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The excess enthalpies of (carbon dioxide + decane) from 283.15 to 323.15 K at 7.58 MPa
M-1434 J. Chem. Thermodynamics1983, 15. 173-180
The excess enthalpies of (carbon dioxide + decane) from 283.15 to 323.15 K at 7.58 MPa C. PANDO, J. A. R. RENUNCIO, T. A. McFALL, R. M. IZATT, and J. J. CHRISTENSEN Departments of ChemicalEngineeringand Chemistryand Contribution278 from the Thermochemical Institute, Brigham Young University, Provo, Utah 84602,U.S.A. (Received19 April 1982; in revisedform 5 August 1982) The excess enthalpies HE for (carbon dioxide + decane) were measured in the vicinity of the carbon-dioxide critical point by means of an isothermal flow calorimeter. Mixtures at 283.15 and 303.15 K and at 7.58 MPa show endothermic mixing except for a moderately exothermic section in the carbon-dioxide-rich region at 303.15 K. Mixtures at 308.15.313.15, and 323.15 K at 7.58 MPa show large negative values of HEwhich vary linearly with mole fraction in the carbon-dioxide-rich region reaching largest negative values at COs mole-fraction values of 0.94, 0.80, and 0.66, respectively. The changes observed in the values of HEwith temperature and the significance of the largest negative values and linear sections of the isotherms are discussed and interpreted in terms ofliquid-vapor equilibrium and critical constants for (carbon dioxide + decane).
1. Introduction Many interesting and to date little explored phenomena occur in the vicinity of the critical locus of binary mixtures. Very few enthalpies of mixing have been obtained in this region due to the difficulties of calorimetrically reaching the critical conditions.“-5’ Those that have been obtained indicate that large exothermic effects are to be expected when the critical locus is approached. Using high-pressure flow calorimeters developed in this laboratory,@,” we have initiated a program to measure enthalpies of mixing of (carbon dioxide + a hydrocarbon) in the critical region. These mixtures are of particular interest because of the potential use@)of supercritical CO, as a solvent in oil-well flooding, for extraction of volatile components from coal, oil shale, and tar sands, and for extraction of oils from vegetable products. The present work reports the excess enthalpies HE for (carbon dioxide + decane) over the entire composition range at 283.15, 303.15, 308.15, 313.15, and 323.15 K and 7.58 MPa.
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure were the same as described previously.(6*7*9*10) All runs were made at 7.58 MPa. Since PCand T, for CO, are 7.38 MPa and 304.21 K, respectively,‘“’ the 0021-9614/83/020173+08
SOZ.OO/O
0 1983 Academic Press Inc. (London) Limited
C. PANDO
174
ET AL.
CO2 enters the calorimeter as a liquid at 283.15 and 303.15 K, and as a fluid at 308.15, 313.15, and 323.15 K. All runs were made in the steady-state (fixed composition) mode. The total flow rate was 0.010 cm3 .ssl for all temperatures except for some mixtures at 308.15 and 313.15 K for which the flow rate was reduced to 0.005 crn3.se1 to decrease the rate of energy generation in the calorimeter. Previous results obtained with this calorimeter were reproducible to + 0.5 per cent or better over most of the mole-fraction range (0.2 < x < 0.8).‘9’ Reproducibility of results in the present investigation was f 1 to f 2 per cent mainly due to difficulties in mixing the components in certain mole-fraction regions. The materials employed were carbon dioxide (Whitmore Oxygen Co. 99.98 moles per cent pure) and decane (Phillips Petroleum Co. 99 moles per cent pure). Before being used, the CO, was filtered through a Matheson gas purifier model 450 which also contains a molecular-sieve desiccant. The decane was stored in sealed 1 L bottles over approximately 50 cm3 of Davison molecular sieves (3 nm effective pore diameter) and, just prior to use, was filtered through a Whatman filter (0.45 urn pore diameter) and degassed for 10 min in an ultrasonic bath. Further purification was not necessary(r2) since the other substances present in small amounts were sufficiently close in nature that HE is not significantly affected. Flow rates measured in cm3 s- ’ were converted to mol-s-’ and to mole fractions using the densities of the two pure materials estimated as follows. The density of decane at 7.58 MPa and 298.15 K (p = 0.7315 g.cme3) was evaluated using its value at atmospheric pressure and the isothermal compressibility obtained by interpolation of values for other hydrocarbons.(‘3’ The density of COz at 7.58 MPa and 298.15 K (p = 0.7590 g-cm-j) was calculated by interpolation of data from the IUPAC Tables.” ’ ) 3. Results and discussion Values of the mole fraction x of COz and experimental excess enthalpies H”(expt) are given in table 1 for the five temperatures studied. The experimental values at each temperature were curve fitted using HE/(J.mol-‘)
= [x(1 -.x)/j1 +k(l-2.x))]
t C,(l-2.x)“. n=O
(1)
The values of the coefficients C, and of k in this equation are given in table 2 together with standard deviations S. The reproducibility at 283.15 K for x < 0.2 was only fair due to mixing problems in the calorimeter and the results should not be considered as definitive. Minor difficulties of a similar nature were experienced in the same molefraction region at other temperatures. The excess enthalpies vary linearly with mole fraction in the CO,-rich region at 308.15,313.15, and 323.15 K, and have been fitted in this region to the equation: @/(J-mol-I)= A,+A,x. (2) The values of the coefficients A, and A,, the standard deviations s, and the molefraction intervals for the linear sections of the isotherms are also given in table 2. The highest value of s corresponds to the 308.15 K isotherm whose linear section is
HE FOR (CARBON DIOXIDE
+ DECANE)
175
TABLE I. Experimental and calculated excess enthalpies HE at 7.58 MPa for xCO,+(l HE/(J.mol-‘) expt talc.
x
X
HE/(J.mol-‘) expt talc.
x
HE/(J ‘mol-‘) expt talc.
