- Email: [email protected]
Critical-locus curves and liquid-vapor equilibria in the binary systems of benzene with carbon dioxide and sulfur dioxide
Fluid Phase Equilibria,
11 (1983) 25 l-265 Elsevier Science Publishers B.V.. Amsterdam
251 -
Printed in The Netherlands
CRITICAL-LOCUS CURVES AND LIQUID-VAPOR EQUILIBRIA IN THE BINARY SYSTEMS OF BENZENE WITH CARBON DIOXIDE AND SULFUR DIOXIDE WEBSTER B. KAY Department
of Chemical Engineering,
Ohio State University, Columbus, OH 43210 (U.S.A.)
ALEKSANDER
KREGLEWSKI
Thermodynamics
Research Center, Texas A & M Uniuersity, College Station, TX 77843 (U.S.A.)
(Received September
*
1, 1982; accepted in final form November
16, 1982)
ABSTRACT Kay, W.B. and Kreglewski, A., 1983. Critical-locus curves and liquid-vapor equilibria in the binary systems of benzene with carbon dioxide and sulfur dioxide. Fluid Phase Equilibria, 11: 251-265. Critical-locus curves F(x) and P”(x) have been determined for the carbon dioxide+ benzene and sulfur dioxide+ benzene systems. The data, together with existing liquid-vapor equilibrium data, are used to construct the complete phase diagrams at high pressures.
INTRODUCTION
Ohgaki and Katayama (1976) and Gupta et al. (1982) determined liquid-vapor equilibrium isotherms for the carbon dioxide + benzene system at 298.15 and 313.15 K, and the bubble points at 353.15 and 393.15 K. These data indicate positive deviations from an ideal system. This fact, however, does not exclude the possibility of specific interactions between the two components. Bowden et al. (1966) determined the liquid-vapor isotherm and the excess chemical potentials py and GE for the sulfur dioxide + benzene system at 255.37 K. The system exhibits small positive deviations from an ideal system. Lorimer et al. (1975) determined ~7 and GE for mixtures of sulfur dioxide with toluene, m-xylene and mesitylene at and below 250 K, and found small negative deviations, increasing with the number of methyl
* Author to whom correspondence 0378-3812/83/$03.00
should be addressed.
0 1983 Elsevier Science Publishers B.V.
252
groups. Thus, specific interactions between SO, and aromatic compounds appear to be weakest in the case of benzene. As reviewed by the above authors, all the systems form complexes in the solid state. We have determined the critical-locus curves T’(x) and P”(x) in order to gain more information about the behavior of these systems at high temperatures, and have correlated the results with the above liquid-vapor equilibrium data. EXPERIMENTAL
Apparatus P-T-x relationships along the critical-locus curves for the two binary systems were obtained by determining the critical temperatures and pressures of a series of mixtures of known composition ranging from one pure component to the other. The apparatus and procedure used have been described by Barber et al. (1982) and in references cited therein to earlier papers by Kay and co-workers. Briefly, a small air-free sample of binary mixture is confined over mercury in a thick-walled glass tube surrounded by a constant-temperature jacket. The temperature is maintained constant by the condensing vapor of a series of pure organic liquids heated at constant and controlled pressure in a side-arm flask attached to the jacket. The experimental tube is held rigidly in a mercury-filled compressor block, with means provided for controlling and measuring the pressure of the sample. The volume of the sample and its variation with pressure and temperature are not measured. To bring about equilibrium quickly, the sample is stirred by means of a steel ball inserted in the tube prior to loading the sample. The ball is moved rapidly through the sample by a magnet moving around the outside of the constant-temperature jacket. The temperature of the vapor jacket surrounding the experimental tube was measured to within +O.Ol K using a platinum resistance thermometer calibrated at the National Bureau of Standards. Pressures along the saturated liquid and vapor curves and at the critical point were measured using a precision spring gauge with a 40-cm dial. This gauge covered a range from 0 to 138 bar in 0.345 bar intervals. Both the dead-weight gauge and the spring gauge were compared with a standard dead-weight gauge. Sources and purity of materials and preparation
of mixtures
Benzene (Phillips Petroleum Company; purity 99.91 mol %), carbon dioxide and sulfur dioxide (purity 99.98 mol 76) were each liquefied in a vacuum train with liquid nitrogen as the refrigerant and brought into contact
253
with freshly activated molecular sieve to remove possible traces of moisture, and then deaerated by a cycle of operations consisting of pumping off non-condensable gases over the solid (at liquid-nitrogen temperature), melting and transferring by distillation to a second vessel, freezing and then pumping off the residual gas. The products were stored in sealed glass ampoules until ready to use, each ampoule containing slightly more than the required quantity of vapor for one loading of the experimental tube. Degassing of liquid benzene An 8 ml sample of benzene was percolated over activated silica gel to remove any possible traces of moisture and was then charged through a rubber septum, by means of a hypodermic syringe, to the degassing apparatus, where air and other non-condensable gases were removed. The degassing operation was quite simple. The sample in the flask below the degasser was warmed and the vapor condensed and frozen on a cold-finger cooled with liquid nitrogen, while non-condensable gases were pumped off. When all of the sample was frozen on the cold finger, the liquid nitrogen was removed and the solid benzene melted and collected in the flask below. It was then transferred by distillation to a storage flask where it was kept refrigerated until used. Preparation of mixtures In the preparation of a binary mixture of known composition containing benzene and carbon dioxide or benzene and sulfur dioxide, a quantity of benzene was transferred by distillation from the storage flask to a small capillary tube whose total volume per unit length had been determined previously. From the length of the tube occupied by the sample at 273.15 K (measured using a cathetometer