol-’ for nitrogen, - 581 cm3 mol-’ for methane, and -279 cm3 mol- ’ for the cross coefficient. Pure-component molar volumes were taken as 35.53 cm3 mol- ’ for methane and 37.75 cm3 mol-’ for nitrogen. The resulting GE equation is (component 1, methane): GE= RT~~x~(0.9001 -0.0026(x1-xz)+0.0018(xl which yields 169.6 J mol-’ for xl = x2 = 0.5.
-x,)“},
(1)
788
D. W. MCCLURE ET AL.
The results of the enthalpy of mixing experiments at 91.5 and 105.0 K are presented in table 2. Liquid mole fractions of methane, total amounts of liquid mixture, corrected energy inputs & per mole of liquid mixture, and excessenthalpies at both the mixture saturation pressure, HE(p’), and corrected to zero pressure, HE(O), are tabulated. The energy inputs have been corrected for the effect of valve opening and uncompensated mixing (arising from the fact that the mixing process could be electrically compensated only in discrete stages). TABLE 2. Excessenthalpiesfor Nz + CH, at 91.5 and 105.0 K, where T is the thermodynamic temperature, x(CH*) is the liquid-phase mole fraction of methane, n the total amount of liquid mixture, Q is the corrected electrical energy input (see text) required to compensate for the mixing process, HE(pS) the molar excess enthalpy at the mixture total vapour pressure, and HE(O) the molar excess enthalpy at zero pressure T/K 91.5
105.0
x(CH,)
n/m01
Q/J mol-1
P(p’)/J
mole1 ZfE(0)/J mol-1
0.286 0.486 0.521 a 0.589 0.753 0.883
0.1956 0.2317 0.1969 a 0.2356 0.2332 0.2277
123.2 125.9 172.1 a 150.6 103.0 36.3
106.8 136.7 139.8 a 136.9 109.9 60.8
106.6 136.6 139.8 a 136.9 109.9 60.8
0.337 0.433 0.514 0.580 0.622 0.714
0.1743 0.2081 0.1801 0.2292 0.2081 0.1814
132.1 117.7 149.5 128.2 113.9 74.6
86.2 101.2 105.3 109.0 105.6 96.9
80.1 95.3 100.0 104.3 101.3 93.9
a Results for experiment using 99.99 moles per cent methane and 99.9995 moles per cent nitrogen.
In the analysis of the experiments, the necessary phase-equilibrium calculations were made using GE values from Parrish and Hiza(‘) and second virial coefficients from McGIashan et a1.,@,9, with a geometric-mean rule deviation parameter of 0.03. Vapour pressures, energies of vaporization, and other relevant properties for nitrogen were taken from the compilation of Strobridge,“” with similar properties of methane from Goodwin.(“) For this system, the difference between the corrected molar enthalpy of mixing Q and the excess enthalpy HE(@) was found to be predominantly the vaporization correction for nitrogen at 91.5 K. At 105 K, significant corrections were needed for vaporization of methane and energy changes for the pure liquids in going from their respective vapour pressuresto the mixture saturation pressure. Small corrections were also made for liquid-phase VE and gas-phase enthalpy of mixing. Higher temperatures could not be studied because the calorimeter could not withstand higher nitrogen vapour pressures,and the uncertainties in the calorimeter corrections were found to increase rapidly with temperature above 105 K. In the conversion from HE(@) to HE(O) estimates of the mixture excesscoefficient of thermal expansion(’ ‘) and excess isothermal compressibility(‘3) were utilized in
HE AND GE FOR LIQUID
789
Nz + CH<
the calculation, which has been outlined by Lewis, Saville, and Staveley.(r4’ These excess properties are large for nitrogen + methane at temperatures above 100 K. In both casesthe composition dependence was taken to be of the form Ax,xz. At 105 K, A was estimated to be -0.007 K-’ for the excess coefficient of thermal expansion and -0.000013 kPa-’ for the excessisothermal compressibility. The result for the one experiment at 91.5 K using the high-purity nitrogen and methane (indicated in table 2) is in excellent agreement with the other results. A similar experiment was not performed at 105 K. Any more volatile impurities in the 99.0 moles per cent methane would have a greater effect on HE derived from experiments at the higher temperature. Thus, the results at 105 K must be considered to have slightly larger uncertainty than those at 91.5 K, where the estimated maximum experimental error is &-3 J mol - l. The liquid-phase mole fractions should be accurate to kO.003. Nitrogen + methane HE(O) results were fit by the least squares method to twoterm Redlich-Kister equations (component 1, methane) : HE(91.5 K) = x,x,(552.6+67.5(x, HE(105.0 K) = x,x,(402.2+131.5(x,
--x2)) J mol-‘, -x2)} J mol-‘.
