The excess enthalpies of (carbon dioxide + cyclohexane) at 470.15, 553.15, and 573.15 K from 7.50 to 12.50 MPa

M-1962 .I. Chem.

Thermodvnamics

1987,

19. 47-56

The excess enthalpies of (carbon dioxide + cyclohexane) at 470.15, 553.15, and 573.15 K from 7.50 to 12.50 MPa J. J. CHRISTENSEN, and R. M. IZATT

T. A. C. WALKER,

D. R. CORDRAY,

Departments of Chemical Engineering and Chemistry, Brigham Young University, Provo, Utah 84602, U.S.A. (Received IO December 1986; in,final,fiwm

14 March

1986)

The excess molar enthalpies Hz{xCO, + (1 -x)c-C,H r2} were measured in the vicinity of the critical locus and in the supercritical region. Large positive H$ were observed depending on the compositions, pressures, and temperatures of the mixtures, in contrast to large negative HEs measured previously at lower temperatures. A modified Soave equation of state was used to correlate Hk over the temperature range of 308.15 to 573.15 K and a pressure range of 7.50 to 12.50 MPa with an average standard deviation of 352 J mol-‘.

1. Introduction A program is under way in this laboratory to measure the excess molar enthalpies Hz of binary mixtures in the vicinity of the critical points of one or both of the components. Results for several (carbon dioxide + a hydrocarbon)“-13’ and (a fluorocarbon + a hydrocarbon)(r4-“’ mixtures have been reported. In these, HE showed increased negative character as the critical point of the component having the lower critical temperature was approached from below along an isobar. In cases where the critical point of the second component was approached, large positive HEs were observed. With the development in this laboratory of a high-temperature flow calorimeter,‘21’ it became possible to extend the temperature range of HL{xCO,+(l -x)c-C,H,,} previously measured at 308.15, 358.15, and 413.15 K.“’ The present work reports values of Hf,{xCO, + (1 -x)c-C6Hi2) at 470.15, 553.15, and 573.15 K from 7.50 to 12.50 MPa. These Hft, values should provide an excellent test for equations used to model the behavior of mixtures near the critical points of their component. In this paper, the Hfi, values have been fitted with a modified form of the Soave equation in an attempt to predict mixing behavior better in the critical region. By acceptance of this article, the publisher acknowledges the right of the US. Government to retain a non-exclusive royalty-free license in and to any copyright covering this paper. 002l-9614,‘87:010047+

IO $02.0010

r.’ 1987 Academic Press Inc. (London) Limited

48

J. J. CHRISTENSEN TABLE .x

Hk/(J expt

1. Experimental molt

‘)

and calculated .Y

cab

excess enthalpies

Hk/( J. mol - I) expt

79 98 203 207 433 716 648 947 1190 1270 1750

69 69 230 230 415 700 700 976 1240 1240 1760

0.3683 0.3934 0.4179 0.4417 0.4417 0.5094 0.5309 0.5309 0.5518 0.5720 0.6208

1780 2080 2130 2560 2540 3120 3300 3360 3600 3760 4240

0.0583 0.1133 0.1820 0.2458 0.3053 0.3609 0.4129 0.4618

35 47 159 266 410 807 1260 1640

31 63 134 266 490 855 1250 1630

0.5077 0.5510 0.5918 0.6304 0.6669 0.6844 0.7015 0.7099

2090 2330 2660 2950 3180 3280 3460 3460

0.0429 0.0789 0.1161 0.1517 0.1860 0.2191 0.2509 0.2815 0.3111 0.3672

4 23 60 80 122 154 251 276 356 614

19 36 56 81 115 160 219 292 382 613

0.3938 0.4195 0.4444 0.4685 0.5145 0.5364 0.5577 0.5983 0.6178 0.6367

747 869 1040 1270 1690 1740 1950 2250 2350 2450

0.0714 0.1054 0.1383 0.2011 0.2311 0.2884

1460 2400 3140 4700 5280 6170

1510 2350 3190 4680 5270 6100

0.3158 0.3424 0.3683 0.3934 0.4417 0.4874

6390 6420 6510 6510 6390 6200

0.0770 0.1133 0.1483 0.1820 0.2144 0.2458

574 919 1380 1800 2370 2880

544 926 1370 1860 2370 2860

0.3053 0.3609 0.4129 0.4377 0.4618 0.5077

3770 4210 4560 4660 4690 4610

I

talc. 470.15

0.1054 0.1054 0.1702 0.1702 0.2311 0.2602 0.2602 0.2884 0.3158 0.3158 0.3683

ET .4L.

