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Excess and unlike-interaction second virial coefficients and excess molar enthalpy of a refrigerant mixture: (0.500CH2FCF3+ 0.500C3H8)
M-3087 J. Chem. Thermodynamics 1995, 27, 1047–1052
Excess and unlike-interaction second virial coefficients and excess molar enthalpy of a refrigerant mixture: (0.500CH2 FCF3+0.500C3 H8 ) Peter J. McElroy Department of Chemical and Process Engineering, University of Canterbury, Christchurch, New Zealand
(Received 22 August 1994; in final form 10 April 1995) The excess second virial coefficient for (1,1,1,2-tetrafluoroethane + propane) has been measured at temperatures of 299.5 K, 313.15 K, 328.15 K, and 343.15 K, using the pressure-change-on-mixing method. The excess enthalpy and unlike-interaction second virial coefficients are also reported. The results have been correlated using the Tsonopoulos equation for virial coefficients. 7 1995 Academic Press Limited
1. Introduction The phasing out of chlorofluorocarbon refrigerant fluids has resulted in a demand for replacement, only some of which has been met by hydrofluorocarbons such as 1,1,1,2-tetrafluoroethane. To provide a broad spectrum of replacement fluids, mixtures have been proposed and design of refrigeration systems with small volumetric hold-up has meant that non-azeotropic mixtures might be acceptable. One proposed mixture is (1,1,1,2-tetrafluoroethane + propane + difluoromethane) and so (p,Vm ,T ) properties are required for that mixture. This work addresses the gas-phase (p,Vm ,T ) behaviour of two of the components. Further studies are in progress. The excess second virial coefficient of a mixture can be determined from the pressure change on mixing the pure components, initially at equal pressure, using the relation: o=RTDp/{p 2(1+Dp/p)2y(1−y)}.
(1)
The excess second virial coefficient o relates to the coefficients Bij as o=B12−(B11+B22 )/2,
(2)
and so the unlike-interaction second virial coefficient B12 can be estimated if B11 and B22 are known. Wormald(1) has shown that for the volume-series virial equation: pVm=RT(1+B/Vm+C/V m2 +· · · ·), 0021–9614/95/091047+06 $12.00/0
(3)
7 1995 Academic Press Limited
1048
P. J. McElroy
the excess molar enthalpy HmE of a two-component mixture is given by HmE =y(1−y)p(2f12−f11−f22 )−(p 2/RT ){Bf−(1−y)B11 f11−yB22 f22 }+ (p 2/RT ){c−(1−y)c111−yc222 },
(4)
where f=B−T·dB/dT and c=C−12 T·dC/dT. The third term containing third virial coefficients C will be smaller than the second term containing B values with a p 2 multiplier and calculations for this mixture show that the magnitude of the second term is similar to that of the uncertainty in HmE . In addition the coefficients to evaluate the third term in equation (4) are not available and so it has not been included in the calculation. We have measured o at four different temperatures and so equation (4) can be used to obtain an estimate of HmE . In the work reported here y=0.500 and for this case it can be shown that f=12 (o−T·do/dT )+12 f11+12 f22 ,
(5)
which is convenient for evaluation of HmE from equation (4).
2. Experimental The apparatus and procedures have been described previously(2) and were unchanged for this work. Equal volumes of the two gases were mixed using a reciprocating circulating pump. The rise in pressure could be followed and circulation was maintained for at least twice the time needed for the rise in pressure to cease. Total pressure was measured on a 100 kPa full-scale Digiquartz model 1015 A-O1 pressure gauge with a claimed accuracy of 0.01 kPa, and pressure change on mixing was measured with an M.K.S. Baratron model 315 BD (270B) diaphragm gauge with a full-scale reading of 133 Pa and a claimed accuracy of 0.33 Pa. Temperature was measured using a platinum resistance thermometer and bridge to within 20.005 K. Temperatures follow the ITS-90. The propane was ‘‘Chemically Pure’’ supplied by New Zealand Industrial Gases and specified as having a mole fraction e0.9997 of C3 H8 with the greatest mole fractions of major impurities as follows: C3 H6 , 0.00013; C2 H6 , 0.00005; N2 , 0.00003; O2 , 0.00004. This gas was used without further purification. The CH2 FCF3 was supplied by I.C.I. Japan Ltd and was specified as having a mole fraction q0.997, with a mole fraction of H2OQ0.00005. It was used without further purification. Second virial coefficients for CH2 FCF3 were reported by Tillner-Roth and Baehr(3) in the form: B/(cm3·mol−1 )=120.32T R0.25−376.3T R1.75−0.14126·exp(4.7539TR ).