12) (3)
Equation (2) represents the 91.5 K results with a standard deviation of 1.2 J mol-‘, while equation (3) represents the 105.0 K results with a standard deviation of 1.1 Jmol- ‘. Curves from these equations and the experimental results are plotted against x(CH,) in figure 1.
120
20 0 0
0.2
0.4 0.6 x(CM,)
0.8
1
FIGURE 1. Excess enthalpy of nitrogen + methane at 91.5 and 105.0 K, where HE is the excess enthaipy at zero pressure, and x(CH,) is the liquid-phase mole fraction of methane. 0, 91.5 K, this work; 0, 105.0 K, this work; --, equations (2) and (3).
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4. Discussion Recently, Parrish and Hiza (2) have compared vapour-liquid equilibrium results of numerous investigations for N, + CH, by plotting the values of GE@= 0.5) against temperature. The relation between HE and GE at constant pressure can be written in the form: a(GE/T)/a(l/T) = HE. (4) Thus, if GE/T is plotted against l/T, the slope at any point is equal to HE. Figure 2 is such a plot for N, + CH,. Except for the GE(O)result from the present work,
1.9 90 t 1
95
loo
T/K 105 110 115 I --r-120
1.0
0.9
1.5 I 8 1.1
I
(NO/ T)/K-t FIGURE 2. Excess Gibbs free energy for mixtures of nitrogen + methane, where G” is the excess Gibbs free energy at zero pressure and x = 0.5, and T the thermodynamic temperature. +, this work; 0, reference 2; 0, reference 17; 0, reference 18; A, reference 19; A, reference 20; curve with slopes equal to P’s from this work. 0, reference 21; n , reference 22; -,
all necessary data were taken from reference 2 and GE was calculated from p, x results using Barker’s method with a consistent set of input parameters. The curve was drawn with slopes at 91.5 and 105.0K in accord with the HE results from the present investigation. The vertical position of the curve may be changed, but the slopes cannot change appreciably. The dashed portion of the curve extends upwards in temperature, under the assumption that HE is linear in temperature. At still higher temperatures, HE becomes strongly non-linear. No attempt has been made to extend the curve into this region. It can be concluded that a number of N2 + CH4 vapour-liquid equilibrium studies are in agreement among themselvesand in accord with the GEand HE values of this study. Previous values of GE(x = 0.5) near 91 K appear to be somewhat low. A modified hard-sphere model has been shown to predict quite closely the temperature dependence of both the excess voIume(‘5*‘6) and the excess Gibbs free energyc2’for N2 + CH.+. Using the model as presented in reference 16, the rnixingrule deviation parameters for determining unlike-molecule characteristic size and
HE AND G’ FOR LIQUID
Nz + CHI
791
energy were evaluated by simultaneous fit of VE(ps, x = 0.5) and HE(ps, x = 0.5) at 105 K. VE(p’) was taken from reference 15 and HE(@) from the present study. The resulting correction factor for the arithmetic-mean rule for size parameters is 1.0106, while the correction factor for the geometric-meanrule for energyparametersis 0.9791. These values are somewhat different from those reported in reference 16, where they were evaluated from GE and VE data. Simultaneous prediction of accurate values for all three excessproperties of Nz + CH, does not seemto be possible with this model in its present form. In figure 3 the model prediction for the temperature dependenceof HE(pS, x = 0.5) is presented. The two experimental points from the current study are also shown.