reading to 0.05 mm) and the density of the liquid at 273.15 K, the weight of the sample was calculated. A correction was made for the weight of the vapor over the liquid using the perfect gas law and knowledge of the vapor pressure. The measured sample was then transferred by distillation to the experimental tube and frozen in the tip by surrounding the end of the tube with a bath of liquid nitrogen. With the mixture frozen, mercury was then added until the tube was filled (Kay and Donham, 1955). The tube was then transferred to the compressor block and a measured volume of either CO, or SO, gas at a known temperature and pressure injected into the tube by means of a gas microburette. The gas microburette consisted essentially of a calibrated section of precision glass capillary connected to a stainless-steel bellows and surrounded by a water jacket for temperature control (for details, see Kay and Rambosek, 1953). The calibrated section was 50 cm long and had a volume of 0.05365 cm3 per cm. An etched scale with lines at 0.1 cm intervals made it possible to
254
read gas volumes to within - 0.001 cm3. The sample mass and composition of the mixture were determined from the isothermal compressibility measurements. Results
Critical temperatures and pressures were determined for up to eight mixtures of known composition for each of the binary systems. This was done by locating first the approximate critical temperature, and then, starting a few degrees below, the P-T bubble-point curve was determined at small temperature intervals until the characteristic critical phenomena were observed. The experimental results are reported in Tables 1 and 2 and shown graphically in the figures. The absolute uncertainty of the results is estimated to be 0.1% for the composition, 0.05 K for T”, and 0.06 bar for PC. The calculated values given in the tables were obtained in a reverse manner: for the given (observed) T”, the mole fraction x1 of CO, or SO,, the critical pressure PC and the critical density pc were calculated by iteration from the equation of state as the TABLE 1 Critical-locus Observed
curve for the carbon dioxide (I)+benzene
values T’/(K)
P/(bar)
0.0000 0.0000 0.1142
562.16 a 562.21 550.30
48.98 a 48.97 64.19
0.1984 0.3485 0.4732 0.8108
540.38 518.28 491.49 430.00 393.15 375.04
76.12 99.97 123.0
0.8204 0.8492
361.57 357.45
0.9233 1.oooo
353.15 333.22 313.15 304.21 ’
128.9 121.0 -
134.1
99.70 73.825 ’
#/(mol
l- ‘)
3.86 a
(2) system Calculated
values b
x,
P/(bar)
0
48.98 -
-
#/(mol 3.9 -
0.215 0.355 0.475 0.665 0.750
78.6 100.6 123.2 147.5 143.2 -
4.30 5.03 6.15 8.87 10.9 -
-
0.830 -
129.8 -
11.7 -
-
0.870 0.925 0.980 1
118.6 100.6 81.0 73.83
12.0 (12.3) 10.6
-
10.6’
a Values selected by Ambrose and Townsend b Calculated at observed values of TC. 'Values selected by Angus et al. (1976).
(1975).
l- ‘)
255 TABLE 2 Critical-locus
curve for the sulfur dioxide (l)+benzene
Observed values
Calculated
Xl
TC,‘(K)
P”/(bar)
p’/(mol I-‘)
0.1143 0.2419 0.3835 0.5127 0.6628 0.8750 1.oOOo 1.oooo
552.87 540.3 1 523.69 508.99 488.59 455.51 430.8 a 430.1
55.76 63.94 72.61 78.04 82.53 82.66 78.84 a -
-
a,b See footnotes
(2) system
8.20 a
XI
-
values b P/(bar)
-
$/(mol
1-l)
-
0.250 0.400 0.515 0.655 0.850
64.0 72.6 78.0 82.5 83.0
4.17 4.67 5.05 5.57 6.75
1
78.8
8.20
to Table 1.
maximum point on the P(X) isotherm (proof that this point is the critical point has been given by Rowlinson (1969)). The P”(x) curve for the CO, + C,H, system appears to have a maximum at - 148 bar, although the experimental glass tube did not permit measurements above - 135 bar. For this reason, there is a gap in the measured values extending from x, = 0.5 to 0.8, and only the calculated values at 430 K are given. Additionally, the calculated critical locus for the three isotherms shown in Fig. 3 is reported in Table 1. Any differences between the observed and calculated values should be attributed to errors in the theory or the uncertainty of the calculated maximum points. CALCULATED
RESULTS
The mole fractions xi, xi and xi’ and the molar densities p, p’ and p” of the coexisting phases were obtained by iteration at the given T and P using Gibbs equilibrium conditions and the following relation for the chemical potential of component i of a mixture: p,/RT
= In xi + A’/RT +py’/RT
+ 2 - 1 + In p - c x, [a( A’/RT)/axj] j-i (k * i,j)
T,p,x, (1)
where 2 is the compressibility factor derived from the following relation for the residual Helmholtz energy (Chen and Kreglewski, 1977): A’/RT=
(a’-
1) In(1 -E)
+ [(a” + 3a)[ - 3at2]/(1
+ c ~%&%‘kT)“(~‘~p)~ n m
- 5)2 (2)
where (Yis a constant depending on the shape of the molecules, 5 = 0.74048 V”p = rN,a3p/6, where Vn is the close-packed volume, which is a simple function of T (with one constant C, usually equal to - 0.12), N, is Avogadro’s number, u is the collision diameter, and p is the molar density of the system. D,,,,, are 24 universal constants obtained from P-V-T and internal-energy data for argon, and ii/k is a certain minimum value of the intermolecular energy, assumed for argon to be equal to the critical temperature, 150.86 K. The excess combinatorial potential pFc‘ may be calculated from the Flory-Huggins equation pyC/RT
= ln( &/x,)
+ 1 - r&/x,
(3)
in which $ = x~~~~/C~X~V~” (k = 1,. . . ); Voo is the value of V” at T = 0 K. The characteristic constants for the three pure components are given in Table 3. The values for sulfur dioxide and benzene reported previously have been revised to conform better with the saturation densities and the critical points. Equation (2) applies for mixtures with (Yassumed to be a linear function of xi and where V0 = c cx,x,y; i
(4)
j
where (5) The interaction energy ii/k for a mixture is assumed to be proportional to the surface fractions cp,= ~~(l/i~~)~~~/C~x,(~~~)*~~ and the surface interactions fir = Ui,/gf, etc., where g, = 1, g, = ( V~“/V/o)1’3, etc., so that
’ k
' i
(6)
i
TABLE 3 Characteristic
constants
of eqn. (2) ’
Component
01
VW/ (cm3 mol - ’ )
C
g/k/(K)
v/k/(K)
Carbon dioxide Sulfur dioxide Benzene
1.0571 1.0710 1.0613
19.703 25.346 54.289
0.12 0.12 0.12
284.28 383.56 529.24
40.0 88.0 72.0
a VW is the value of V” at T= 0 K. The relation V”(T) with one-constant by Chen and Kreglewski (1977).
