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Excess second virial coefficients for (benzene + n-hexane) and (cyclohexane + n-hexane)
M-1404 J. Chem. Thermodynamics 1983, 15, 83188
Excess sec@nd virial coefficients for (benzene + n-hexane) and (cyclohexane + n-hexane) R. BATTINO,” R. MALHOTRA, A. G. WILLIAMSON
P. J. MCELROY, and
Department of Chemical Engineering, Christchurch, New Zeuland
University of Canterbury,
(Received 5 January 1982; in revised form 6 July 1982) For (benzene + n-hexane) and (cyclohexane + n-hexane) measurements are reported of the pressure change on mixing and the excess second virial coefficient .si2 calculated therefrom. Measurements at the following temperatures are reported: 298.15, 323.15, 373.15, and 398.15 K. The correlations due to Tsonopoulos and to Hayden and O’Connell are typically in error by 50 cm3. mol-’ or more; further development of the latter correlation appears justified.
1. Introduction Knowledge of the (p, V, 7) behaviour of gases and gas mixtures is essential for accurate gas-phase engineering calculations and for liquid-vapour equilibrium studies. For moderate to low pressures the virial equation of state is widely used, partly because the coefficients are simply related to intermolecular energies but principally because pure-component second virial coefficients Bii have been measured for many substances.“) While second virial coefficients B(y) have been measured for a considerable number of mixtures, and composition dependence is simply accounted for by the expression : WY) = (1 -YY~11+2Y(I
-YPl,+YZ~,,?
(1)
where y denotes the mole fraction .of component 2, it is quite inconceivable that all possible mixtures be studied. Accurate studies on a range of mixtures are required so that reliable combining rules for predicting the behaviour of any mixture may be established. The pressure change Ap on mixing two gases at constant total volume and temperature, and initially both at the same pressure p, is given by@) RTAP/WU
+AP/PPYU
-Y,>
= &z-(&1
+B,,)P
= ~12,
(2)
and since it is possible to measure srZ with greater accuracy than B, r or B,,, B,, can be estimated with an uncertainty little greater than 6B. o Department of Chemistry, Wright Smte University, Dayton, Ohio 45435, U.S.A. 0021-9614/83/010083 +06 %02.00/0
0 1983 Academic Press Inc. (London) Limited
84
R. BATTINO
ET .4/L
In liquid-vapour equilibrium studies the fugacity coefficients $i and 42 in the gas phase are required. The expressions for @i and 4Z are (RT/p)ln 4, = B,, +2y2q2,
(RT/p)ln d1 = B,,+2(1
2. Experimental
-y)‘~,,.
uncertainties
The major source of error in the measurement of srZ is the uncertainty measured Ap. An error analysis’3’ of the method indicates 6t: 12 z
~~~6~ipJAp
(3)
z2RT8Ap/p2.
in the (4)
At low temperatures errors are greatest since p must always be less than about 70 per cent of saturation to ensure that the possible extent of adsorption is acceptable. In previous work (3’ the possible effect of adsorption was considered and the results were corrected for it. Assuming a B.E.T. isothermt4’ and using the same parameters as previously, resulted in negligible corrections in this work except at the lowest temperature: 298.15 K. At this temperature, however. no reduction in the spread of measured values resulted. Consequently, in the absence of experimentally determined adsorption parameters, no correction has been attempted. 3. Pure-component
B values
CYCLOHEXANE
Measurements on cyclohexane up to 1980 were reviewed by McElroy rt ~11.~~) While a number of studies have been carried out, a clear consensus is not apparent. However McGlashan and Potter’s equation :(5) B/1/, = 0.43 -0.886TR-'
-0.694TR-'
with n = 3.8 gives a good fit particularly The Tsonopoulos equation :(‘j)
-O.O375(n-
1 )TR-4’5,
(5)
to those results considered most accurate.