(6)
The values used are listed in table 2. Goodwin and Haynes(4) critically reviewed the measurements of second virial coefficients of C3 H8 and produced the fitting equation: BR=0.4784915−1.2300138/TR−0.4680172/T R3 ,
(7)
1049
Virial coefficients of (0.500CH2 FCF3+0.500C3 H8 )
where TR=T/(369.85 K) and B/(cm3·mol−1 )=BR /5·10−3 .
(8)
The values obtained and used to generate the B12 values are listed in table 2. The Tsonopoulos(5) extension of the Pitzer and Curl(6) correlation has been shown effectively to represent second-virial-coefficient behaviour of a wide range of compounds and mixtures. The correlation has the form: Bpc /RTc=f (0)(TR )+v·f (1)(TR )+f (2)(TR ),
(9)
where TR is T/Tc and the functional forms of f (0) and f (1) have been reproduced often.(7) We were unable to find a reported value of the acentric factor v for 1,1,1,2-tetrafluoroethane but vapour-pressure measurements are available and so it can be derived using the relation: v=−lg{pRsat(TR=0.7)}−1,
(10)
The reported(8) critical temperature and critical pressure are Tc=374.18 K and pc=4056 kPa. The temperature for which TR=0.7 is T=261.93 K and at that temperature the vapour pressure reported is 192.07 kPa. Use of the equation above gives v=0.325. The function f (2)(TR ) has the simple form: f (2)(TR )=aR /TR6 ,
(11)
where aR is a function of reduced dipole moment pR defined by Tsonopoulos as pR=1.7132·1013·{p/(C·m)}2(pc /Pa)/(kTc /J)2
(12)
Tsonopoulos(9) determined values for a number of alkyl halides by fitting the second virial coefficients and found that a simple relation appears to exist between pR and a. The dipole moment of 1,1,1,2-tetrafluoroethane has been measured by Meyer
B11/(cm3 · mol–1)
–350 –400 –450 –500
290
300
310
320
330
340
T/K FIGURE 1. Second virial coefficient B11 of CH2 FCF3 . W, Tillner-Roth and Baehr;(3) ——, Tsonopoulos relation.(5)
1050
P. J. McElroy
and Morrison(10) to be p=6.865·10−30 C·m which gives pR=122.6. We would expect then that the aR value for 1,1,1,2-tetrafluoroethane would lie between those of CH3Cl with pR=143.2 corresponding to aR=−0.00903 and C2 H5Cl with pR=102.1 corresponding to aR=−0.006595. For CF3CH2 F then we adopted an aR value of −0.0075. The Tsonopoulos equation prediction of the second virial coefficient using the values of v, p, and aR as described, is plotted in figure 1 along with the experimental measurements of Tillner-Roth and Baehr.(3) As is evident from the plot, the agreement is very good.