C has been given
251
where c lJ
=
cp,[ 1 + TJiJ/kT + ( sij/kT)2]
Ey/= 2yiJ(l/4+
l/e;J’
Here yiJ, qij/k, cYij/k and usually, but not always, k,, are constants given system. For pure fluids, eqn. (6) becomes Ei/k = (U’,‘k)( 1 + q,‘kT)
(8) for a
(9)
because no attempts have been made to determine 6/k for pure fluids. As shown by Twu et al. (1976) and by Gubbins and Twu (1978), dipolar and quadrupolar forces greatly affect the phase diagrams of fluid mixtures. The Helmholtz energies A, and A, vary according to (/CT)-’ and ( kT)-2, respectively, in the case both of dipolar and of quadrupolar forces, and have slightly differing dependences on the reduced density 5 than A,, due to London forces. In the present treatment the relation for A’ is simplified, as it contains terms proportional to q/kT and (6/kT j2, whereas the dependence on < is the same as for argon (with the same values of the constants D,,). Moreover, Si, is an empirical parameter relative to Si, = Sjj = 0 for the pure components. For systems containing inert components, 77112: (Vii +
Vjj)/2
(10)
For systems with specific interactions, qij may be lower than the arithmetic mean value; however, we have found that it is best to evaluate qij/k using eqn. (10) and, initially keeping Sij/k = 0, to fit y,, (or E:/) to the critical-locus curve or other data at several temperatures. Most often, cpJ appears to be a linear function of Tw2. The slope and the limiting value at l/T* = 0 then yield yij and S;,/k. The choice of the weights gi in eqn. (6) has a strong effect on the value of yij but affects very little the shapes of the liquid-vapor isotherms or the critical curves. The assumption that g,: ( Koo)‘/3 is the simplest one, and in this case yij 2: 1 for systems containing inert components (Kreglewski and Kay, 1969). Kreglewski (1980) found that addition of the excess combinatorial term to A’/RT improves the agreement with critical densities for alkane + alkane systems. It appears to have a large effect on the liquid-vapor loops near the critical point, as shown in Fig. 1 for the nitrogen + ethane system. The values of yiJ, qij/k and S,,/k used to calculate the dashed and full curves were the same, but the dashed curves were obtained for pFc= 0 and kjj = 1.30, whereas the full curves result for kj, = 1.22 and ,uFc calculated
258
Fig. 1. Effect of combinatorial term prc on vapor-liquid equilibrium of N,( l)+C,H,(2) system at 172.04 K: circles, data of Stryjek et al. (1974); full curves, calculated with p:c from eqn. (3); dashed curves, calculated with nFc = 0.
using eqn. (3) *. For I*,EC= 0 the loop does not close at the observed critical point, and, in addition, k,, is too large and yields too low densities of the liquid phase. It should be pointed out that for the systems CH, + CO, and N, + CO, a similar, although smaller, correction of pi is required in order to close the loops at the observed critical points, but the combinatorial term does not help in these cases because of the similar molecular sizes of the components, On the other hand, the correction appears to be too large for the SO, + C,H, system. Therefore, it is possible that the correction term required in the critical region has nothing to do with ~7’. The carbon dioxide + benzene system The interaction parameters were fitted initially to both the critical-locus curve and the bubble points of the four isotherms. The final values of rji and si,/k were fitted to the 393.15 and 313.15 K isotherms, whereas kij was
* The graph in Fig. 1 was obtained using raw, initial values of the interaction parameters, and may be improved further. The tabulated results, including derived functions such as the residual potentials (fugacities of the components), enthalpies, etc., for the systems considered in this paper and several other systems will be published subsequently by the Thermodynamics Research Center.
259 TABLE 4 Binary interaction
parameters
System
Y‘J
v,,/k
&,/k
k,,
CO, + C,H,
0.827 0.967
56.0 80.0
130.0 51.5
0.533+1.15x10-3T-0.15x, 0.972 - 0.092 X,
SO, + C,H,
a
a X, is the mole fraction of CO, or SO,.
/
or I,
0
0.2
0.4
0.6
0.8
1.0 XI
Fig. 2. P’(x) curve for CO,(l)+C,H,(Z) system: circles. experimental data from this work; dashed line, calculated curve; full curves, liquid-vapor isotherms calculated at T = 540.38 K (I), 518.28 K (2) 491.49 K (3), 430.00 K (4), 367.57 K (5). and 333.22 K (6).
0 0
0.2
0.4
0.6
0.8
1.0
XI Fig. 3. Liquid-vapor isotherms for CO,(l)+C,H,(Z) system at T= 393.15 K (l), 353.15 K (2), 313.15 K (3), and 298.15 K (4): curves, calculated results (dashed line explained in text): open circles, experimental data of Gupta et al. (1982); filled circles, experimental data of Ohgaki and Katayama (1976).
fitted to the critical-locus curve. k,j appears to vary with both T and X, (Table 4). When kij is assumed to depend on T only, that is, is fitted to the critical point and kept constant along an isotherm, for example 393.15 K, the dashed curve in Fig. 3 is obtained. The empirical relation for ki, is reported in Table 4. This relation affects aV”/i3x, and a2Yo/a~,2 significantly but the effect on aV”/3T and the enthalpy is small and we have neglected it. The relation for kii may be regarded as a simple correction of
261
0
0.2
0.4
0.6
0.8
1.0 xl
Fig. 4. Calculated densities of saturated liquid and vapor for CO,(l)+C,H,(2) system at T = 298.15 IS (I), 353.15 K (2), 430.00 K (3), 491.49 K (4). and 540.38 K (5): dashed line, p”(x); circles, selected experimental data for pure components.
$_ 50 a
01
0
0.2
0.4
0.6
0.8
1.0
Xl Fig. 5. P”(r) curve for SO,(l)+C,H,(Z) system: circles, experimental data from this work; dashed line, calculated curve; full curves, liquid-vapor isotherms calculated at T = 540.31 K (l), 508.99 K (2), 455.51 K (3), and 420.00 K (4).