Bp,/RT, =f'"'(TR)+~f(l)(TR), fco)(TR) = 0.1445-0.33T;’ -0.1385T~2-0.0121T~3, f"'(T,)=0.073+0.46T,-1-0.097T,-3-0.0073T,-*,
(6)
(7) (8)
has been applied to cyclohexane previously’3’ and gives quite good agreement over the full range of temperatures studied although compared with equation (5) it gives values slightly too negative, particularly at low temperatures. Hayden and O’Connell’s correlation expressed the second virial coefficient as follows : Bij = (Bnonpolarhj+ (BFo,ar)ij + (BEetastabie)ij+ (BbD,und)ij+ (BZemicnOij* (9) Here F denotes relatively “free” molecules (weak physical forces), and D denotes relatively “bound” or dimerized molecules (“chemical forces”). The detailed equations are incorporated in the original paper”’ and are listed in clearer form by Prausnitz er al.@’ (note sign error in their equation A-4). The values of the parameters used in the equation as well as those used in equations (5) and (6) are listed in table 1.
EXCESS VIRIAL TABLE
COEFFICIENTS
85
1. Pararfleters used in equations (5), (6), and (9)”
Compound
UK
n-hexane cyclohexane benzene
507.4 553.4 562.1
p./MPa 2.969 4.073 4.898
Rdw
b
0.3812 0.3261 0.3004
0 Dipole moments and solvation parameters all zero. b Mean radius of gyration. BENZENE
Second-virial-coefficient measurements on benzene until 1978 were reviewed by Clarke et LI/.‘~’ The agreement amongst the more accurate measurements is such that the virial coefficient is well defined over a considerable temperature range. Equation (5) gives a best fit to the datac3) when n = 4.1. The Tsonopoulos and the Hayden and O’Connell equations are almost indistinguishable for benzene and give good agreement with experiment above about 400 K. Below 400 K calculated values are progressingly more negative until at 295 K they both appear to be almost 200 cm3 .mol-’ too negative. n-HEXANE
McGlashan and Potter(5’ reviewed the B measurements for the normal alkanes from propane to octane until 1961 and obtained excellent agreement between experiment and the correlation they proposed, equation (5). Recent measurements by Chun et aI. for n-hexane also confirmed this agreement. Couldwell et al.‘“’ also obtained B values for n-hexane which were in good agreement with those of McGlashan and Potter when interpreted in an identical manner. Couldwell et al., however, made measurements over a pressure range, extrapolated to zero pressure, and hence calculated second virial coefficients in the low-pressure limit which are consistently approximately 80 cm3 .mol-’ more negative. The Joule-Thomson coefficients of Al-Bizreh and Wormald Cl‘) have been used, assuming a functional form for B, to calculate B values”’ in the limit of zero pressure which are in agreement with McGlashan and Potter’s equation for n-hexane. There is disagreement then as to whether measurements which have not been extrapolated to zero pressure have nevertheless been made at sufficiently low pressures to ensure that a true B has been determined. This will be resolved only when further careful experimental work has been carried out and until then the correlations will be tested against the existing nonextrapolated results. Hayden and O’Connell’s equation gives excellent agreement with experiment. The Tsonopoulos equation while also good appears to be approximately 50 cm3. mol - ’ too negative over the temperature range 300 to 350 K. Since McGlashan and Potter’s equation with best-fit n values is in excellent agreement with the data for all three systems, in subsequent calculations of .sl 2, and of B12, we will assume that pure-component experimental results may be represented by this equation.
R. BATTINO
86
4. Experimental
ET
.4L.
apparatus
and procedure
The apparatus, which has been described previously,‘“’ was modified in a number of minor ways to facilitate ease of operation but the principle and procedure of operation were unchanged. The n-hexane and cyclohexane used were “analytical-reagent” grade supplied by May and Baker Ltd. The benzene, also “analytical-reagent”, was “thiophene-free”, supplied by Koch Light Ltd. All chemicals were dried over calcium sulphate, distilled in a 50 cm spinning-band (“Teflon”) column [Nester/Faust Manufacturing Corp model (S-1179)] with at least 150 theoretical plates. Before use all reagents were thoroughly degassed and then distilled directly into the apparatus.