3. Results and discussion The excess second virial coefficient o and the measured pressures and temperatures are presented in table 1. From the plot in figure 2 it is apparent that o is a smoothly varying function of temperature. The values of do/dT were read from the plot and used to estimate HmE at an average pressure of 64 kPa, which is also reported in table 1. Values of the unlike-interaction virial coefficient B12 determined from o and the pure-component B values discussed in the previous section are also listed in table 2. The B12 values are also plotted in figure 3. The Tsonopoulos modification of the Pitzer and Curl equation often provides a good representation of B12 behaviour. Combining rules are required and those commonly adopted are 1/3 1/3 3 pc,12=4Tc,12{(pc,1Vc,1 /Tc,1 )+(pc,2Vc,2 /Tc,2 )}/(Vc,1 +Vc,2 ),
(13)
v12=12 (v1+v2 ),
(14)
Tc,12=(Tc,1Tc,2 )1/2·(1−k12 ),
(15)
and aR,12=0 if either aR,1 or aR,2 is zero. For this mixture aR of C3 H8 is zero and so aR,12 is also. The value of k12 can sometimes be estimated from other properties of the mixture but in this case no suitable information is available and so we have simply used k12 as a parameter. The Tsonopoulos equation applied to the mixture and
TABLE 1. Experimental results for (0.500CH2 FCF3+0.500C3 H8 ) T K
p kPa
Dp Pa
o cm3·mol−1
HmE (p=64 kPa) J·mol−1
299.93 299.93 313.15 313.15 328.15 328.15 343.15 343.15
61.6646 60.8560 63.5735 65.4763 63.0047 62.9934 69.6364 69.3344
95.17 92.39 85.66 90.20 70.11 70.66 72.82 72.18
124.621.5 124.221.5 110.221.5 109.421.5 96.321.5 97.021.5 85.621.5 85.621.5
15.222 12.522 11.322 10.222
1051
Virial coefficients of (0.500CH2 FCF3+0.500C3 H8 )
130
ε/(cm3 · mol–1)
120
110
100
90
80 300
315
330
345
T/K FIGURE 2. Excess second virial coefficient for (0.500CH2 FCF3+0.500C3 H8 ). e, This work; ——, best-fit line.
using k12=0.1 is plotted in figure 3 and evidently provides an excellent representation of the measured B12 values. As documented by Dantzler et al.(11) 12 (fluorocarbon+hydrocarbon) mixtures with two or more carbon atoms all give k12 values in the range 0.09 to 0.11 and so this result is consistent with their work. Morrison and McLinden(12) also determined a k12 value for this system by fitting an equation of state to (liquid+vapour) equilibria and also found that k12=0.1 gave a best fit. TABLE 2. Selected second virial coefficients B for CH2 FCF3 and C3 H8 and measured values of B12 for CH2 FCF3 —C3 H8 T K
B(C2 F4 H2 ) cm3·mol−1
B(C3 H8 ) cm3·mol−1
B12 cm3·mol−1
299.93 299.93 313.15 313.15 328.13 328.15 343.15 343.15
−480.2 −480.2 −429.5 −429.5 −381.1 −381.1 −340.1 −340.1
−385.9 −385.9 −350.9 −350.9 −317.0 −317.0 −287.7 −287.7
−308.425 −308.825 −280.025 −280.825 −252.825 −252.125 −228.325 −228.325
1052
P. J. McElroy
–210
B12/(cm3 · mol–1)
–230
–250
–270
–290
–310
–330
300
310
320 T/K
330
340
FIGURE 3. Unlike-interaction second virial coefficient for CH2 FCF3 —C3 H8 . e, This work; ——, Tsonopoulos equation(5) with k12=0.1.
The assistance of Mr S. Buchanan in making the measurements and a grant from the New Zealand Lotteries Board for equipment purchase is acknowledged with gratitude.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Wormald, C. J. J. Chem. Thermodynamics 1977, 9, 901. McElroy, P. J.; Battino, R.; Dowd, M. K. J. Chem. Thermodynamics 1990, 22, 505. Tillner-Roth, R.; Baehr, H. D. J. Chem. Thermodynamics 1992, 24, 413. Goodwin, R. D.; Haynes, W. M. N.B.S. monograph No. 170 . 1982. Tsonopoulos, C. A.I.Ch.E.J. 1974, 20, 263. Pitzer, K. S.; Curl, R. F., Jr. J. Am. Chem. Soc. 1957, 79, 2369. McElroy, P. J.; Ji, F.; Ababio, B. D. J. Chem. Eng. Data 1993, 38, 410. McLinden, M. O.; Gallagher, J. S.; Weber, L. A.; Morrison, G.; Ward, D.; Goodwin, A. R. H.; Moldover, M. R.; Schmidt, J. W.; Chae, H. B.; Bruno, T. J.; Ely, J. F.; Huber, M. L. ASHRAE Trans. 1989, 95, Pt. 2, 263. Tsonopoulos, C. A.I.Ch.E.J. 1975, 21, 827. Meyer, C. W.; Morrison, G. J. Phys. Chem. 1991, 95, 3860. Dantzler, E. M.; Siebert, E.; Knobler, C. M. J. Phys. Chem. 1971, 75, 3863. Morrison, G.; McLinden, M. O. Int. J. Refrig. 1993, 16, 129.