262 15-
0.2
0
0.4
0.8
0.6
1.0 XI
Fig. 6. Calculated densities of saturated liquid and vapor for SO,(l)+C,H,(2) values of T, see Fig. 5): dashed line, p’(x)
system (for
\ \ \
300 0
0.2
0.4
0.6
0.6
Fig. 7. P(x) curves for CO,(I)+qH,(2) and SO,(I)+C,H,(2) from this work and calculated curves (dashed).
systems: experimental data
263
deviations from the random-mixing approximation. This treatment is not sufficiently accurate and causes some deviations from the observed critical points, particularly points 1 and 5 in Fig. 2. The sulfur dioxide + benzene system The liquid-vapor equilibrium data of Bowden et al. (1966) at 255.37 K are below the range of validity of the equation of state for this system. Therefore, a simplified equation with one D,, constant (D,r) was used to estimate epJ at this temperature. The values of y,], S,,/k and ki, were then estimated from the critical-,locus curve. Only a weak dependence of ki, on X, was detected. For X, > 0.6 the calculated critical compositions are too small, so that T” calculated for a given x1 are slightly lower than the observed values for SO,-rich mixtures (Fig. 7). The proper value of vi/k for this system should be lower than the arithmetic mean, because of the polarity of SO,. The resulting positive deviations from an ideal system would be compensated by a larger value of 6,/k. The experimental data are insufficient to estimate all three constants of eqn. (7) and one of them had to be fixed. DISCUSSION
According to the theory of Gubbins and co-workers and as suggested earlier by Rowlinson (1969), negative deviations from an ideal system may occur when the quadrupole moments Q of the components have opposite signs. Buckingham (1970) determined Q for CO, (- 4.3 X 1O-26 e.s.u. cm2) and Hanna (1968) for C,H, (- 14.5 x 1O-26 e.s.u. cm*). The sign of Q for SO, is not known, but it must be positive. Otherwise, electrostatic theory would not suffice to explain the behavior of SO, + aromatic systems. An analysis of ordering effects due to large differences in TC (or ii/k) of the components, as carried out by Rowlinson (1969) leads to complicated relations, and an empirical treatment is justified. The abnormal value of Sjj/k and the variation of kij with X, and T for the CO, + C,H, system are due partly to this effect. However, y;, for this system is very low and the deviations from an ideal system are positive at all temperatures, as expected on the basis of electrostatic theory. The positive deviations for the SO, + C,H, system should be even larger, because of the polarity of SO, and apparently weaker ordering effects. There must exist an opposing factor in this system, presumably due to quadrupole moments of opposite signs. The variation of kjj with x, and T for the above systems is unusual, because for other systems containing quadrupolar molecules and with large
264
ratios T,C/T,” for the components, kj j is approximately constant.
such as N, + C,H,,
N, + CO, or N, + H,S,
ACKNOWLEDGEMENT
Partial support (A.K.) is gratefully
from the National acknowledged.
Science
Foundation
for one of us
LIST OF SYMBOLS
T P
iz R
xi ‘pi %
A G Pi
z
ii/k u Voo ~ij. y;j> q;j/k,
‘i,/k
temperature (K) pressure (bar) density (mol 1-l) Boltzmann constant gas constant mole fraction surface fraction volume fraction Helmholtz energy Gibbs energy chemical potential of component i compressibility factor minimum value of intermolecular energy u( r)/k collision diameter (average) close-packed volume at T = 0 K surface weighing factor (g, = 1; g,? = ( ~oo/V~o)2/3) mixture interaction parameters
Subscripts i,j,
k
components
Superscripts r E C
residual property (i.e., value of property for real fluid minus value for perfect gas at same T and p) excess property (relative to ideal mixture) critical (gas-liquid)
REFERENCES Ambrose, D. and Townsend, R., 1975. Vapor-Liquid (U.K.), Teddington, Gt. Britain.
Critical
Properties.
Natl. Phys. Lab.
265 Angus, S., Armstrong, B. and de Reuck, K.M., 1976. International Thermodynamic Tables of the Fluid State: Carbon Dioxide. Pergamon, New York. Barber, J.R., Kay, W.B. and Teja, A.S., 1982. A study of the volumetric and phase behavior of binary systems. Part I. Am. Inst. Chem. Eng. J., 28: 134-138. Bowden, W.W., Staton, J.C. and Smith, B.D., 1966. Vapor-liquid equilibrium of the pentane + sulfur dioxide+ benzene system at O’F. J. Chem. Eng. Data, 11: 2966303. Buckingham, A.D., 1970. In: D. Henderson (Ed.), Physical Chemistry. Vol. 4. Academic Press, New York, Chap. 8. Chen, S.S. and Kreglewski, A., 1977. Applications of the augmented van der Waals theory of fluids. Part I. Ber. Bunsenges. Phys. Chem., 81: 10481052. Gubbins, K.E. and Twu, C.H., 1978. Thermodynamics of p’olyatomic fluid mixtures. Chem. Eng. Sci., 33: 8633878. Gupta, M.K., Li, Y.H., Hulsey, B.J. and Robinson, Jr., R.L., 1982. Phase equilibrium for carbon dioxide+benzene at 313.2, 353.2 and 393.2 K. J. Chem. Eng. Data, 27: 55-57. Hanna. M.W., 1968. Bonding in donor-acceptor complexes. Part 1. J. Am. Chem. Sot., 90: 285-291. Kay, W.B. and Donham, W.E., 1955. Liquid-vapor equilibrium relations in binary systems: n-butanol-iso-butanol, n-butanol-methanol, n-butanol-diethylether systems. Chem. Eng. Sci., 5: l-16. Kay, W.B. and Rambosek, G.M., 1953. Liquid-vapor equilibrium relations in binary systems: propane-hydrogen sulfide system. Ind. Eng. Chem., 45: 221-226. Kreglewski, A., 1980. Applications of the augmented van der Waals theory of fluids. Part III. J. Chim. Phys., 77: 441-444. Kreglewski, A. and Kay, W.B., 1969. The critical constants of conformal mixtures. J. Phys. Chem., 73: 3359-3366.
Lorimer, J.W., Smith, B.C. and Smith, G.H., 1975. Total vapour pressures, thermodynamic excess functions and complex formation in binary liquid mixtures of some organic solvents with sulphur dioxide. J. Chem. Sot., Faraday Trans. 1, 71: 2232-2250. Ohgaki, K. and Katayama, T., 1976. Isothermal vapor-liquid equilibrium data for binary systems containing carbon dioxide at high pressures. J. Chem. Eng. Data, 21: 53-55. Rowlinson, J.S., 1969. Liquids and Liquid Mixtures. Butterworth, London, Chaps. 6 and 9. Stryjek, R., Chappelear, P.S. and Kobayashi, R., 1974. Low-temperature vapor-liquid equilibria of nitrogen+ethane system. J. Chem. Eng. Data, 19: 340-343. Twu, C.H., Gubbins, K.E. and Gray, C.G., 1976. Thermodynamics of mixtures of non-spherical molecules. Part III. J. Chem. Phys., 64: 5 186-5197.