5. Results The measured values of c, 2 for the two mixtures are set out in table 2. Deviations in measurements repeated at the same temperature are within the experimental error. The values at 298.15 K have greater errors due to the low p. Values of p/p<, where p, denotes vapour pressure, nevertheless are highest at low temperatures to reduce TABLE
2. Excess second
TlU kO.01
p:Pa * 10
P,
29X.15
764Y 8428 20450 22300 40770 43440 46590 40680 46560 57300 45190 48950 47170 51500
0.60 0.67 0.56 0.62 0.47 0.50 0.54 0.47 0.26 0.32 0.25 0.14 0.14 0.15
P
Benzene
323.15 348.15
373.15
398.15
Cyclohexane 298.15
323.15 348.15 373.15
398.15
9034 8679 9017 23950 21740 44440 47930 47180 45080 47840 44170 49400
0.69 0.66 0.69 0.66 0.60 0.52 0.56 0.27 0.26 0.27 0.14 0.15
wrial
coefficients
AP Pa rl-hexane 0.6~0.1 0.8~0.1 2.4+0.2 2.7io.2 6.4+0.5 x.3+0.5 7.4kO.5 5.6kO.5 6.5 kO.5 12.1 io.5 6.9 F 0.5 5.6kO.5 5.2kO.5 6.2kO.5
4x+x 59*7 3lF’ 39+2 22-t’ 26&Z 20*2 20&? 1X.6+1.5 22.8 f 1 .o ‘0.9 * I .5 15.5il.5 15.4+ 1.5 15.4+ 1.5
-1644 -163.1 -1326 - 1327 ~ 1094 1091 ~ I(r)6 - 1096 -917 -913 -Yl5 - 7x3 ~ 7x3 - 783
Z&7 - 12+7 -- 15+7 -7*2 -7&2 -4.7fl.5 -4.2k1.5 -4.2il.5 ~ 2.9 f 1.5 -4.0&1.5 -4.1*1.5 - 3. I & 1.5
- 1764 - 1780 - 1782 ~ 1428 ~ 142x -1177 -1177 -98Y -988 -9x9 - 846 - 845
+ rl-hexane 0.O-tO.l -0.2+0.1 -0.2+0.1 -0.7+0.2 -0.6+0.’ -1.6+0.5 ~1.7+0.5 -1.5io.5 - I .o* 0.5 -1.5kO.5 ~ 1.2kO.5 ~ 1. I * 0.5
EXCE$S
VIRIAL
87
COEFFICIENTS
errors from this source and as a result these values have a higher probability of interference due to adsorption. Equation (5) fitted to the flure-component measurements has been used in conjunction with firstly the Hayden and O’Connell correlation and secondly the Tsonopoulos correlation in producing the plots in figure 1. Similarly purecomponent values using equation (5) have been used in calculating the B,, values listed in table 2 and plotted in figure 2 along the predictions of the Tsonopoulos and Hayden-O’Connell correlations. 6. Discussion As illustrated in figure 1 neither predictive equation tested was at all adequate in reproducing the aI Z values measured for either mixture. However, the predictions are dependent on accurate Bii values and since the .s12values span only 75 cm3 .mol-’ this is a severe test. Conversely, the difficulty in predicting s12 emphasizes the advantage of direct s12 measurement when it is the quantity required in situations illustrated by equation (3). B,, prediction is probably a more realistic expectation of the correlations. Figure 2 illustrates that both equations predict B,, within about + 50 cm3 .mol-’ (better at high temperatures). For (n-hexane + benzene) the correlations are almost indistinguishable but for (cyclohexane + n-hexane) the Hayden-O’Connell
-i 3 g
30-
3 54
lo-
8
20,
CT
---
/ A
300
/
320
340
360
38:
400
T/K FIGURE 42: -, correlations
1. Excess second virial coef&ients. (n-Hexane + benzene): 0, experimental; correlations for Hayden and O’Connell ; - - -. Tsonopoulos. (n-Hexane + cyclohexane) : a, experimental ; for B, z : - - -, Hayden and O’Connell ; ~ -, Tsonopoulos.