Excess and unlike-interaction second virial coefficients and excess molar enthalpy of a refrigerant mixture: (0.500CH2 FCF3+0.500C3 H8 ) Peter J. McElroy Department of Chemical and Process Engineering, University of Canterbury, Christchurch, New Zealand
(Received 22 August 1994; in final form 10 April 1995) The excess second virial coefficient for (1,1,1,2-tetrafluoroethane + propane) has been measured at temperatures of 299.5 K, 313.15 K, 328.15 K, and 343.15 K, using the pressure-change-on-mixing method. The excess enthalpy and unlike-interaction second virial coefficients are also reported. The results have been correlated using the Tsonopoulos equation for virial coefficients. 7 1995 Academic Press Limited
1. Introduction The phasing out of chlorofluorocarbon refrigerant fluids has resulted in a demand for replacement, only some of which has been met by hydrofluorocarbons such as 1,1,1,2-tetrafluoroethane. To provide a broad spectrum of replacement fluids, mixtures have been proposed and design of refrigeration systems with small volumetric hold-up has meant that non-azeotropic mixtures might be acceptable. One proposed mixture is (1,1,1,2-tetrafluoroethane + propane + difluoromethane) and so (p,Vm ,T ) properties are required for that mixture. This work addresses the gas-phase (p,Vm ,T ) behaviour of two of the components. Further studies are in progress. The excess second virial coefficient of a mixture can be determined from the pressure change on mixing the pure components, initially at equal pressure, using the relation: o=RTDp/{p 2(1+Dp/p)2y(1−y)}.
(1)
The excess second virial coefficient o relates to the coefficients Bij as o=B12−(B11+B22 )/2,
(2)
and so the unlike-interaction second virial coefficient B12 can be estimated if B11 and B22 are known. Wormald(1) has shown that for the volume-series virial equation: pVm=RT(1+B/Vm+C/V m2 +· · · ·), 0021–9614/95/091047+06 $12.00/0
(3)
7 1995 Academic Press Limited
1048
P. J. McElroy
the excess molar enthalpy HmE of a two-component mixture is given by HmE =y(1−y)p(2f12−f11−f22 )−(p 2/RT ){Bf−(1−y)B11 f11−yB22 f22 }+ (p 2/RT ){c−(1−y)c111−yc222 },
(4)
where f=B−T·dB/dT and c=C−12 T·dC/dT. The third term containing third virial coefficients C will be smaller than the second term containing B values with a p 2 multiplier and calculations for this mixture show that the magnitude of the second term is similar to that of the uncertainty in HmE . In addition the coefficients to evaluate the third term in equation (4) are not available and so it has not been included in the calculation. We have measured o at four different temperatures and so equation (4) can be used to obtain an estimate of HmE . In the work reported here y=0.500 and for this case it can be shown that f=12 (o−T·do/dT )+12 f11+12 f22 ,
(5)
which is convenient for evaluation of HmE from equation (4).
2. Experimental The apparatus and procedures have been described previously(2) and were unchanged for this work. Equal volumes of the two gases were mixed using a reciprocating circulating pump. The rise in pressure could be followed and circulation was maintained for at least twice the time needed for the rise in pressure to cease. Total pressure was measured on a 100 kPa full-scale Digiquartz model 1015 A-O1 pressure gauge with a claimed accuracy of 0.01 kPa, and pressure change on mixing was measured with an M.K.S. Baratron model 315 BD (270B) diaphragm gauge with a full-scale reading of 133 Pa and a claimed accuracy of 0.33 Pa. Temperature was measured using a platinum resistance thermometer and bridge to within 20.005 K. Temperatures follow the ITS-90. The propane was ‘‘Chemically Pure’’ supplied by New Zealand Industrial Gases and specified as having a mole fraction e0.9997 of C3 H8 with the greatest mole fractions of major impurities as follows: C3 H6 , 0.00013; C2 H6 , 0.00005; N2 , 0.00003; O2 , 0.00004. This gas was used without further purification. The CH2 FCF3 was supplied by I.C.I. Japan Ltd and was specified as having a mole fraction q0.997, with a mole fraction of H2OQ0.00005. It was used without further purification. Second virial coefficients for CH2 FCF3 were reported by Tillner-Roth and Baehr(3) in the form: B/(cm3·mol−1 )=120.32T R0.25−376.3T R1.75−0.14126·exp(4.7539TR ).