11 (1983) 25 l-265 Elsevier Science Publishers B.V.. Amsterdam
251 -
Printed in The Netherlands
CRITICAL-LOCUS CURVES AND LIQUID-VAPOR EQUILIBRIA IN THE BINARY SYSTEMS OF BENZENE WITH CARBON DIOXIDE AND SULFUR DIOXIDE WEBSTER B. KAY Department
of Chemical Engineering,
Ohio State University, Columbus, OH 43210 (U.S.A.)
ALEKSANDER
KREGLEWSKI
Thermodynamics
Research Center, Texas A & M Uniuersity, College Station, TX 77843 (U.S.A.)
(Received September
*
1, 1982; accepted in final form November
16, 1982)
ABSTRACT Kay, W.B. and Kreglewski, A., 1983. Critical-locus curves and liquid-vapor equilibria in the binary systems of benzene with carbon dioxide and sulfur dioxide. Fluid Phase Equilibria, 11: 251-265. Critical-locus curves F(x) and P”(x) have been determined for the carbon dioxide+ benzene and sulfur dioxide+ benzene systems. The data, together with existing liquid-vapor equilibrium data, are used to construct the complete phase diagrams at high pressures.
INTRODUCTION
Ohgaki and Katayama (1976) and Gupta et al. (1982) determined liquid-vapor equilibrium isotherms for the carbon dioxide + benzene system at 298.15 and 313.15 K, and the bubble points at 353.15 and 393.15 K. These data indicate positive deviations from an ideal system. This fact, however, does not exclude the possibility of specific interactions between the two components. Bowden et al. (1966) determined the liquid-vapor isotherm and the excess chemical potentials py and GE for the sulfur dioxide + benzene system at 255.37 K. The system exhibits small positive deviations from an ideal system. Lorimer et al. (1975) determined ~7 and GE for mixtures of sulfur dioxide with toluene, m-xylene and mesitylene at and below 250 K, and found small negative deviations, increasing with the number of methyl
* Author to whom correspondence 0378-3812/83/$03.00
should be addressed.
0 1983 Elsevier Science Publishers B.V.
252
groups. Thus, specific interactions between SO, and aromatic compounds appear to be weakest in the case of benzene. As reviewed by the above authors, all the systems form complexes in the solid state. We have determined the critical-locus curves T’(x) and P”(x) in order to gain more information about the behavior of these systems at high temperatures, and have correlated the results with the above liquid-vapor equilibrium data. EXPERIMENTAL
Apparatus P-T-x relationships along the critical-locus curves for the two binary systems were obtained by determining the critical temperatures and pressures of a series of mixtures of known composition ranging from one pure component to the other. The apparatus and procedure used have been described by Barber et al. (1982) and in references cited therein to earlier papers by Kay and co-workers. Briefly, a small air-free sample of binary mixture is confined over mercury in a thick-walled glass tube surrounded by a constant-temperature jacket. The temperature is maintained constant by the condensing vapor of a series of pure organic liquids heated at constant and controlled pressure in a side-arm flask attached to the jacket. The experimental tube is held rigidly in a mercury-filled compressor block, with means provided for controlling and measuring the pressure of the sample. The volume of the sample and its variation with pressure and temperature are not measured. To bring about equilibrium quickly, the sample is stirred by means of a steel ball inserted in the tube prior to loading the sample. The ball is moved rapidly through the sample by a magnet moving around the outside of the constant-temperature jacket. The temperature of the vapor jacket surrounding the experimental tube was measured to within +O.Ol K using a platinum resistance thermometer calibrated at the National Bureau of Standards. Pressures along the saturated liquid and vapor curves and at the critical point were measured using a precision spring gauge with a 40-cm dial. This gauge covered a range from 0 to 138 bar in 0.345 bar intervals. Both the dead-weight gauge and the spring gauge were compared with a standard dead-weight gauge. Sources and purity of materials and preparation
of mixtures
Benzene (Phillips Petroleum Company; purity 99.91 mol %), carbon dioxide and sulfur dioxide (purity 99.98 mol 76) were each liquefied in a vacuum train with liquid nitrogen as the refrigerant and brought into contact
253
with freshly activated molecular sieve to remove possible traces of moisture, and then deaerated by a cycle of operations consisting of pumping off non-condensable gases over the solid (at liquid-nitrogen temperature), melting and transferring by distillation to a second vessel, freezing and then pumping off the residual gas. The products were stored in sealed glass ampoules until ready to use, each ampoule containing slightly more than the required quantity of vapor for one loading of the experimental tube. Degassing of liquid benzene An 8 ml sample of benzene was percolated over activated silica gel to remove any possible traces of moisture and was then charged through a rubber septum, by means of a hypodermic syringe, to the degassing apparatus, where air and other non-condensable gases were removed. The degassing operation was quite simple. The sample in the flask below the degasser was warmed and the vapor condensed and frozen on a cold-finger cooled with liquid nitrogen, while non-condensable gases were pumped off. When all of the sample was frozen on the cold finger, the liquid nitrogen was removed and the solid benzene melted and collected in the flask below. It was then transferred by distillation to a storage flask where it was kept refrigerated until used. Preparation of mixtures In the preparation of a binary mixture of known composition containing benzene and carbon dioxide or benzene and sulfur dioxide, a quantity of benzene was transferred by distillation from the storage flask to a small capillary tube whose total volume per unit length had been determined previously. From the length of the tube occupied by the sample at 273.15 K (measured using a cathetometer reading to 0.05 mm) and the density of the liquid at 273.15 K, the weight of the sample