- x)C,&~ X
HE/(J.mol-‘) expt talc.
T = 283.15 K 0.0631 0.0631 0.1480 0.1480 0.2230 0.2230 0.2897 0.3495
293 411 627 890 974 977
347 347 735 735 loo5 1005
0.3495 0.4033
1336 1424
1155 1321
0.0631 0.1480 0.2230 0.2897 0.3495 0.3495 0.4033
127 281 389 444 465 473 489
1314 1393
0.4521
1441
1439
1190 1314
0.4964 0.5369 0.6083 0.6692 0.6692
1476 1446 1412 1375 1329
1460 1462 1426 1353 1353
134 280 379 442 476 476 487
0.4033 0.4521 0.4964 0.4964 0.5369 0.6083 0.6692
486 474 458 462 433 347 220
487 481 460 460 421 336 221
T =
T = 0.o631 0.0631 0.1209 0.1209 0.1480 0.1480 0.2230
0.2230 0.2230 0.2897
-1442 -1612 -1870 -2117 -2572
-1448 -1666 -1882 -2096 -2512
0.7676 0.8078 0.8435 0.8753 0.9038
-1097
-505 -490 -612 -645 -979 -947 -1203
-490 -490 -614 -680 -940 -940 -1212
0.3495 0.4033 0.4964 0.5371 0.6083 0.6693 0.7218
-1438 -1454 - 1668 -1682 -2186 -2380 -2839 -3236 -3635
-2151 -2391 -2840 -3245 -3626
-464 -428 -453 -778 -1053 -1422
-449 -449 -449 -769 -1073 -1398
0.3495 0.4521 0.4521 0.4964 0.5369 0.5369
-1697 -2226 -2214 -2458 -2644 -2617
-1709 -2225 -2225 -2438 -2636 -2636
0.2230 0.2897
1146 loo2 loo2 901 749 762
1256 1256 1142 1017 1017 885 748 748
0.9038 0.9296 0.9296 0.9530 0.9743 0.9743
619 461 471 333 166 17.5
608 467 467 326 186 186
102 -45 -50 -176 -261 -368 -457
95 -35 -35 -162 -280 -382 -460
0.9296 0.9530 0.9143 0.9939
-502 -506 -412 -94
0.9296 0.9530 0.9603 0.9675 0.9843 0.9939
-4750 -4490 -3761 -3010 -1276 -5.1
-4657 -4546 -3755 -2974
0.9038 0.9530 0.9743 0.9939
-2158 -999 -480 -29
-2073 -980 -507 -72
0.9038 0.9296 0.9530 0.9743 0.9939
-851 -612 -412 -168
-865 -616 -390 -184
-504 -494 -399
-144
308.15 K 0.6693
0.2897 0.3495 0.4033 0.4522 0.4996 0.5371 0.6083
T =
1 0.0631 0.0631 0.1480
0.063
0.7217 0.7674 0.7674 0.8077 0.8434 0.8752 0.9038
-1205
-208 -208 -409 -409 -503 -503 -767
1241
1274
303.15 K
-1005 -1230
-246 -182 -457 -354 -563 -442 -723
T=
0.0631 0.0631 0.1209 0.1480
0.7217 0.7217 0.7674 0.8077 0.8077 0.8434 0.8752 0.8752
-2920
0.7218 -3228
313.15
-3516 -3839 -4064 -4291 -4434
-2905 -3259 -3570 -3838 -4066 -4263 -4447
K 0.7218 - 3602 -3626 0.7676 0.7676 0.7883 0.8078 0.8435 0.8753
-4004 -4073 -4161 -4146 -3421 -2725
-4009 -4009 -4200 -4206 -3413 -2706
-3006 -3106 -2660 -2175 -1808
-3005 -3132 -2625 -2183 -1794 -1142
-1153 -112
323.15 K 0.6083 0.6692 0.7217 0.7614 0.8077 0.8752
-1146
4.9
confined to those values of x close to unity. Values of s decrease considerably as the temperature and the linear interval increase. Figure la is a plot of HE against x for the five temperatures studied. The isotherms at 283.15 and 303.15 K exhibit the usual pattern for the enthalpy of mixing, i.e. moderately positive values with a maximum at x z 0.5. In addition, the 303.15 K plot presents an exothermic section in the CO,-rich region but the values of HE are
5.3
176
C. PANDO
TABLE
2. Coefficients
T/K :
and standard deviation xC0, + (1 - x)C,,H,,
283.15
303.15
5843.4 -441.49 893.72 - 398.85
1828.9 3007.0 - 897.10 420.19
ET AL.. s for least-squares representations by equations (1) and (2)
A0 ,4, s ‘I For 0.94 < x < 0.99.
HE
for
308.15 equation
0 45
of
(I ) -1595.4 2504.2 - 2234. I - 1571.7 2602. I
0.9093 15
I .0170 56
equation (2) ~ 107860.9 ’ 1084W.7” 88 ’ b For 0.80 < x < 0.99.