T/K FIGURE 3. Excess enthalpy for mixtures of nitrogen + methane, where HE is the excess enthalpy at the mixture saturation pressure and x = 0.5, and T the thermodynamic temperature. 0, this work; -, calculations based on model adapted from reference 16.
Calculated and experimental temperature dependencesare in good agreement. The model predicts highly non-linear behaviour for HE(@) as the temperature approaches the critical temperature of nitrogen. In particular, HE(@) is predicted to become negative at temperatures above 118 K. In a previous flow-calorimeter study,‘3’ a negative HE value was actually observed. HE = -28 J mol-’ was measured at 122.4 K and 3.25 MPa, with x(N,) = 0.519. This value is in reasonable agreement with the curve on figure 3. One author (R.C.M.) is grateful to the U.S. National Science Foundation and the University of Wyoming for financial support. Two of the authors (D.W.M. and R.C.M.) wish to thank New College for their kind hospitality. REFERENCES 1. Hiza, M. J. ; Kidnay, A. J. ; Miller, R. C. Eqrrilibrium Properties of Fluid Mixtures, A Bibliography of Data on Fluids of Cryogenic Interest. IFI/Plenum: New York. 1975. 2. Parrish, W. R.; Hiza, M. J. A&. Cryo. Z%gr. 1974, 19, 300. 54
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3. Lewis, K. L. Ph.D. Thesis, Bristol University. 1972. 4. Mathot, V.; Staveley, L. A, K.; Young, J. A.; Parsonage, N. G. Trans. Fuaday Sot. 1956, 52, 1488. Davies, R. H.; Duncan, A. G.; Saville, G.; Staveley, L. A. K. ibid. 1%7, 63, 855. 5. Lewis, K. L.; Staveley, L. A. K. J. Chem. Thermoaynamics 1975, 7, 855. 6. Miller, R. C.; Staveley, L. A. K. Adv. Cryo. Engr. 1976, 21, to be published. 7. Barker, J. A. Aust. J. Chem. 1953, 6, 207. 8. McGlashan, M. L.; Potter, D. J. B. Proc. Roy. Sot. 1962, A267,478, 9. McGlashan, M. L.; Wormafd, C. J. Trans. Furaday Sot. 1964,60,646. 10. Strobridge, T. R. The Thermodynamic Properties of Nitrogen from 64 to 300 K Between 0.1 and 200 Atmospheres, NBS Tech. Note 129, 1962. 11. Goodwin, R. D. The Thermophysical Properties of Methane, from 90 to 500 K at Pressures to 700 Bar, NBS Tech. Note 653,1974. 12. Liu, Y. P.; Miller, R. C. J. Chem. Thermodynamics lQ72, 4, 85, 13. Miller, R. C. Accurate Density Correlations for LNG. Annual Report to the Amer. Gas Assoc. 1973. 14. Lewis, K. L.; Saville, G. ; Staveley, L. A. K. J. Chem. Thermodynamics 1975, 7, 389. 15. Massengill, D. R.; Miller, R. C. J. Chem. Thermodynamics 1973, 5, 207. 16. Rodosevich, J. B.; Miller, R. C. Adv. Cryo. Engr. 1974, 19, 339. 17. Chang, S.-D. ; Lu, B. C.-Y. Chem. Engr. Progr. Symp. Series 1%7, 63, 18. 18. Cines, M. R.; Roach, J. T. ; Hogan, R. J. ; Roland, C. H. Chem. Engr. Progr. Symp. Series 1%3,49, 1. 19. Sprow, F. B.; Prausnitz, J. M. AIChE J. 1966, 12, 780. 20. Fuks, S.; Bellemans, A. Bull. Sac. Chim. Belg. 1967, 76, 290. 21. Miller, R. C.; Kidnay, A. J.; Hiza, M. J. AZChE J. 1973, 19, 145. 22. Stryjek, R.; Chappelear, P. S.; Kobayashi, R. J. Chem. Eng. Data 1974, 19, 334.