(6)
The values used are listed in table 2. Goodwin and Haynes(4) critically reviewed the measurements of second virial coefficients of C3 H8 and produced the fitting equation: BR=0.4784915−1.2300138/TR−0.4680172/T R3 ,
(7)
1049
Virial coefficients of (0.500CH2 FCF3+0.500C3 H8 )
where TR=T/(369.85 K) and B/(cm3·mol−1 )=BR /5·10−3 .
(8)
The values obtained and used to generate the B12 values are listed in table 2. The Tsonopoulos(5) extension of the Pitzer and Curl(6) correlation has been shown effectively to represent second-virial-coefficient behaviour of a wide range of compounds and mixtures. The correlation has the form: Bpc /RTc=f (0)(TR )+v·f (1)(TR )+f (2)(TR ),
(9)
where TR is T/Tc and the functional forms of f (0) and f (1) have been reproduced often.(7) We were unable to find a reported value of the acentric factor v for 1,1,1,2-tetrafluoroethane but vapour-pressure measurements are available and so it can be derived using the relation: v=−lg{pRsat(TR=0.7)}−1,
(10)
The reported(8) critical temperature and critical pressure are Tc=374.18 K and pc=4056 kPa. The temperature for which TR=0.7 is T=261.93 K and at that temperature the vapour pressure reported is 192.07 kPa. Use of the equation above gives v=0.325. The function f (2)(TR ) has the simple form: f (2)(TR )=aR /TR6 ,
(11)
where aR is a function of reduced dipole moment pR defined by Tsonopoulos as pR=1.7132·1013·{p/(C·m)}2(pc /Pa)/(kTc /J)2
(12)
Tsonopoulos(9) determined values for a number of alkyl halides by fitting the second virial coefficients and found that a simple relation appears to exist between pR and a. The dipole moment of 1,1,1,2-tetrafluoroethane has been measured by Meyer
B11/(cm3 · mol–1)
–350 –400 –450 –500
290
300
310
320
330
340
T/K FIGURE 1. Second virial coefficient B11 of CH2 FCF3 . W, Tillner-Roth and Baehr;(3) ——, Tsonopoulos relation.(5)
1050
P. J. McElroy
and Morrison(10) to be p=6.865·10−30 C·m which gives pR=122.6. We would expect then that the aR value for 1,1,1,2-tetrafluoroethane would lie between those of CH3Cl with pR=143.2 corresponding to aR=−0.00903 and C2 H5Cl with pR=102.1 corresponding to aR=−0.006595. For CF3CH2 F then we adopted an aR value of −0.0075. The Tsonopoulos equation prediction of the second virial coefficient using the values of v, p, and aR as described, is plotted in figure 1 along with the experimental measurements of Tillner-Roth and Baehr.(3) As is evident from the plot, the agreement is very good.
3. Results and discussion The excess second virial coefficient o and the measured pressures and temperatures are presented in table 1. From the plot in figure 2 it is apparent that o is a smoothly varying function of temperature. The values of do/dT were read from the plot and used to estimate HmE at an average pressure of 64 kPa, which is also reported in table 1. Values of the unlike-interaction virial coefficient B12 determined from o and the pure-component B values discussed in the previous section are also listed in table 2. The B12 values are also plotted in figure 3. The Tsonopoulos modification of the Pitzer and Curl equation often provides a good representation of B12 behaviour. Combining rules are required and those commonly adopted are 1/3 1/3 3 pc,12=4Tc,12{(pc,1Vc,1 /Tc,1 )+(pc,2Vc,2 /Tc,2 )}/(Vc,1 +Vc,2 ),
(13)
v12=12 (v1+v2 ),
(14)
Tc,12=(Tc,1Tc,2 )1/2·(1−k12 ),
(15)
and aR,12=0 if either aR,1 or aR,2 is zero. For this mixture aR of C3 H8 is zero and so aR,12 is also. The value of k12 can sometimes be estimated from other properties of the mixture but in this case no suitable information is available and so we have simply used k12 as a parameter. The Tsonopoulos equation applied to the mixture and
TABLE 1. Experimental results for (0.500CH2 FCF3+0.500C3 H8 ) T K
p kPa
Dp Pa
o cm3·mol−1
HmE (p=64 kPa) J·mol−1
299.93 299.93 313.15 313.15 328.15 328.15 343.15 343.15
61.6646 60.8560 63.5735 65.4763 63.0047 62.9934 69.6364 69.3344
95.17 92.39 85.66 90.20 70.11 70.66 72.82 72.18
124.621.5 124.221.5 110.221.5 109.421.5 96.321.5 97.021.5 85.621.5 85.621.5
15.222 12.522 11.322 10.222
1051
Virial coefficients of (0.500CH2 FCF3+0.500C3 H8 )
130
ε/(cm3 · mol–1)
120
110
100
90
80 300
315
330
345
T/K FIGURE 2. Excess second virial coefficient for (0.500CH2 FCF3+0.500C3 H8 ). e, This work; ——, best-fit line.