- 8686.2 11406 ~ 14767 4921.7 512.38 37307 -46918 0 34 -22151.5h 22215.4 h 49 h
-9823.3 9655.0 - 10545 17315 - 12970 - 3409.9 - 923.26 0 24 9598.7 c 9663.0’ 18’
’ For 0.66 < x < 0.99.
small, especially by comparison with the large negative values corresponding to the 308.15, 313.15, and 323.15 K isotherms. The changes in the values of HE with composition are best understood by reference to the liquid-vapor equilibrium diagram for (carbon dioxide + decane) in figure 2. Data to construct this diagram are taken from Reamer and Sage.‘14,r5’ The line representing the boundary between the liquid and the (liquid + vapor) phases is obtained by interpolation of their data at 8.62 and 6.90 MPa using an experimental point at 7.58 MPa. The values of the excess enthalpies at 308.15, 313.15, and 323.15 K reach their most negative values at values of x corresponding to those fixing the liquid boundary in figure 2 and become less negative linearly as x increases in the (liquid + vapor) region. The mole fractions x corresponding to the most negative values of HE can be obtained by extrapolation to the intersection of the curve represented by equation (1) and the straight line represented by equation (2) for each of the isotherms. The points, at the intersection of the dashed lines in figure la, have x coordinates of 0.94, 0.80, and 0.66 for the 308.15. 313.15, and 323.15 K isotherms, respectively. Essentially the same values of x are obtained from figure 2 from the intersection of the dashed tie lines with the liquid-boundary line indicating excellent agreement between the present results and those of Reamer and Sage. Since a given mixture of composition x consists of amounts of substance n, of liquid mixture of composition xl and ng of vapor mixture of composition xg, the excess enthalpy in the two-phase region may be expressed as HE = H$t, +Hpt,, (3) where Hr is the enthalpy of mixing of the liquid mixture, and Hz is the enthalpy of mixing of the vapor mixture. Both Hy and Hr have as initial states the fluid CO1 and the liquid decane entering the calorimeter. Therefore, the contributions to the enthalpies due to changes of state of the pure components are included in Hy and HF.
HE FOR (CARBON DIOXIDE
+ DECANE)
177
(4
-6000
0
I 0.2
T/K I 0.4
I 0.6
I 0.8
_I
1
X
FIGURE I. Plots (a) of HE against x for (xC0, + (I - x)C,,H,,} as a function of temperature and (b) of pressure against temperature indicating conditions at which HE was measured. 0. This work.
Values of n, and n, are related to the mole fractions x,, xg, and x by the relations: xlnl+ xgng = x(n, +n,), (4) (l-x,)n,+(l--x&I,= (I-x)(n,+n,); (5) x, and xg have constant values for each isotherm due to the two phases being in equilibrium at a fixed pressure and temperature. Figure 2 indicates that the vapor mixtures at 308.15,313.15, and 323.15 K consist mainly of COZ (see horizontal lines at 308.15, 313.15, and 323.15 K joining the liquid and vapor regions). Values for xg can be estimated for all three temperatures from the data of Reamer and Sage.‘14’ The values are all greater than 0.999 and this allows us to assume without introducing any significant error that xg = 1. Therefore, the only important contribution to H! is the enthalpy change associated with the fluid CO, becoming vapor. The value of x, at each of the temperatures studied is that corresponding to the two-phase boundary, and, consequently to the most negative value of HE in figure la. In other words, the process taking place in the calorimeter for any given mixture of composition x is the
C. PANDO
178
FIGURE and vapor
2. Phase diagram for j&O, regions together with critical
+ (1 - x)C,,H,, locus.
ET AL.
I at 7.58 M Pa showing
Iiqiid.
(liquid
+ vapor ).
formation of a liquid of fixed composition x, and the gasification of the remaining carbon dioxide. Substituting into equation (3) the expressions for n, and ng obtained from equations (4) and (5) when .xg = 1, we have HE = fx(Hr-HE:)+x,H~-H~)/(.w,-
1).
(6)
In the vicinity of the critical locus (figure lb), we may assume that the enthalpy of vaporization H: of CO, is sufficiently small to be neglected. This is confirmed by the experimental values of the excess enthalpy since it can be seen from equation (6) that HE goes to H! when x goes to unity. If we substitute into equation (6) the values of Hy and x, estimated from figures la and 2, we obtain for each temperature a straight line. Values of HE for the three temperatures calculated from equation (6) together with the experimental HE values in the two-phase region have been plotted against x in figure 3. The good agreement obtained between the calculated and experimental HE values indicates that equation (6) adequately describes the behavior of (carbon dioxide + decane) in the two-phase region. The small endothermic section observed for the 323.15 K isotherm (see table 1, x > 0.99) corresponds closely to that region in figure 2 which lies between the intersections of the isotherm with the critical locus and with the pure COZ line. No measurements were made in the corresponding regions at 313.15 and 308.15 K. We can now interpret the variations observed in the value of HE with x at 308.15, 313.15, and 323.15 K. If we start our experiment with a mixture rich in C02, most of the fluid COZ will become vapor while a small portion will dissolve into the liquid
HE FOR (CARBON DIOXIDE
+ DECANE)
179
0
0.6
0.7
0.8
0.9
1
X
FIGURE 3. Plot of HE against {xCO,+(~-X)C~,,H~~} experimental results, 0, for high x.