was calculated. A correction was made for the weight of the vapor over the liquid using the perfect gas law and knowledge of the vapor pressure. The measured sample was then transferred by distillation to the experimental tube and frozen in the tip by surrounding the end of the tube with a bath of liquid nitrogen. With the mixture frozen, mercury was then added until the tube was filled (Kay and Donham, 1955). The tube was then transferred to the compressor block and a measured volume of either CO, or SO, gas at a known temperature and pressure injected into the tube by means of a gas microburette. The gas microburette consisted essentially of a calibrated section of precision glass capillary connected to a stainless-steel bellows and surrounded by a water jacket for temperature control (for details, see Kay and Rambosek, 1953). The calibrated section was 50 cm long and had a volume of 0.05365 cm3 per cm. An etched scale with lines at 0.1 cm intervals made it possible to
254
read gas volumes to within - 0.001 cm3. The sample mass and composition of the mixture were determined from the isothermal compressibility measurements. Results
Critical temperatures and pressures were determined for up to eight mixtures of known composition for each of the binary systems. This was done by locating first the approximate critical temperature, and then, starting a few degrees below, the P-T bubble-point curve was determined at small temperature intervals until the characteristic critical phenomena were observed. The experimental results are reported in Tables 1 and 2 and shown graphically in the figures. The absolute uncertainty of the results is estimated to be 0.1% for the composition, 0.05 K for T”, and 0.06 bar for PC. The calculated values given in the tables were obtained in a reverse manner: for the given (observed) T”, the mole fraction x1 of CO, or SO,, the critical pressure PC and the critical density pc were calculated by iteration from the equation of state as the TABLE 1 Critical-locus Observed
curve for the carbon dioxide (I)+benzene
values T’/(K)
P/(bar)
0.0000 0.0000 0.1142
562.16 a 562.21 550.30
48.98 a 48.97 64.19
0.1984 0.3485 0.4732 0.8108
540.38 518.28 491.49 430.00 393.15 375.04
76.12 99.97 123.0
0.8204 0.8492
361.57 357.45
0.9233 1.oooo
353.15 333.22 313.15 304.21 ’
128.9 121.0 -
134.1
99.70 73.825 ’
#/(mol
l- ‘)
3.86 a
(2) system Calculated
values b
x,
P/(bar)
0
48.98 -
-
#/(mol 3.9 -
0.215 0.355 0.475 0.665 0.750
78.6 100.6 123.2 147.5 143.2 -
4.30 5.03 6.15 8.87 10.9 -
-
0.830 -
129.8 -
11.7 -
-
0.870 0.925 0.980 1
118.6 100.6 81.0 73.83
12.0 (12.3) 10.6
-
10.6’
a Values selected by Ambrose and Townsend b Calculated at observed values of TC. 'Values selected by Angus et al. (1976).
(1975).
l- ‘)
255 TABLE 2 Critical-locus
curve for the sulfur dioxide (l)+benzene
Observed values
Calculated
Xl
TC,‘(K)
P”/(bar)
p’/(mol I-‘)
0.1143 0.2419 0.3835 0.5127 0.6628 0.8750 1.oOOo 1.oooo
552.87 540.3 1 523.69 508.99 488.59 455.51 430.8 a 430.1
55.76 63.94 72.61 78.04 82.53 82.66 78.84 a -
-
a,b See footnotes
(2) system
8.20 a
XI
-
values b P/(bar)
-
$/(mol
1-l)
-
0.250 0.400 0.515 0.655 0.850
64.0 72.6 78.0 82.5 83.0
4.17 4.67 5.05 5.57 6.75
1
78.8
8.20
to Table 1.
maximum point on the P(X) isotherm (proof that this point is the critical point has been given by Rowlinson (1969)). The P”(x) curve for the CO, + C,H, system appears to have a maximum at - 148 bar, although the experimental glass tube did not permit measurements above - 135 bar. For this reason, there is a gap in the measured values extending from x, = 0.5 to 0.8, and only the calculated values at 430 K are given. Additionally, the calculated critical locus for the three isotherms shown in Fig. 3 is reported in Table 1. Any differences between the observed and calculated values should be attributed to errors in the theory or the uncertainty of the calculated maximum points. CALCULATED
RESULTS
The mole fractions xi, xi and xi’ and the molar densities p, p’ and p” of the coexisting phases were obtained by iteration at the given T and P using Gibbs equilibrium conditions and the following relation for the chemical potential of component i of a mixture: p,/RT
= In xi + A’/RT +py’/RT
+ 2 - 1 + In p - c x, [a( A’/RT)/axj] j-i (k * i,j)
T,p,x, (1)
where 2 is the compressibility factor derived from the following relation for the residual Helmholtz energy (Chen and Kreglewski, 1977): A’/RT=
(a’-
1) In(1 -E)
+ [(a” + 3a)[ - 3at2]/(1
+ c ~%&%‘kT)“(~‘~p)~ n m
- 5)2 (2)
where (Yis a constant depending on the shape of the molecules, 5 = 0.74048 V”p = rN,a3p/6, where Vn is the close-packed volume, which is a simple function of T (with one constant C, usually equal to - 0.12), N, is Avogadro’s number, u is the collision diameter, and p is the molar density of the system. D,,,,, are 24 universal constants obtained from P-V-T and internal-energy data for argon, and ii/k is a certain minimum value of the intermolecular energy, assumed for argon to be equal to the critical temperature, 150.86 K. The excess combinatorial potential pFc‘ may be calculated from the Flory-Huggins equation pyC/RT
= ln( &/x,)
+ 1 - r&/x,
(3)
in which $ = x~~~~/C~X~V~” (k = 1,. . . ); Voo is the value of V” at T = 0 K. The characteristic constants for the three pure components are given in Table 3. The values for sulfur dioxide and benzene reported previously have been revised to conform better with the saturation densities and the critical points. Equation (2) applies for mixtures with (Yassumed to be a linear function of xi and where V0 = c cx,x,y; i
(4)
j
where (5) The interaction energy ii/k for a mixture is assumed to be proportional to the surface fractions cp,= ~~(l/i~~)~~~/C~x,(~~~)*~~ and the surface interactions fir = Ui,/gf, etc., where g, = 1, g, = ( V~“/V/o)1’3, etc., so that
’ k
' i
(6)
i
TABLE 3 Characteristic
constants
of eqn. (2) ’
Component
01
VW/ (cm3 mol - ’ )
C
g/k/(K)
v/k/(K)
Carbon dioxide Sulfur dioxide Benzene
1.0571 1.0710 1.0613
19.703 25.346 54.289
0.12 0.12 0.12
284.28 383.56 529.24
40.0 88.0 72.0
a VW is the value of V” at T= 0 K. The relation V”(T) with one-constant by Chen and Kreglewski (1977).