1760 2010 2240 2480 2480 3140 3350 3350 3550 3750 4230 470.15 1980 2310 2630 2920 3200 3340 3440 3420

Hk for [rCO,

+ ( I - .x)~,-C~H,

zj

Hk/(J.mol-‘) expt

cab

4460 4770 4710 4740 4670 4730 4540 4530 4230 3890 3690

4500 4750 4750 4750 4680 4680 4570 4440 4270 3870 3650

0.8116 0.8539 0.8675 0.8937 0.9190 0.9432

3390 2610 2350 1920 1510 1050

3410 2670 2420 1930 1460 1010

0.9891

166

188

3440 3280 3200 3120 3130 2810 2530 2220

3390 3320 3230 3120 3120 2860 2560 2230

0.8765 0.9012 0.9248 0.9474 0.9691 0.9899

1870 1590 1190 858 513 163

1890 1540 1190 844 501 165

2630 2640 2690 2630 2600 2520 2500 2290 2100 1860

2550 2610 2640 2660 2620 2510 2510 2340 2120 1870

0.8794 0.8794 0.9036 0.9267 0.9488 0.9699 0.9902

1610 1600 1340 1060 737 435 145

1600 1600 1320 1030 732 437 144

5950 5490 5170 4780 3930 3080

5870 5510 5140 4750 3960 3160

0.8116 0.8675 0.9190 0.9432 0.9666

2790 1990 1210 898 444

2760 1970 1210 848 497

4450 4300 4140 3700 3300 2800

4510 4330 4120 3600 3310 2840

0.8237 0.8765 0.9012 0.9474 0.969 1

2320 1670 1340 765 413

2340 1680 1350 720 422

K. 7.50 MPa 0.6487 0.6843 0.6843 0.6843 0.7015 0.7015 0.7183 0.7347 0.7507 0.7818 0.7969 K, 10.50 MPa 0.7182 0.7344 0.7502 0.7656 0.7656 0.7953 0.8237 0.8507

470. I5 K. 12.50 MPa 753 907 1070 1250 1610 1790 1950 2250 2370 2480 553.15 6340 6480 6550 6560 6430 6180 553.15 3700 4270 4560 4630 4660 4630

0.6550 0.6729 0.6903 0.7072 0.7396 0.7705 0.7705 0.7997 0.8276 0.8541 K, 7.50 MPa 0.5308 0.5740 0.6113 0.6486 0.7182 0.7818 K. 10.50 MPa 0.5509 0.5918 0.6303 0.7015 0.7344 0.7806

H:{.rCO:+(l-.x)c-C,H,,; TABLE .Y

H~l(J.mol~‘)

x

Hk/(J’mol

expt

talc.

expt

0.0403 0.1 161 0.1517 0.1860 0.2191 0.2509

29s 910 1110 1460 1700 2070

299 859 1140 1430 1740 2050

0.2815 0.3111 0.3672 0.3938 0.4195 0.4444

2370 2630 3210 3470 3680 3830

0.0714 0.1054 0.1383 0.2011 0.2311 0.2602 0.2884 0.3158

1520 2510 3750 5200 5640 5960 6110 6050

1520 2580 3650 5250 5690 5930 6040 6070

0.3158 0.3424 0.3683 0.3935 0.4417 0.4875 0.5309 0.5309

6090 5970 6060 5900 5690 5540 5310 5340

0.0393 0.0770 0.1133 0.1820 0.2145 0.2458 0.2761 0.3336

231 809 1180 2450 2980 3330 3750 4300

234 701 1270 2440 2950 3390 3760 4280

0.3609 0.3609 0.3873 0.4129 0.4378 0.4618 0.5077 0.5510

4440 4400 4570 4650 4650 4700 4590 4340

0.0402 0.0789 0.1161 0.1517 0.1860 0.2191 0.2509 0.2815 0.2815

378 666 1030 1390 1830 2120 2500 2900 2910

335 679 1040 1410 1790 2170 2540 2890 2890

0.3111 0.3396 0.3672 0.4195 0.4195 0.4444 0.4685 0.4919 0.5145

3200 3530 3590 3940 3930 3910 3960 3980 3930

49

l--continued ‘)

9

talc. 553.15 2370 2680 3230 3460 3640 3790

*

Hi/(J.mol-‘)

Hi/(J

mol

expt

talc.