comparing
equation (6), -,
with
decane to form a certain amount of a liquid mixture whose fixed composition at a given temperature corresponds to that of the two-phase boundary in figure 2. The amount of this liquid mixture will depend on the amount of decane entering the calorimeter. As the amount of decane is increased at a given temperature values of HE become increasingly negative due to the greater amount of the liquid mixture present until a most negative value is reached corresponding to the two-phase boundary. Further increases in (1 -x) moves the mixture into the liquid region and leads to decreasingly negative values of HE. This could be the result of the proportionately smaller amounts of fluid CO2 being dissolved into liquid decane. The value of x corresponding to the most negative value of HE (figure la) can be predicted from the phase diagram (figure 2). For instance, at 330 K a value of x of 0.62 is determined from the two-phase boundary line (figure 2) and this value should correspond to the value of x for the most negative value of HE. The changes in HE with temperature from 283.15 to 323.15 K appear to be a combination of the solution of fluid COz into liquid decane and the change in the value of AC, for the mixture. As mentioned previously, the most negative values for HE at 308.15,313.15, and 323.15 K occur at x given by the liquid boundary shown in figure 2 where at each temperature, the maximum possible amount of CO, has been dissolved in the liquid decane. This indicates that the enthalpy change associated with the solution of fluid CO1 into liquid decane contributes to the large negative values of HE observed at each of these temperatures. Also, since the values of x corresponding to the most negative values of HE increase considerably as the temperature decreases from 323.15 to 308.15 K, it can be seen why the most negative values of HE and, in general, the values of HE in the two-phase region, are increasingly negative as the temperature is decreased in this interval. Also contributing to the magnitude of HE is the change in the value of AC, for the mixture with temperature. For a pure substance, at a constant pressure slightly greater than the critical pressure, as the temperature is increased through the critical temperature the heat capacity at
C. PANDO ET AL.
180
constant pressure C, exhibits a maximum. (16) This maximum becomes larger and sharper as the critical pressure is approached. Thus, since @H/BT), = C,. the change in the value of H becomes larger as the critical point of a pure component is approached. The same effect has been noted for the variation of HE with P and T in mixtures such as (methane + argon).‘3’ For ;xcoz+(l -x)C,oH22; (aHE/aT)p = AC, where ACp = (C&mixture)-xC,(CO,)-(1 -x)C,(C,,H,,)i. At a pressure slightly higher than the critical pressure and near the critical temperature of CO,, especially at high x, AC, will become large and negative as C,(C02) increases. The effect of temperature on AC, at x = 0.5 can be seen in figure la where the excess enthalpy experiences a moderate decrease (less positive) when the temperature is increased from 283.15 to 303.15 K, a large decrease (more negative) from 303.15 to 308.15 K (T, for CO1 is 304.21 K) and a small decrease (more negative) from 308.15 to 323.15 K. We have measured”” the HE values of (Freon-12 +N&‘dimethylacetamide) over a temperature range of 263.15 to 413.15 K spanning the critical point of Freon-12 (T, = 384.65 K). This mixture shows the same rapid change of HE with temperature near the critical point as (carbon dioxide + decane) indicating a similar effect of AC, on H". We appreciate the helpful discussions with Dr John L. Oscarson and his assistance with some of the experimental set-up and the help of Michael E. Post who made some of the experimental determinations. C. Pando wishes to acknowledge the Board of Foreign Scholarships and the Spanish Ministry of Education for their support through a Fulbright/MUI award. REFERENCES I. Christensen, J. J.; Hanks, R. W.; Izatt. R. M. Handbook @Heuts ofMi.Sng. Wiley-Interscience: New York. 1982. 2. Lewis, K. L.; Mosedale. S. E.; Wormald. C. J. .I. Chem. Thermo~~wamics 1977, 9. 221. 3. Mosedale. S. E.; Wormald, C. J. J. Chem. Thermo&namics 1977, 9, 483. 4. McFall, T. A.; Post. M. E.; Christensen. J. J.; Izatt. R. M. J. Chem. Thermodynamics 1981, 13. 441. 5. Christensen. J. J.; Izatt, R. M.; Post. M. E. ; McFall. T. A. Thermochim. Acta 1981. 50. 73. 6. Christensen, J. J.; Hansen, L. D.; Eatough. D. J.; Izatt, R. M.: Hart. R. M. Rev. Sci. Instrum. 1976, 47. 730. I. Christensen. J. J.; Hansen, L. D.; Izatt, R. M.; Eatough, D. J.; Hart. R. M. Rev. Sci. Insrrum. 1981, 52. 1226. 8. Schneider, G. M.; Stahl, E.; Wilke, G. : editors. Extraction with Supercritical Gases. Verlag Chemie : Weinheim. 1980. 9. Christensen, J. J.; Izatt. R. M.; Eatough. D. J.; Hansen, L. D. J. Chem. Thermo&numics 1978, IO, 25. IO. McFaII, T. A.; Post. M. E.; Collins. S. G. ; Christensen. J. J. : Izatt. R. M. J. Chem. Thermod~wzmics 1981, 13, 41.
Il. IUPAC Carbon Dioxide Infernational Thermo&wnic Tables of the Fluid State. Pergamon Press: Oxford. 1976. 12. Savini. C. G.; Winterhalter. D. R.; Van Ness, H. C. J. Chem. Eng. Dota 1965, 10. 168. 13. Handbookfor Chemistry and Physics 56th edition. The Chemical Rubber Company: Cleveland. Ohio, 1975-1976.
14. Reamer, H. H.; Sage, B. H. J. Chem. Ena. Data 1%3, 15. Reamer. H. H.; Sage, B. H. J. Chem. Eni. Data 1965, 16. Hirschfelder. J. 0.: Curtiss. C. F.: Bird. R. B. Molecular Wiley: New York. 1964, p. 367. 17. Schofield. R. S.; Post, M. E.; McFall. T. A.; Thermodynamics to be published.