C has been given
251
where c lJ
=
cp,[ 1 + TJiJ/kT + ( sij/kT)2]
Ey/= 2yiJ(l/4+
l/e;J’
Here yiJ, qij/k, cYij/k and usually, but not always, k,, are constants given system. For pure fluids, eqn. (6) becomes Ei/k = (U’,‘k)( 1 + q,‘kT)
(8) for a
(9)
because no attempts have been made to determine 6/k for pure fluids. As shown by Twu et al. (1976) and by Gubbins and Twu (1978), dipolar and quadrupolar forces greatly affect the phase diagrams of fluid mixtures. The Helmholtz energies A, and A, vary according to (/CT)-’ and ( kT)-2, respectively, in the case both of dipolar and of quadrupolar forces, and have slightly differing dependences on the reduced density 5 than A,, due to London forces. In the present treatment the relation for A’ is simplified, as it contains terms proportional to q/kT and (6/kT j2, whereas the dependence on < is the same as for argon (with the same values of the constants D,,). Moreover, Si, is an empirical parameter relative to Si, = Sjj = 0 for the pure components. For systems containing inert components, 77112: (Vii +
Vjj)/2
(10)
For systems with specific interactions, qij may be lower than the arithmetic mean value; however, we have found that it is best to evaluate qij/k using eqn. (10) and, initially keeping Sij/k = 0, to fit y,, (or E:/) to the critical-locus curve or other data at several temperatures. Most often, cpJ appears to be a linear function of Tw2. The slope and the limiting value at l/T* = 0 then yield yij and S;,/k. The choice of the weights gi in eqn. (6) has a strong effect on the value of yij but affects very little the shapes of the liquid-vapor isotherms or the critical curves. The assumption that g,: ( Koo)‘/3 is the simplest one, and in this case yij 2: 1 for systems containing inert components (Kreglewski and Kay, 1969). Kreglewski (1980) found that addition of the excess combinatorial term to A’/RT improves the agreement with critical densities for alkane + alkane systems. It appears to have a large effect on the liquid-vapor loops near the critical point, as shown in Fig. 1 for the nitrogen + ethane system. The values of yiJ, qij/k and S,,/k used to calculate the dashed and full curves were the same, but the dashed curves were obtained for pFc= 0 and kjj = 1.30, whereas the full curves result for kj, = 1.22 and ,uFc calculated
258
Fig. 1. Effect of combinatorial term prc on vapor-liquid equilibrium of N,( l)+C,H,(2) system at 172.04 K: circles, data of Stryjek et al. (1974); full curves, calculated with p:c from eqn. (3); dashed curves, calculated with nFc = 0.
using eqn. (3) *. For I*,EC= 0 the loop does not close at the observed critical point, and, in addition, k,, is too large and yields too low densities of the liquid phase. It should be pointed out that for the systems CH, + CO, and N, + CO, a similar, although smaller, correction of pi is required in order to close the loops at the observed critical points, but the combinatorial term does not help in these cases because of the similar molecular sizes of the components, On the other hand, the correction appears to be too large for the SO, + C,H, system. Therefore, it is possible that the correction term required in the critical region has nothing to do with ~7’. The carbon dioxide + benzene system The interaction parameters were fitted initially to both the critical-locus curve and the bubble points of the four isotherms. The final values of rji and si,/k were fitted to the 393.15 and 313.15 K isotherms, whereas kij was
* The graph in Fig. 1 was obtained using raw, initial values of the interaction parameters, and may be improved further. The tabulated results, including derived functions such as the residual potentials (fugacities of the components), enthalpies, etc., for the systems considered in this paper and several other systems will be published subsequently by the Thermodynamics Research Center.
259 TABLE 4 Binary interaction
parameters
System
Y‘J
v,,/k
&,/k
k,,
CO, + C,H,
0.827 0.967
56.0 80.0
130.0 51.5
0.533+1.15x10-3T-0.15x, 0.972 - 0.092 X,
SO, + C,H,
a
a X, is the mole fraction of CO, or SO,.
/
or I,
0
0.2
0.4
0.6
0.8
1.0 XI
Fig. 2. P’(x) curve for CO,(l)+C,H,(Z) system: circles. experimental data from this work; dashed line, calculated curve; full curves, liquid-vapor isotherms calculated at T = 540.38 K (I), 518.28 K (2) 491.49 K (3), 430.00 K (4), 367.57 K (5). and 333.22 K (6).
0 0
0.2
0.4
0.6
0.8
1.0
XI Fig. 3. Liquid-vapor isotherms for CO,(l)+C,H,(Z) system at T= 393.15 K (l), 353.15 K (2), 313.15 K (3), and 298.15 K (4): curves, calculated results (dashed line explained in text): open circles, experimental data of Gupta et al. (1982); filled circles, experimental data of Ohgaki and Katayama (1976).
fitted to the critical-locus curve. k,j appears to vary with both T and X, (Table 4). When kij is assumed to depend on T only, that is, is fitted to the critical point and kept constant along an isotherm, for example 393.15 K, the dashed curve in Fig. 3 is obtained. The empirical relation for ki, is reported in Table 4. This relation affects aV”/i3x, and a2Yo/a~,2 significantly but the effect on aV”/3T and the enthalpy is small and we have neglected it. The relation for kii may be regarded as a simple correction of
261
0
0.2
0.4
0.6
0.8
1.0 xl
Fig. 4. Calculated densities of saturated liquid and vapor for CO,(l)+C,H,(2) system at T = 298.15 IS (I), 353.15 K (2), 430.00 K (3), 491.49 K (4). and 540.38 K (5): dashed line, p”(x); circles, selected experimental data for pure components.
$_ 50 a
01
0
0.2
0.4
0.6
0.8
1.0
Xl Fig. 5. P”(r) curve for SO,(l)+C,H,(Z) system: circles, experimental data from this work; dashed line, calculated curve; full curves, liquid-vapor isotherms calculated at T = 540.31 K (l), 508.99 K (2), 455.51 K (3), and 420.00 K (4).