R. BATTINO
88
ET .4/I.
-9OO-
/
-1900~ 300
1 320
340
360
380
400
7-/K FIGURE 2. Unlike-interaction second virial coefficient B, ?. t/t-Hexane + benzene): 0. experimental; . Hayden and O’Connell equation ; ~ -. Tsonopoulos equation. (rt-Hexane + cyclohexane): 0, experimental; - -, Hayden and O’Connell equation : -. Tsonopoulos equation.
correlation is significantly inferior probably due to inadequacies in a number arbitrary combining rules which need to be employed in predicting B, 2 values. The support of the U.S./New Zealand Cooperative INT-7906175) for R.B. is gratefully acknowledged.
Science Programme
(Grant
of
No.
REFERENCES I. Dymond, J. H.: Smtth. E. B. Tlte I irid/ Cwfficiwf.s o/ Pun, (;rr.\ra ~r)td Mizfwcs C‘larendon Press: Oxford. 1980. 2. Knobler. C. M. Rn. Sci. Ir~rum. 1%7. 38. 184. 3. McElroy. P. J.; Shannon, T. W.; Williamson. A. G. J. C/tent. Thrrnro~r~rrmric,~ 1980, I?. 371. 4. Brunauer. S.: Emmett, P. H.; Teller, E. .I. Am. C/rem. Sot. 1938, 60. 309. 5. McGlashan, M. L.; Potter, D. J. B. Proc. R. .SOC~.London .4 1%2, 267. 214. 6. Tsonopoulos. C. AIChE J. 1974, 20, 263. 7. Hayden, J. G.; O’Connell. J. P. Ind. Eng. Cbm. P~OW.V.V Dc.c. Der. 1975, I?. 22 I, 8. Prausnitz. J. M. ; Anderson, T. F.; Grens. E. A.; Eckert. C. PI. ; Hsieh. R. ; O’Connell, J. P. C,,rrtptdrrr Culcukrtion.s,fiw Mulri-con7ponc,nl Vupour-Liquid and Liquid Liquid Equilibriu. Prentice-Hall : New Jersey. 1980, p. 130. 9. Clarke, P. H.: Francis, P. G.; George, M.: Phutela, R. C.: Roberts, G. K. St. C. J. (‘het?t. Tharmmfy7m7ics 1979, I 1. 175. IO. Chun, S. W.; Kay. W. B.; Teja, A. S. .I. Chem. BIG. Lkrrtr 1981, 26. 300. I 1. Couldwell, C. M. ; O’Neill, S. P. ; Pandya. M. V. : Williamson, A. G. .4u,s/. J. C/nnt. 1978, 3 1. ‘3 I. 12. Al-Bizreh, N.; Wormald. C. J. J. Chm7. Thrrmodynamicy 1978, IO, 231.
Excess sec@nd virial coefficients for (benzene + n-hexane) and (cyclohexane + n-hexane) R. BATTINO,” R. MALHOTRA, A. G. WILLIAMSON
P. J. MCELROY, and
Department of Chemical Engineering, Christchurch, New Zeuland
University of Canterbury,
(Received 5 January 1982; in revised form 6 July 1982) For (benzene + n-hexane) and (cyclohexane + n-hexane) measurements are reported of the pressure change on mixing and the excess second virial coefficient .si2 calculated therefrom. Measurements at the following temperatures are reported: 298.15, 323.15, 373.15, and 398.15 K. The correlations due to Tsonopoulos and to Hayden and O’Connell are typically in error by 50 cm3. mol-’ or more; further development of the latter correlation appears justified.