0.6729 0.7396 0.8276 0.8794 0.9488

3520 3030 2200 1590 694

3510 3020 ‘180 1590 716

5040 4730 4380 4010 3630 3230 2840 2470

0.8401 0.8675 0.8937 0.9190 0.9432 0.9666 0.9891

2060 1760 1460 1150 752 476 134

3100 1760 1430 1110 796 485 166

4160 3870 3650 3410 3190 2790 2620 2190

4170 3930 3670 3400 3120 2830 2530 2230

0.8507 0.8765 0.9012 0.9248 0.9474 0.969 I 0.9899

1930 1630 1350 979 657 393 170

1930 1620 1310 1010 709 417 136

3830 3760 3650 3480 3320 2820 2680 2290 2090

3870 3800 3630 3450 3250 2830 2600 2360 2100

0.8541 0.8794 0.9036 0.9267 0.9267 0.9488 0.9699 0.9902

1850 1540 1250 908 929 621 438 174

1820 1540 1240 943 943 651 375 118

expt

talc.

3890 3960 4000 3940 3860 3690

3890 3960 3990 3980 3880 3710

5080 4690 4370 4010 3570 3280 2790 1500

’)

K. 12.50 MPa 0.4685 0.4919 0.5145 0.5577 0.5983 0.6367

573.15 K. 7.50 MPa 6070 6040 5990 5920 5740 5540 5310 5310 573.15 4450 4450 4560 4620 4650 4640 4550 4390 573.15 3190 3450 3650 3900 3900 3960 3980 3960 3920

0.5721 0.6113 0.6487 0.6843 0.7183 0.7508 0.7819 0.8116 K. 10.50 MPa 0.5918 0.6304 0.6669 0.7015 0.7344 0.7656 0.7953 0.8237 K. 12.50 MPa 0.5364 0.5577 0.5983 0.6367 0.6729 0.7396 0.7705 0.7997 0.8276

2. Experimental The high-temperature flow calorimeter used for the measurements and the experimental procedure have been described. Q” All runs were made in the steadystate (fixed-composition) mode. Two high-pressure ISCO syringe pumps supply at a constant rate the two fluids to be mixed. The total flow rate was 0.008333 cm3. s- ’ for all temperatures and pressures studied. Previous results obtained with the calorimeter were reproducible to 0.8 per cent or better over most of the molefraction range (0.2 < x < 0.8). (21) Reproducibility of results in the present

50

J. J. CHRISTENSEN

TABLE 2. Coefficients {xCOz +(l -x)c-C,HIZ}

and standard deviation s for by equations (I) and (2) and liquid x, and xu Equation

PIMPa

Co

7.50 10.50 12.50

13205 8708.6 5971.7

7.50 10.50 12.50

24397 18552 15893

7.50 10.50 12.50

21905 18286 15805

C,

Cl

C3 --~

C4

-14081 -17857 - 11447

0 11193 6983.1

0 0 0

0 0

0 0 19889

0 0 0

0 5341.4 0

0 -2576.5 0

0

0 0 0 573.15

-11300

0 -8293.0

0

0 Equation

4

A,

- 1847.8 - 1914.7

9792.2 7675.0

470.15 7.50 10.50 12.50

(1)

553.15

,’

D,

1.0463 0.5492 0.7515

1.6408 0.8452 1.3987

0 0 0

0 0 0

0 0 0

45 30 29

-0.5703 -0.1602 - 1.3341

0.0957 0.2647 1.8169

0.4255 0.8667 0

0.4147 1.2633 0

0 0.4546 0

50 43 29

-0.6961 0.7414 0 0 1.3556 0.1894

1.2572 0 -0.8669

49 50 45

K

K

K -0.4708 0 -0.1922

-0.2522 0 0.4452

(2) s

interval xcxcx,

K 49 34

0.245 4 x $ 0.673 0.313
K

7.50 10.50 12.50

none none none 573.15

7.50 10.50 12.50

Da

D,

D2

0 0 0 553.15

-24560

least-squares representation of Hk for and vapor equilibrium phase compositions,

D, ~~~~ ~~ ~-

470.15

PIMPa

ET /tL

-

K none none none

investigation was + 1 and &2 per cent. This uncertainty was due mainly 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 cyclohexane (Phillips Petroleum Co., greater than 99 moles per cent pure). Before being used, the CO, was filtered through a Matheson gas pruifier model 450 which also contained a molecular-sieve desiccant. The cyclohexane was stored in sealed 1 dm3 bottles over approximately 50 cm3 of Davison molecular sieve (0.3 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. 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