262 15-
0.2
0
0.4
0.8
0.6
1.0 XI
Fig. 6. Calculated densities of saturated liquid and vapor for SO,(l)+C,H,(2) values of T, see Fig. 5): dashed line, p’(x)
system (for
\ \ \
300 0
0.2
0.4
0.6
0.6
Fig. 7. P(x) curves for CO,(I)+qH,(2) and SO,(I)+C,H,(2) from this work and calculated curves (dashed).
systems: experimental data
263
deviations from the random-mixing approximation. This treatment is not sufficiently accurate and causes some deviations from the observed critical points, particularly points 1 and 5 in Fig. 2. The sulfur dioxide + benzene system The liquid-vapor equilibrium data of Bowden et al. (1966) at 255.37 K are below the range of validity of the equation of state for this system. Therefore, a simplified equation with one D,, constant (D,r) was used to estimate epJ at this temperature. The values of y,], S,,/k and ki, were then estimated from the critical-,locus curve. Only a weak dependence of ki, on X, was detected. For X, > 0.6 the calculated critical compositions are too small, so that T” calculated for a given x1 are slightly lower than the observed values for SO,-rich mixtures (Fig. 7). The proper value of vi/k for this system should be lower than the arithmetic mean, because of the polarity of SO,. The resulting positive deviations from an ideal system would be compensated by a larger value of 6,/k. The experimental data are insufficient to estimate all three constants of eqn. (7) and one of them had to be fixed. DISCUSSION
According to the theory of Gubbins and co-workers and as suggested earlier by Rowlinson (1969), negative deviations from an ideal system may occur when the quadrupole moments Q of the components have opposite signs. Buckingham (1970) determined Q for CO, (- 4.3 X 1O-26 e.s.u. cm2) and Hanna (1968) for C,H, (- 14.5 x 1O-26 e.s.u. cm*). The sign of Q for SO, is not known, but it must be positive. Otherwise, electrostatic theory would not suffice to explain the behavior of SO, + aromatic systems. An analysis of ordering effects due to large differences in TC (or ii/k) of the components, as carried out by Rowlinson (1969) leads to complicated relations, and an empirical treatment is justified. The abnormal value of Sjj/k and the variation of kij with X, and T for the CO, + C,H, system are due partly to this effect. However, y;, for this system is very low and the deviations from an ideal system are positive at all temperatures, as expected on the basis of electrostatic theory. The positive deviations for the SO, + C,H, system should be even larger, because of the polarity of SO, and apparently weaker ordering effects. There must exist an opposing factor in this system, presumably due to quadrupole moments of opposite signs. The variation of kjj with x, and T for the above systems is unusual, because for other systems containing quadrupolar molecules and with large
264
ratios T,C/T,” for the components, kj j is approximately constant.
such as N, + C,H,,
N, + CO, or N, + H,S,
ACKNOWLEDGEMENT
Partial support (A.K.) is gratefully
from the National acknowledged.
Science
Foundation
for one of us
LIST OF SYMBOLS
T P
iz R
xi ‘pi %
A G Pi
z
ii/k u Voo ~ij. y;j> q;j/k,
‘i,/k
temperature (K) pressure (bar) density (mol 1-l) Boltzmann constant gas constant mole fraction surface fraction volume fraction Helmholtz energy Gibbs energy chemical potential of component i compressibility factor minimum value of intermolecular energy u( r)/k collision diameter (average) close-packed volume at T = 0 K surface weighing factor (g, = 1; g,? = ( ~oo/V~o)2/3) mixture interaction parameters
Subscripts i,j,
k
components
Superscripts r E C
residual property (i.e., value of property for real fluid minus value for perfect gas at same T and p) excess property (relative to ideal mixture) critical (gas-liquid)
REFERENCES Ambrose, D. and Townsend, R., 1975. Vapor-Liquid (U.K.), Teddington, Gt. Britain.
Critical
Properties.
Natl. Phys. Lab.
265 Angus, S., Armstrong, B. and de Reuck, K.M., 1976. International Thermodynamic Tables of the Fluid State: Carbon Dioxide. Pergamon, New York. Barber, J.R., Kay, W.B. and Teja, A.S., 1982. A study of the volumetric and phase behavior of binary systems. Part I. Am. Inst. Chem. Eng. J., 28: 134-138. Bowden, W.W., Staton, J.C. and Smith, B.D., 1966. Vapor-liquid equilibrium of the pentane + sulfur dioxide+ benzene system at O’F. J. Chem. Eng. Data, 11: 2966303. Buckingham, A.D., 1970. In: D. Henderson (Ed.), Physical Chemistry. Vol. 4. Academic Press, New York, Chap. 8. Chen, S.S. and Kreglewski, A., 1977. Applications of the augmented van der Waals theory of fluids. Part I. Ber. Bunsenges. Phys. Chem., 81: 10481052. Gubbins, K.E. and Twu, C.H., 1978. Thermodynamics of p’olyatomic fluid mixtures. Chem. Eng. Sci., 33: 8633878. Gupta, M.K., Li, Y.H., Hulsey, B.J. and Robinson, Jr., R.L., 1982. Phase equilibrium for carbon dioxide+benzene at 313.2, 353.2 and 393.2 K. J. Chem. Eng. Data, 27: 55-57. Hanna. M.W., 1968. Bonding in donor-acceptor complexes. Part 1. J. Am. Chem. Sot., 90: 285-291. Kay, W.B. and Donham, W.E., 1955. Liquid-vapor equilibrium relations in binary systems: n-butanol-iso-butanol, n-butanol-methanol, n-butanol-diethylether systems. Chem. Eng. Sci., 5: l-16. Kay, W.B. and Rambosek, G.M., 1953. Liquid-vapor equilibrium relations in binary systems: propane-hydrogen sulfide system. Ind. Eng. Chem., 45: 221-226. Kreglewski, A., 1980. Applications of the augmented van der Waals theory of fluids. Part III. J. Chim. Phys., 77: 441-444. Kreglewski, A. and Kay, W.B., 1969. The critical constants of conformal mixtures. J. Phys. Chem., 73: 3359-3366.
Lorimer, J.W., Smith, B.C. and Smith, G.H., 1975. Total vapour pressures, thermodynamic excess functions and complex formation in binary liquid mixtures of some organic solvents with sulphur dioxide. J. Chem. Sot., Faraday Trans. 1, 71: 2232-2250. Ohgaki, K. and Katayama, T., 1976. Isothermal vapor-liquid equilibrium data for binary systems containing carbon dioxide at high pressures. J. Chem. Eng. Data, 21: 53-55. Rowlinson, J.S., 1969. Liquids and Liquid Mixtures. Butterworth, London, Chaps. 6 and 9. Stryjek, R., Chappelear, P.S. and Kobayashi, R., 1974. Low-temperature vapor-liquid equilibria of nitrogen+ethane system. J. Chem. Eng. Data, 19: 340-343. Twu, C.H., Gubbins, K.E. and Gray, C.G., 1976. Thermodynamics of mixtures of non-spherical molecules. Part III. J. Chem. Phys., 64: 5 186-5197.