1. Introduction Knowledge of the (p, V, 7) behaviour of gases and gas mixtures is essential for accurate gas-phase engineering calculations and for liquid-vapour equilibrium studies. For moderate to low pressures the virial equation of state is widely used, partly because the coefficients are simply related to intermolecular energies but principally because pure-component second virial coefficients Bii have been measured for many substances.“) While second virial coefficients B(y) have been measured for a considerable number of mixtures, and composition dependence is simply accounted for by the expression : WY) = (1 -YY~11+2Y(I
-YPl,+YZ~,,?
(1)
where y denotes the mole fraction .of component 2, it is quite inconceivable that all possible mixtures be studied. Accurate studies on a range of mixtures are required so that reliable combining rules for predicting the behaviour of any mixture may be established. The pressure change Ap on mixing two gases at constant total volume and temperature, and initially both at the same pressure p, is given by@) RTAP/WU
+AP/PPYU
-Y,>
= &z-(&1
+B,,)P
= ~12,
(2)
and since it is possible to measure srZ with greater accuracy than B, r or B,,, B,, can be estimated with an uncertainty little greater than 6B. o Department of Chemistry, Wright Smte University, Dayton, Ohio 45435, U.S.A. 0021-9614/83/010083 +06 %02.00/0
0 1983 Academic Press Inc. (London) Limited
84
R. BATTINO
ET .4/L
In liquid-vapour equilibrium studies the fugacity coefficients $i and 42 in the gas phase are required. The expressions for @i and 4Z are (RT/p)ln 4, = B,, +2y2q2,
(RT/p)ln d1 = B,,+2(1
2. Experimental
-y)‘~,,.
uncertainties
The major source of error in the measurement of srZ is the uncertainty measured Ap. An error analysis’3’ of the method indicates 6t: 12 z
~~~6~ipJAp
(3)
z2RT8Ap/p2.
in the (4)
At low temperatures errors are greatest since p must always be less than about 70 per cent of saturation to ensure that the possible extent of adsorption is acceptable. In previous work (3’ the possible effect of adsorption was considered and the results were corrected for it. Assuming a B.E.T. isothermt4’ and using the same parameters as previously, resulted in negligible corrections in this work except at the lowest temperature: 298.15 K. At this temperature, however. no reduction in the spread of measured values resulted. Consequently, in the absence of experimentally determined adsorption parameters, no correction has been attempted. 3. Pure-component
B values
CYCLOHEXANE
Measurements on cyclohexane up to 1980 were reviewed by McElroy rt ~11.~~) While a number of studies have been carried out, a clear consensus is not apparent. However McGlashan and Potter’s equation :(5) B/1/, = 0.43 -0.886TR-'
-0.694TR-'
with n = 3.8 gives a good fit particularly The Tsonopoulos equation :(‘j)
-O.O375(n-
1 )TR-4’5,
(5)
to those results considered most accurate.
Bp,/RT, =f'"'(TR)+~f(l)(TR), fco)(TR) = 0.1445-0.33T;’ -0.1385T~2-0.0121T~3, f"'(T,)=0.073+0.46T,-1-0.097T,-3-0.0073T,-*,
(6)
(7) (8)
has been applied to cyclohexane previously’3’ and gives quite good agreement over the full range of temperatures studied although compared with equation (5) it gives values slightly too negative, particularly at low temperatures. Hayden and O’Connell’s correlation expressed the second virial coefficient as follows : Bij = (Bnonpolarhj+ (BFo,ar)ij + (BEetastabie)ij+ (BbD,und)ij+ (BZemicnOij* (9) Here F denotes relatively “free” molecules (weak physical forces), and D denotes relatively “bound” or dimerized molecules (“chemical forces”). The detailed equations are incorporated in the original paper”’ and are listed in clearer form by Prausnitz er al.@’ (note sign error in their equation A-4). The values of the parameters used in the equation as well as those used in equations (5) and (6) are listed in table 1.