8, 509. 10. 49. Theor\, ofGases
crnd Liauid.7 2nd edition. John
Izatt. R. M.: Christensen. J. J. J. Chem.
The excess enthalpies of (carbon dioxide + decane) from 283.15 to 323.15 K at 7.58 MPa C. PANDO, J. A. R. RENUNCIO, T. A. McFALL, R. M. IZATT, and J. J. CHRISTENSEN Departments of ChemicalEngineeringand Chemistryand Contribution278 from the Thermochemical Institute, Brigham Young University, Provo, Utah 84602,U.S.A. (Received19 April 1982; in revisedform 5 August 1982) The excess enthalpies HE for (carbon dioxide + decane) were measured in the vicinity of the carbon-dioxide critical point by means of an isothermal flow calorimeter. Mixtures at 283.15 and 303.15 K and at 7.58 MPa show endothermic mixing except for a moderately exothermic section in the carbon-dioxide-rich region at 303.15 K. Mixtures at 308.15.313.15, and 323.15 K at 7.58 MPa show large negative values of HEwhich vary linearly with mole fraction in the carbon-dioxide-rich region reaching largest negative values at COs mole-fraction values of 0.94, 0.80, and 0.66, respectively. The changes observed in the values of HEwith temperature and the significance of the largest negative values and linear sections of the isotherms are discussed and interpreted in terms ofliquid-vapor equilibrium and critical constants for (carbon dioxide + decane).
1. Introduction Many interesting and to date little explored phenomena occur in the vicinity of the critical locus of binary mixtures. Very few enthalpies of mixing have been obtained in this region due to the difficulties of calorimetrically reaching the critical conditions.“-5’ Those that have been obtained indicate that large exothermic effects are to be expected when the critical locus is approached. Using high-pressure flow calorimeters developed in this laboratory,@,” we have initiated a program to measure enthalpies of mixing of (carbon dioxide + a hydrocarbon) in the critical region. These mixtures are of particular interest because of the potential use@)of supercritical CO, as a solvent in oil-well flooding, for extraction of volatile components from coal, oil shale, and tar sands, and for extraction of oils from vegetable products. The present work reports the excess enthalpies HE for (carbon dioxide + decane) over the entire composition range at 283.15, 303.15, 308.15, 313.15, and 323.15 K and 7.58 MPa.
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure were the same as described previously.(6*7*9*10) All runs were made at 7.58 MPa. Since PCand T, for CO, are 7.38 MPa and 304.21 K, respectively,‘“’ the 0021-9614/83/020173+08
SOZ.OO/O
0 1983 Academic Press Inc. (London) Limited
C. PANDO
174
ET AL.
CO2 enters the calorimeter as a liquid at 283.15 and 303.15 K, and as a fluid at 308.15, 313.15, and 323.15 K. All runs were made in the steady-state (fixed composition) mode. The total flow rate was 0.010 cm3 .ssl for all temperatures except for some mixtures at 308.15 and 313.15 K for which the flow rate was reduced to 0.005 crn3.se1 to decrease the rate of energy generation in the calorimeter. Previous results obtained with this calorimeter were reproducible to + 0.5 per cent or better over most of the mole-fraction range (0.2 < x < 0.8).‘9’ Reproducibility of results in the present investigation was f 1 to f 2 per cent mainly due to difficulties in mixing the components in certain mole-fraction regions. The materials employed were carbon dioxide (Whitmore Oxygen Co. 99.98 moles per cent pure) and decane (Phillips Petroleum Co. 99 moles per cent pure). Before being used, the CO, was filtered through a Matheson gas purifier model 450 which also contains a molecular-sieve desiccant. The decane was stored in sealed 1 L bottles over approximately 50 cm3 of Davison molecular sieves (3 nm effective pore diameter) and, just prior to use, was filtered through a Whatman filter (0.45 urn pore diameter) and degassed for 10 min in an ultrasonic bath. Further purification was not necessary(r2) since the other substances present in small amounts were sufficiently close in nature that HE is not significantly affected. Flow rates measured in cm3 s- ’ were converted to mol-s-’ and to mole fractions using the densities of the two pure materials estimated as follows. The density of decane at 7.58 MPa and 298.15 K (p = 0.7315 g.cme3) was evaluated using its value at atmospheric pressure and the isothermal compressibility obtained by interpolation of values for other hydrocarbons.(‘3’ The density of COz at 7.58 MPa and 298.15 K (p = 0.7590 g-cm-j) was calculated by interpolation of data from the IUPAC Tables.” ’ ) 3. Results and discussion Values of the mole fraction x of COz and experimental excess enthalpies H”(expt) are given in table 1 for the five temperatures studied. The experimental values at each temperature were curve fitted using HE/(J.mol-‘)
= [x(1 -.x)/j1 +k(l-2.x))]
t C,(l-2.x)“. n=O
(1)
The values of the coefficients C, and of k in this equation are given in table 2 together with standard deviations S. The reproducibility at 283.15 K for x < 0.2 was only fair due to mixing problems in the calorimeter and the results should not be considered as definitive. Minor difficulties of a similar nature were experienced in the same molefraction region at other temperatures. The excess enthalpies vary linearly with mole fraction in the CO,-rich region at 308.15,313.15, and 323.15 K, and have been fitted in this region to the equation: @/(J-mol-I)= A,+A,x. (2) The values of the coefficients A, and A,, the standard deviations s, and the molefraction intervals for the linear sections of the isotherms are also given in table 2. The highest value of s corresponds to the 308.15 K isotherm whose linear section is
HE FOR (CARBON DIOXIDE
+ DECANE)
175
TABLE I. Experimental and calculated excess enthalpies HE at 7.58 MPa for xCO,+(l HE/(J.mol-‘) expt talc.
x
X
HE/(J.mol-‘) expt talc.
x
HE/(J ‘mol-‘) expt talc.