H:{xCO,+(l-x)c-C,H,:}

51

densities of carbon dioxide at 298.15 K and at 7.50, 10.50, and 12.50 MPa (0.755, 0.822, and 0.846 g*cme3, respectively) were calculated by interpolation from the IUPAC tables.“” The densities of cyclohexane at 298.15 K and these pressures (0.782, 0.785, and 0.787 g.cme3, respectively) were extrapolated from those reported at 310.93 K and 344.26 K for pressures from 6.9 to 13.8 MPa by Reamer and Sage.‘*“’

A.

FIGURE 1. Plot of Hfi, against x for (xCO,+(l-x)c-C,H,,} as a function 10.50; and 0, 12.50 MPa: at (a), 470.15 K: (b). 553.15 K; and (c), 573.15 K.

of pressure.

0.

7.50;

52

.I. J. CHRISTENSEN

ET AL

3. Results and discussion Excess molar enthalpies entire composition range The results are given in studied were curve fitted Hk/(J.mol-‘)

=

were determined for [.uCO, + ( 1 - x)c-C,H, zi- over the at 470.15. 553.15. and 573.15 K from 7.50 to 12.50 MPa. table 1. Values for HG at each temperature and pressure using the equation: 1+ f

D,(l-2.~)

a& C,( 1 -2x)“.

(1)

n=l

The coefficients C, and D, are given in table 2 together with standard deviations. Where the Hz values vary linearly with x in the CO?-rich region they have been fitted to the equation: Hz/(J . mol- ‘) = A, + A I x.

(2)

The coefficients A, and A,, the standard deviation s. and the mole-fraction intervals for the linear sections of the isotherms are also given in table 2. Figure 1 gives the plots of HE(x) for the three temperatures studied. The linear sections of the isotherms in figure l(a) correspond to the two-phase region where a gaseous and a liquid mixture of fixed composition, for a certain condition of pressure and temperature, are in equilibrium. The vapor and liquid equilibrium phase compositions (xB and x, respectively) can be determined from figure l(a) as the x coordinates of the intersections of the extrapolated straight lines and the curves describing the excess enthalpy outside the two-phase region. These values of xg and x, are given in table 2. Figure 2 shows a critical-locus curve for this mixture from Krichevskii and Sorina.‘“4’ Also shown in figure 2 are the critical points of the

T/K FIGURE 2. Plot of p against T for {.xCO, + (1 - u)c-C,H ,*} showing critical points and critical locus. The conditions at which the measurements were made are indicated: 0, this study; 0. previous study.‘5’

53

TIK

FIGURE 3. Plot of kAB against T for {xCO, +(I -x)c-C,H average k,, giving best correlation at each temperature; -.

, z/ for this study and a previous study: @. based on equation (I?).

two pure components as well as points indicating the conditions under which the Hk values were measured in this and a previous study.‘5’ We have modeled HE for several previous binary mixtures of (carbon dioxide + a hydrocarbon)‘*-’ 3, and (a fluorocarbon + a hydrocarbon)“8-20’ using various equations of state. A combination of the hard-sphere repulsion term derived by Andrews et ~1.‘~~’ with the attraction term proposed by Soave’26’ has given the best correlation of past results. In this paper we have compared> the observed variation of Hk with the Andrews-Soave (ASV) equation of state. Hff,s from both this study and from a previous studyf5’ were used in the correlations. The ASV equation may be written as p = Po-a[1+mll-(T/T,)‘“).]2/jVm(I/m+b)),

(3a)

or as P = Po-d{Kl(K+~))~

(3b)

where m = (0.48508+ 1.55171w-0.15613~‘) and o is Pitzer’s acentric factor.‘2” The coefficients in the equation for m were taken from the correlation of Graboski and Daubert.(28) The values of w from Reid, Prausnitz, and Sherwood’29’ were used. The hard-sphere repulsion term p. is RT[28q2/bq-(4/b)ln(l

- q)-( 14.38/b)ln 4 -(47.31/b)ln((l

-0.721Oq)/(l

- 1.35O~)jJ

(4)

where q = b/4vm and 4 = (1 -2.071q+0.9736q2). The derivation of residual molar enthalpies Hi(&',, T) from an equation of state has been outlined by Lewis et .1.‘30’ and yields

HR,(& T) = a+m(T/T,)1~2cc”2}(a/b)ln{V~/(V~+h)}+pV~-RT.