EXCESS VIRIAL TABLE
COEFFICIENTS
85
1. Pararfleters used in equations (5), (6), and (9)”
Compound
UK
n-hexane cyclohexane benzene
507.4 553.4 562.1
p./MPa 2.969 4.073 4.898
Rdw
b
0.3812 0.3261 0.3004
0 Dipole moments and solvation parameters all zero. b Mean radius of gyration. BENZENE
Second-virial-coefficient measurements on benzene until 1978 were reviewed by Clarke et LI/.‘~’ The agreement amongst the more accurate measurements is such that the virial coefficient is well defined over a considerable temperature range. Equation (5) gives a best fit to the datac3) when n = 4.1. The Tsonopoulos and the Hayden and O’Connell equations are almost indistinguishable for benzene and give good agreement with experiment above about 400 K. Below 400 K calculated values are progressingly more negative until at 295 K they both appear to be almost 200 cm3 .mol-’ too negative. n-HEXANE
McGlashan and Potter(5’ reviewed the B measurements for the normal alkanes from propane to octane until 1961 and obtained excellent agreement between experiment and the correlation they proposed, equation (5). Recent measurements by Chun et aI. for n-hexane also confirmed this agreement. Couldwell et al.‘“’ also obtained B values for n-hexane which were in good agreement with those of McGlashan and Potter when interpreted in an identical manner. Couldwell et al., however, made measurements over a pressure range, extrapolated to zero pressure, and hence calculated second virial coefficients in the low-pressure limit which are consistently approximately 80 cm3 .mol-’ more negative. The Joule-Thomson coefficients of Al-Bizreh and Wormald Cl‘) have been used, assuming a functional form for B, to calculate B values”’ in the limit of zero pressure which are in agreement with McGlashan and Potter’s equation for n-hexane. There is disagreement then as to whether measurements which have not been extrapolated to zero pressure have nevertheless been made at sufficiently low pressures to ensure that a true B has been determined. This will be resolved only when further careful experimental work has been carried out and until then the correlations will be tested against the existing nonextrapolated results. Hayden and O’Connell’s equation gives excellent agreement with experiment. The Tsonopoulos equation while also good appears to be approximately 50 cm3. mol - ’ too negative over the temperature range 300 to 350 K. Since McGlashan and Potter’s equation with best-fit n values is in excellent agreement with the data for all three systems, in subsequent calculations of .sl 2, and of B12, we will assume that pure-component experimental results may be represented by this equation.
R. BATTINO
86
4. Experimental
ET
.4L.
apparatus
and procedure
The apparatus, which has been described previously,‘“’ was modified in a number of minor ways to facilitate ease of operation but the principle and procedure of operation were unchanged. The n-hexane and cyclohexane used were “analytical-reagent” grade supplied by May and Baker Ltd. The benzene, also “analytical-reagent”, was “thiophene-free”, supplied by Koch Light Ltd. All chemicals were dried over calcium sulphate, distilled in a 50 cm spinning-band (“Teflon”) column [Nester/Faust Manufacturing Corp model (S-1179)] with at least 150 theoretical plates. Before use all reagents were thoroughly degassed and then distilled directly into the apparatus.