- x)C,&~ X
HE/(J.mol-‘) expt talc.
T = 283.15 K 0.0631 0.0631 0.1480 0.1480 0.2230 0.2230 0.2897 0.3495
293 411 627 890 974 977
347 347 735 735 loo5 1005
0.3495 0.4033
1336 1424
1155 1321
0.0631 0.1480 0.2230 0.2897 0.3495 0.3495 0.4033
127 281 389 444 465 473 489
1314 1393
0.4521
1441
1439
1190 1314
0.4964 0.5369 0.6083 0.6692 0.6692
1476 1446 1412 1375 1329
1460 1462 1426 1353 1353
134 280 379 442 476 476 487
0.4033 0.4521 0.4964 0.4964 0.5369 0.6083 0.6692
486 474 458 462 433 347 220
487 481 460 460 421 336 221
T =
T = 0.o631 0.0631 0.1209 0.1209 0.1480 0.1480 0.2230
0.2230 0.2230 0.2897
-1442 -1612 -1870 -2117 -2572
-1448 -1666 -1882 -2096 -2512
0.7676 0.8078 0.8435 0.8753 0.9038
-1097
-505 -490 -612 -645 -979 -947 -1203
-490 -490 -614 -680 -940 -940 -1212
0.3495 0.4033 0.4964 0.5371 0.6083 0.6693 0.7218
-1438 -1454 - 1668 -1682 -2186 -2380 -2839 -3236 -3635
-2151 -2391 -2840 -3245 -3626
-464 -428 -453 -778 -1053 -1422
-449 -449 -449 -769 -1073 -1398
0.3495 0.4521 0.4521 0.4964 0.5369 0.5369
-1697 -2226 -2214 -2458 -2644 -2617
-1709 -2225 -2225 -2438 -2636 -2636
0.2230 0.2897
1146 loo2 loo2 901 749 762
1256 1256 1142 1017 1017 885 748 748
0.9038 0.9296 0.9296 0.9530 0.9743 0.9743
619 461 471 333 166 17.5
608 467 467 326 186 186
102 -45 -50 -176 -261 -368 -457
95 -35 -35 -162 -280 -382 -460
0.9296 0.9530 0.9143 0.9939
-502 -506 -412 -94
0.9296 0.9530 0.9603 0.9675 0.9843 0.9939
-4750 -4490 -3761 -3010 -1276 -5.1
-4657 -4546 -3755 -2974
0.9038 0.9530 0.9743 0.9939
-2158 -999 -480 -29
-2073 -980 -507 -72
0.9038 0.9296 0.9530 0.9743 0.9939
-851 -612 -412 -168
-865 -616 -390 -184
-504 -494 -399
-144
308.15 K 0.6693
0.2897 0.3495 0.4033 0.4522 0.4996 0.5371 0.6083
T =
1 0.0631 0.0631 0.1480
0.063
0.7217 0.7674 0.7674 0.8077 0.8434 0.8752 0.9038
-1205
-208 -208 -409 -409 -503 -503 -767
1241
1274
303.15 K
-1005 -1230
-246 -182 -457 -354 -563 -442 -723
T=
0.0631 0.0631 0.1209 0.1480
0.7217 0.7217 0.7674 0.8077 0.8077 0.8434 0.8752 0.8752
-2920
0.7218 -3228
313.15
-3516 -3839 -4064 -4291 -4434
-2905 -3259 -3570 -3838 -4066 -4263 -4447
K 0.7218 - 3602 -3626 0.7676 0.7676 0.7883 0.8078 0.8435 0.8753
-4004 -4073 -4161 -4146 -3421 -2725
-4009 -4009 -4200 -4206 -3413 -2706
-3006 -3106 -2660 -2175 -1808
-3005 -3132 -2625 -2183 -1794 -1142
-1153 -112
323.15 K 0.6083 0.6692 0.7217 0.7614 0.8077 0.8752
-1146
4.9
confined to those values of x close to unity. Values of s decrease considerably as the temperature and the linear interval increase. Figure la is a plot of HE against x for the five temperatures studied. The isotherms at 283.15 and 303.15 K exhibit the usual pattern for the enthalpy of mixing, i.e. moderately positive values with a maximum at x z 0.5. In addition, the 303.15 K plot presents an exothermic section in the CO,-rich region but the values of HE are
5.3
176
C. PANDO
TABLE
2. Coefficients
T/K :
and standard deviation xC0, + (1 - x)C,,H,,
283.15
303.15
5843.4 -441.49 893.72 - 398.85
1828.9 3007.0 - 897.10 420.19
ET AL.. s for least-squares representations by equations (1) and (2)
A0 ,4, s ‘I For 0.94 < x < 0.99.
HE
for
308.15 equation
0 45
of
(I ) -1595.4 2504.2 - 2234. I - 1571.7 2602. I
0.9093 15
I .0170 56
equation (2) ~ 107860.9 ’ 1084W.7” 88 ’ b For 0.80 < x < 0.99.