(5)

The predicted excess molar enthalpy is given by

H: = H:{xCO, +(l -x)c-C,H,,}

-xHR,(CO,)-(1

-x)H;(c-C,H,&

(6)

54

J. J. CHRISTENSEN

ET AL.

1 -i ‘;j E 0 2 Y WE z -1 -2

0

0.2

0.4

x

0.6

0.X

0

I

0.2

0.4

.r

0.6

0.X

FIGURE 4. Plot of Hi against x for {xCO1+(l-x)c-C,H,,} (a), at T= 358.15 K; (b), at T = 553.15 K: 0, IJ, experimental; - - -, from ASV equation with k,, = 0.885; -, from ASV equation with k,, from equation (12).

The constants a and b in equation (5) for the pure components were obtained from the critical conditions @p/a&), = 0 and (a2p/aV,‘), = O:(25,31+32P a = 0.461891R2T,2/p,

(7)

b = 0.105007RT,/p,.

63)

and The mixtures were treated as single fluids having the constants

b= xi xibiy a = cj xi XiXjUij,

(9) (10)

and aAB

=

kAB(aAA

aBB)1’29

(11)

where A = CO2 and B = C-C,H,,. A mole-fraction weighted mean of the w values of the pure components was used for the o values of the mixtures (equation 9 with w replacing b). Similarly, a geometric mean of the T, values of the pure components was used for the pseudo-critical temperature of each mixture with TM-9 = {T,(A) T,@))“2 equation (10) with T, replacing a. The interaction parameter k,, was varied to obtain the best overall fit (lowest standard deviation) with the values at all temperatures and mole fractions. A value of b = 0.885 achieves the best fit, resulting in a standard deviation of

H:fxCC& + (1 -x)c-C,H,

55

2i

FIGURE 5. Plot of 195 against T for fxCOz +(I -x)c-C,H,,j as a function of pressure for s = 0.5: 0, ,& and 0. experimental; -. from the ASV equation wi& kAB from equation (12).

717 J.mol-‘. When values from individual tem~ratures and pressures were correlated independently, the optimum values of k,, were found to vary strongly with temperature and weakly with pressure. Variation of kAB with temperature has also been found in other mixtures!‘2v33’ A plot of optimum k,, values averaged over all pressures at each temperature is shown in figure 3. A cubic equation in temperature gives the best fit through the kAB values and results in the equation: k,, = 5.4679-0.0366(T/K)+9.2560~

10-5(7-/K)2-7.36f1

x 10-s(T/K)3.

(12)

Incorporating equation (12) into the ASV equation resulted in a standard deviation of 352 J.mol-‘. Figure 4 shows the correlation of the ASV equation with the ex~rimental results for two tem~ratures using both methods for dete~ining k,,. In figure 4(a) little improvement is seen by using one method over another while figure 4(b) shows a great improvement when values of k,, are obtained from equation (12). A comparison of HE,s caiculated from the ASV equation {using equation (12) for k,,} with experimental WLs at various temperatures for three different pressures at x = 0.5 is shown in figure 5. The equation correctly predicts the shape of the curves and generally gives good estimates for the values of HjLZI.The usual assumption is that k,, is independent of temperature, pressure, and composition. However, with results covering a wide temperature range, this assumption is not valid and a better understanding of the physical significance of the interaction parameter is needed. This work was funded by U.S. apartment Sciences. Contract No. DE-AC02-82ER13024

of Energy, Office of Basic Energy and by the Donors of the Petroleum

J. J. CHRISTENSEN

56

ET >4L.

Research Fund administered by the American Chemical Society. We appreciate the aid given to us in collecting the results by P. W. Faux. P. R. Harding, and C. Orme. REFERENCES I. Pando. C.: Renuncio. J. A. R.; McFall, Thermodynamics

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