5. Results The measured values of c, 2 for the two mixtures are set out in table 2. Deviations in measurements repeated at the same temperature are within the experimental error. The values at 298.15 K have greater errors due to the low p. Values of p/p<, where p, denotes vapour pressure, nevertheless are highest at low temperatures to reduce TABLE
2. Excess second
TlU kO.01
p:Pa * 10
P,
29X.15
764Y 8428 20450 22300 40770 43440 46590 40680 46560 57300 45190 48950 47170 51500
0.60 0.67 0.56 0.62 0.47 0.50 0.54 0.47 0.26 0.32 0.25 0.14 0.14 0.15
P
Benzene
323.15 348.15
373.15
398.15
Cyclohexane 298.15
323.15 348.15 373.15
398.15
9034 8679 9017 23950 21740 44440 47930 47180 45080 47840 44170 49400
0.69 0.66 0.69 0.66 0.60 0.52 0.56 0.27 0.26 0.27 0.14 0.15
wrial
coefficients
AP Pa rl-hexane 0.6~0.1 0.8~0.1 2.4+0.2 2.7io.2 6.4+0.5 x.3+0.5 7.4kO.5 5.6kO.5 6.5 kO.5 12.1 io.5 6.9 F 0.5 5.6kO.5 5.2kO.5 6.2kO.5
4x+x 59*7 3lF’ 39+2 22-t’ 26&Z 20*2 20&? 1X.6+1.5 22.8 f 1 .o ‘0.9 * I .5 15.5il.5 15.4+ 1.5 15.4+ 1.5
-1644 -163.1 -1326 - 1327 ~ 1094 1091 ~ I(r)6 - 1096 -917 -913 -Yl5 - 7x3 ~ 7x3 - 783
Z&7 - 12+7 -- 15+7 -7*2 -7&2 -4.7fl.5 -4.2k1.5 -4.2il.5 ~ 2.9 f 1.5 -4.0&1.5 -4.1*1.5 - 3. I & 1.5
- 1764 - 1780 - 1782 ~ 1428 ~ 142x -1177 -1177 -98Y -988 -9x9 - 846 - 845
+ rl-hexane 0.O-tO.l -0.2+0.1 -0.2+0.1 -0.7+0.2 -0.6+0.’ -1.6+0.5 ~1.7+0.5 -1.5io.5 - I .o* 0.5 -1.5kO.5 ~ 1.2kO.5 ~ 1. I * 0.5
EXCE$S
VIRIAL
87
COEFFICIENTS
errors from this source and as a result these values have a higher probability of interference due to adsorption. Equation (5) fitted to the flure-component measurements has been used in conjunction with firstly the Hayden and O’Connell correlation and secondly the Tsonopoulos correlation in producing the plots in figure 1. Similarly purecomponent values using equation (5) have been used in calculating the B,, values listed in table 2 and plotted in figure 2 along the predictions of the Tsonopoulos and Hayden-O’Connell correlations. 6. Discussion As illustrated in figure 1 neither predictive equation tested was at all adequate in reproducing the aI Z values measured for either mixture. However, the predictions are dependent on accurate Bii values and since the .s12values span only 75 cm3 .mol-’ this is a severe test. Conversely, the difficulty in predicting s12 emphasizes the advantage of direct s12 measurement when it is the quantity required in situations illustrated by equation (3). B,, prediction is probably a more realistic expectation of the correlations. Figure 2 illustrates that both equations predict B,, within about + 50 cm3 .mol-’ (better at high temperatures). For (n-hexane + benzene) the correlations are almost indistinguishable but for (cyclohexane + n-hexane) the Hayden-O’Connell
-i 3 g
30-
3 54
lo-
8
20,
CT
---
/ A
300
/
320
340
360
38:
400
T/K FIGURE 42: -, correlations
1. Excess second virial coef&ients. (n-Hexane + benzene): 0, experimental; correlations for Hayden and O’Connell ; - - -. Tsonopoulos. (n-Hexane + cyclohexane) : a, experimental ; for B, z : - - -, Hayden and O’Connell ; ~ -, Tsonopoulos.
R. BATTINO
88
ET .4/I.
-9OO-
/
-1900~ 300
1 320
340
360
380
400
7-/K FIGURE 2. Unlike-interaction second virial coefficient B, ?. t/t-Hexane + benzene): 0. experimental; . Hayden and O’Connell equation ; ~ -. Tsonopoulos equation. (rt-Hexane + cyclohexane): 0, experimental; - -, Hayden and O’Connell equation : -. Tsonopoulos equation.
correlation is significantly inferior probably due to inadequacies in a number arbitrary combining rules which need to be employed in predicting B, 2 values. The support of the U.S./New Zealand Cooperative INT-7906175) for R.B. is gratefully acknowledged.
Science Programme
(Grant
of
No.
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