- 8686.2 11406 ~ 14767 4921.7 512.38 37307 -46918 0 34 -22151.5h 22215.4 h 49 h
-9823.3 9655.0 - 10545 17315 - 12970 - 3409.9 - 923.26 0 24 9598.7 c 9663.0’ 18’
’ For 0.66 < x < 0.99.
small, especially by comparison with the large negative values corresponding to the 308.15, 313.15, and 323.15 K isotherms. The changes in the values of HE with composition are best understood by reference to the liquid-vapor equilibrium diagram for (carbon dioxide + decane) in figure 2. Data to construct this diagram are taken from Reamer and Sage.‘14,r5’ The line representing the boundary between the liquid and the (liquid + vapor) phases is obtained by interpolation of their data at 8.62 and 6.90 MPa using an experimental point at 7.58 MPa. The values of the excess enthalpies at 308.15, 313.15, and 323.15 K reach their most negative values at values of x corresponding to those fixing the liquid boundary in figure 2 and become less negative linearly as x increases in the (liquid + vapor) region. The mole fractions x corresponding to the most negative values of HE can be obtained by extrapolation to the intersection of the curve represented by equation (1) and the straight line represented by equation (2) for each of the isotherms. The points, at the intersection of the dashed lines in figure la, have x coordinates of 0.94, 0.80, and 0.66 for the 308.15. 313.15, and 323.15 K isotherms, respectively. Essentially the same values of x are obtained from figure 2 from the intersection of the dashed tie lines with the liquid-boundary line indicating excellent agreement between the present results and those of Reamer and Sage. Since a given mixture of composition x consists of amounts of substance n, of liquid mixture of composition xl and ng of vapor mixture of composition xg, the excess enthalpy in the two-phase region may be expressed as HE = H$t, +Hpt,, (3) where Hr is the enthalpy of mixing of the liquid mixture, and Hz is the enthalpy of mixing of the vapor mixture. Both Hy and Hr have as initial states the fluid CO1 and the liquid decane entering the calorimeter. Therefore, the contributions to the enthalpies due to changes of state of the pure components are included in Hy and HF.
HE FOR (CARBON DIOXIDE
+ DECANE)
177
(4
-6000
0
I 0.2
T/K I 0.4
I 0.6
I 0.8
_I
1
X
FIGURE I. Plots (a) of HE against x for (xC0, + (I - x)C,,H,,} as a function of temperature and (b) of pressure against temperature indicating conditions at which HE was measured. 0. This work.
Values of n, and n, are related to the mole fractions x,, xg, and x by the relations: xlnl+ xgng = x(n, +n,), (4) (l-x,)n,+(l--x&I,= (I-x)(n,+n,); (5) x, and xg have constant values for each isotherm due to the two phases being in equilibrium at a fixed pressure and temperature. Figure 2 indicates that the vapor mixtures at 308.15,313.15, and 323.15 K consist mainly of COZ (see horizontal lines at 308.15, 313.15, and 323.15 K joining the liquid and vapor regions). Values for xg can be estimated for all three temperatures from the data of Reamer and Sage.‘14’ The values are all greater than 0.999 and this allows us to assume without introducing any significant error that xg = 1. Therefore, the only important contribution to H! is the enthalpy change associated with the fluid CO, becoming vapor. The value of x, at each of the temperatures studied is that corresponding to the two-phase boundary, and, consequently to the most negative value of HE in figure la. In other words, the process taking place in the calorimeter for any given mixture of composition x is the
C. PANDO
178
FIGURE and vapor
2. Phase diagram for j&O, regions together with critical
+ (1 - x)C,,H,, locus.
ET AL.
I at 7.58 M Pa showing
Iiqiid.
(liquid
+ vapor ).
formation of a liquid of fixed composition x, and the gasification of the remaining carbon dioxide. Substituting into equation (3) the expressions for n, and ng obtained from equations (4) and (5) when .xg = 1, we have HE = fx(Hr-HE:)+x,H~-H~)/(.w,-
1).
(6)
In the vicinity of the critical locus (figure lb), we may assume that the enthalpy of vaporization H: of CO, is sufficiently small to be neglected. This is confirmed by the experimental values of the excess enthalpy since it can be seen from equation (6) that HE goes to H! when x goes to unity. If we substitute into equation (6) the values of Hy and x, estimated from figures la and 2, we obtain for each temperature a straight line. Values of HE for the three temperatures calculated from equation (6) together with the experimental HE values in the two-phase region have been plotted against x in figure 3. The good agreement obtained between the calculated and experimental HE values indicates that equation (6) adequately describes the behavior of (carbon dioxide + decane) in the two-phase region. The small endothermic section observed for the 323.15 K isotherm (see table 1, x > 0.99) corresponds closely to that region in figure 2 which lies between the intersections of the isotherm with the critical locus and with the pure COZ line. No measurements were made in the corresponding regions at 313.15 and 308.15 K. We can now interpret the variations observed in the value of HE with x at 308.15, 313.15, and 323.15 K. If we start our experiment with a mixture rich in C02, most of the fluid COZ will become vapor while a small portion will dissolve into the liquid
HE FOR (CARBON DIOXIDE
+ DECANE)
179
0
0.6
0.7
0.8
0.9
1
X
FIGURE 3. Plot of HE against {xCO,+(~-X)C~,,H~~} experimental results, 0, for high x.