using k12=0.1 is plotted in figure 3 and evidently provides an excellent representation of the measured B12 values. As documented by Dantzler et al.(11) 12 (fluorocarbon+hydrocarbon) mixtures with two or more carbon atoms all give k12 values in the range 0.09 to 0.11 and so this result is consistent with their work. Morrison and McLinden(12) also determined a k12 value for this system by fitting an equation of state to (liquid+vapour) equilibria and also found that k12=0.1 gave a best fit. TABLE 2. Selected second virial coefficients B for CH2 FCF3 and C3 H8 and measured values of B12 for CH2 FCF3 —C3 H8 T K
B(C2 F4 H2 ) cm3·mol−1
B(C3 H8 ) cm3·mol−1
B12 cm3·mol−1
299.93 299.93 313.15 313.15 328.13 328.15 343.15 343.15
−480.2 −480.2 −429.5 −429.5 −381.1 −381.1 −340.1 −340.1
−385.9 −385.9 −350.9 −350.9 −317.0 −317.0 −287.7 −287.7
−308.425 −308.825 −280.025 −280.825 −252.825 −252.125 −228.325 −228.325
1052
P. J. McElroy
–210
B12/(cm3 · mol–1)
–230
–250
–270
–290
–310
–330
300
310
320 T/K
330
340
FIGURE 3. Unlike-interaction second virial coefficient for CH2 FCF3 —C3 H8 . e, This work; ——, Tsonopoulos equation(5) with k12=0.1.
The assistance of Mr S. Buchanan in making the measurements and a grant from the New Zealand Lotteries Board for equipment purchase is acknowledged with gratitude.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Wormald, C. J. J. Chem. Thermodynamics 1977, 9, 901. McElroy, P. J.; Battino, R.; Dowd, M. K. J. Chem. Thermodynamics 1990, 22, 505. Tillner-Roth, R.; Baehr, H. D. J. Chem. Thermodynamics 1992, 24, 413. Goodwin, R. D.; Haynes, W. M. N.B.S. monograph No. 170 . 1982. Tsonopoulos, C. A.I.Ch.E.J. 1974, 20, 263. Pitzer, K. S.; Curl, R. F., Jr. J. Am. Chem. Soc. 1957, 79, 2369. McElroy, P. J.; Ji, F.; Ababio, B. D. J. Chem. Eng. Data 1993, 38, 410. McLinden, M. O.; Gallagher, J. S.; Weber, L. A.; Morrison, G.; Ward, D.; Goodwin, A. R. H.; Moldover, M. R.; Schmidt, J. W.; Chae, H. B.; Bruno, T. J.; Ely, J. F.; Huber, M. L. ASHRAE Trans. 1989, 95, Pt. 2, 263. Tsonopoulos, C. A.I.Ch.E.J. 1975, 21, 827. Meyer, C. W.; Morrison, G. J. Phys. Chem. 1991, 95, 3860. Dantzler, E. M.; Siebert, E.; Knobler, C. M. J. Phys. Chem. 1971, 75, 3863. Morrison, G.; McLinden, M. O. Int. J. Refrig. 1993, 16, 129.