comparing
equation (6), -,
with
decane to form a certain amount of a liquid mixture whose fixed composition at a given temperature corresponds to that of the two-phase boundary in figure 2. The amount of this liquid mixture will depend on the amount of decane entering the calorimeter. As the amount of decane is increased at a given temperature values of HE become increasingly negative due to the greater amount of the liquid mixture present until a most negative value is reached corresponding to the two-phase boundary. Further increases in (1 -x) moves the mixture into the liquid region and leads to decreasingly negative values of HE. This could be the result of the proportionately smaller amounts of fluid CO2 being dissolved into liquid decane. The value of x corresponding to the most negative value of HE (figure la) can be predicted from the phase diagram (figure 2). For instance, at 330 K a value of x of 0.62 is determined from the two-phase boundary line (figure 2) and this value should correspond to the value of x for the most negative value of HE. The changes in HE with temperature from 283.15 to 323.15 K appear to be a combination of the solution of fluid COz into liquid decane and the change in the value of AC, for the mixture. As mentioned previously, the most negative values for HE at 308.15,313.15, and 323.15 K occur at x given by the liquid boundary shown in figure 2 where at each temperature, the maximum possible amount of CO, has been dissolved in the liquid decane. This indicates that the enthalpy change associated with the solution of fluid CO1 into liquid decane contributes to the large negative values of HE observed at each of these temperatures. Also, since the values of x corresponding to the most negative values of HE increase considerably as the temperature decreases from 323.15 to 308.15 K, it can be seen why the most negative values of HE and, in general, the values of HE in the two-phase region, are increasingly negative as the temperature is decreased in this interval. Also contributing to the magnitude of HE is the change in the value of AC, for the mixture with temperature. For a pure substance, at a constant pressure slightly greater than the critical pressure, as the temperature is increased through the critical temperature the heat capacity at
C. PANDO ET AL.
180
constant pressure C, exhibits a maximum. (16) This maximum becomes larger and sharper as the critical pressure is approached. Thus, since @H/BT), = C,. the change in the value of H becomes larger as the critical point of a pure component is approached. The same effect has been noted for the variation of HE with P and T in mixtures such as (methane + argon).‘3’ For ;xcoz+(l -x)C,oH22; (aHE/aT)p = AC, where ACp = (C&mixture)-xC,(CO,)-(1 -x)C,(C,,H,,)i. At a pressure slightly higher than the critical pressure and near the critical temperature of CO,, especially at high x, AC, will become large and negative as C,(C02) increases. The effect of temperature on AC, at x = 0.5 can be seen in figure la where the excess enthalpy experiences a moderate decrease (less positive) when the temperature is increased from 283.15 to 303.15 K, a large decrease (more negative) from 303.15 to 308.15 K (T, for CO1 is 304.21 K) and a small decrease (more negative) from 308.15 to 323.15 K. We have measured”” the HE values of (Freon-12 +N&‘dimethylacetamide) over a temperature range of 263.15 to 413.15 K spanning the critical point of Freon-12 (T, = 384.65 K). This mixture shows the same rapid change of HE with temperature near the critical point as (carbon dioxide + decane) indicating a similar effect of AC, on H". We appreciate the helpful discussions with Dr John L. Oscarson and his assistance with some of the experimental set-up and the help of Michael E. Post who made some of the experimental determinations. C. Pando wishes to acknowledge the Board of Foreign Scholarships and the Spanish Ministry of Education for their support through a Fulbright/MUI award. REFERENCES I. Christensen, J. J.; Hanks, R. W.; Izatt. R. M. Handbook @Heuts ofMi.Sng. Wiley-Interscience: New York. 1982. 2. Lewis, K. L.; Mosedale. S. E.; Wormald. C. J. .I. Chem. Thermo~~wamics 1977, 9. 221. 3. Mosedale. S. E.; Wormald, C. J. J. Chem. Thermo&namics 1977, 9, 483. 4. McFall, T. A.; Post. M. E.; Christensen. J. J.; Izatt. R. M. J. Chem. Thermodynamics 1981, 13. 441. 5. Christensen. J. J.; Izatt, R. M.; Post. M. E. ; McFall. T. A. Thermochim. Acta 1981. 50. 73. 6. Christensen, J. J.; Hansen, L. D.; Eatough. D. J.; Izatt, R. M.: Hart. R. M. Rev. Sci. Instrum. 1976, 47. 730. I. Christensen. J. J.; Hansen, L. D.; Izatt, R. M.; Eatough, D. J.; Hart. R. M. Rev. Sci. Insrrum. 1981, 52. 1226. 8. Schneider, G. M.; Stahl, E.; Wilke, G. : editors. Extraction with Supercritical Gases. Verlag Chemie : Weinheim. 1980. 9. Christensen, J. J.; Izatt. R. M.; Eatough. D. J.; Hansen, L. D. J. Chem. Thermo&numics 1978, IO, 25. IO. McFaII, T. A.; Post. M. E.; Collins. S. G. ; Christensen. J. J. : Izatt. R. M. J. Chem. Thermod~wzmics 1981, 13, 41.
Il. IUPAC Carbon Dioxide Infernational Thermo&wnic Tables of the Fluid State. Pergamon Press: Oxford. 1976. 12. Savini. C. G.; Winterhalter. D. R.; Van Ness, H. C. J. Chem. Eng. Dota 1965, 10. 168. 13. Handbookfor Chemistry and Physics 56th edition. The Chemical Rubber Company: Cleveland. Ohio, 1975-1976.
14. Reamer, H. H.; Sage, B. H. J. Chem. Ena. Data 1%3, 15. Reamer. H. H.; Sage, B. H. J. Chem. Eni. Data 1965, 16. Hirschfelder. J. 0.: Curtiss. C. F.: Bird. R. B. Molecular Wiley: New York. 1964, p. 367. 17. Schofield. R. S.; Post, M. E.; McFall. T. A.; Thermodynamics to be published.
8, 509. 10. 49. Theor\, ofGases
crnd Liauid.7 2nd edition. John
Izatt. R. M.: Christensen. J. J. J. Chem.