The critical constants and orthobaric densities of acetone, chloroform, benzene, and carbon tetrachloride1

The critical constants and orthobaric densities of acetone, chloroform, benzene, and carbon tetrachloride1 A. N. CAMPBELL AND R. M. CHATTEIUEE Department of Chemistry, University of Manitoba, Winnipeg, Manitoba Received April 18, 1969 The specific volumes and pressures in the saturated states of the pure liquids acetone, benzene, chloroform, and carbon tetrachloride have been determined from a temperature of 100 "C and a pressure of about 2 atm up to the highest temperatures and pressures at which liquid and vapor coexist. The critical temperatures have been determined by the method of disappearance of meniscus, critical densities from the law of the rectilinear diameter, and critical pressures by extrapolation of the log P vs. l/tline to the critical temperature. Canadian Journal of Chemistry, 47, 3893 (1969) Acetone, chloroform, benzene, and carbon tetrachloride were chosen for study as a preliminary to an investigation of critical phenomena in binary systems containing them. The literature data, even of well known liquids such as those of this research, are surprisingly limited. A survey of critical data, measured in different ways, shows not only a wide variation in the values reported by different investigators for a single liquid, but very frequently a considerable variation in the data of the same investigator. Campbell, Kartzmark, and Chatterjee (1) have investigated the excess volumes and total and partial pressures of the binary systems acetonechloroform, benzene-chloroform, acetonebenzene, and of the ternary system acetonechloroform-benzene. From these data, the excess Gibbs free energies and excess entropies were calculated. Since the publication of this work, Abbott (2) has obtained second virial coefficients from measurements on a vapor density balance. The orthobaric densities and vapor pressures of acetone, chloroform, and benzene have previously been reported by us (3). Experimental The methods of purification, experimental technique, and results have already been reported for acetone, chloroform, and benzene (3). It remains only to report the purification of carbon tetrachloride. This was distilled through a vacuum jacketed column with glass helix 'An extensive bibliography and complete details of experimental procedure are to be found in the Ph.D. thesis of Chatterjee at University of Manitoba, Winnipeg, Manitoba, 1968. packing. The temperature of distillation was found to be constant throughout (76.6 "C at 750 mm Hg). The middle third fraction was examined for purity by gas chromatography. A column of 6 ft length, containing dimethylformamide on chromosorb P as supporting material for the liquid stationary phase, was used. The carrier gas was helium. Only one main peak was observed. All liquids were transferred to the vacuum line (for removal of noncondensible gases) in a dry-box. Experimental Results The orthobaric densities and vapor pressures of acetone, benzene, and chloroform have been reported previously (3). Table I gives the saturated densities of carbon tetrachloride at approximately 40 temperatures, ranging from near the standard boiling point to the critical point. Critical phenomena were observed, at a constant temperature of 283.1 5 "C, at the following densities: 0.4953, 0.5095, 0.5424, 0.5578, 0.5829, and 0.6047 g/cc. The vapor pressures of carbon tetrachloride are shown in Table 11. The critical temperatures of all 4 liquids were observed visually with the following results: acetone, 235.0"; benzene, 288.95"; chloroform, 262.9"; carbon tetrachloride, 283.15". Discussion Because of the difficulties discussed by Campbell and Chatterjee (3), we obtained the critical pressure by an extension of the log P vs. 1/T line to the critical temperature; the agreement with the latest published data is good. Our results are Acetone PC = 46.96 atm Benzene PC = 48.22 atm Chloroform PC = 52.59 atm Carbon tetrachloride PC = 44.98 atm

CANADIAN JOURNAL OF CHEMISTRY. VOL. 47, 1969 TABLE I Orthobaric densities of carbon tetrachloride (t, = 283.5") Density of liquid (g/cc) Temperature Density of vapor (g/cc), PC) Experimental Calculated experimental (t, - t)'i3 - - 0.9641 0.9419 0.9120 0.8838 0.8560 0.8261 0.8059 0.7910 0.7612-0.7284 0.9659 0.1960 0.9444 0.2122 0.9139 0.2351 0.8869 0.2568 0.8567 0.2792 0.8241 0.3076 0.8015 0.3258 0.7886 0.3386 - - 0.3788 - - "Values were calculated using eq. [I] and the constants given in Table 111. The critical density can only be obtained by extrapolation of results obtained at lower temperatures and it is the most difficult of the 3 constants to measure accurately. The most commonly used method is to extrapolate the mean of the orthobaric liquid and vapor densities to the critical temperature, that is, to employ the law of Cailletet and Mathias, expressed analytically as +(PI + P") = P C + b(tc - t) We restricted the application to a range of 50" below the critical temperature and obtained the following results Acetone p, = 0.269 g/cc Benzene p, = 0.306 g/cc Chloroform p, = 0.491 g/cc Carbon tetrachloride p, = 0.557 g/cc The method of the rectilinear diameter, whatever may be its theoretical basis, or lack of it, does in fact work rather well if the true values of the orthobaric densities are known. It has been shown repeatedly (4) that the dependence of both orthobaric densities on temperature are represented by a leading term

CAMPBELL AND CHATTERJEE: CRITICAL CONSTANTS AND ORTHOBARIC DENSITIES 3895 TABLE I1 baric density vs. (T, - T)'/~, two straight lines Vapor pressure of carbon tetrachloride are obtained for each substance, which, presumably, intersect at the critical density for Pressure (atm) Temperature (T, - T) = 0. Since, however, our experimental ("c) Experimental* Calculatedt measurements do not extend quite to the critical temperature, we are really not justified in assum- 374.65 2.014 2 008 383.00 2.464 2:473 ing that the 113 power relation extends all the way 389.50 2.892 2.891 and, even if it does, the possibility of a truly 394.00 3.217 397.25 3.453 : horizontal top still exists. There is no doubt that 401.50 3.788 3.801 the top is "flat" in the ordinary sense of the 405.70 4.167 4.167 word, but whether it is truly horizontal in the 411.30 4.701 415.65 5.037 : mathematical sense can never be decided. It is 418.95 5.492 5.493 an old observation, recently reaffirmed by 420.80 5.771 5.707 Lorentzen (5), that the disappearance of the 425.50 6.253 6.253 433.05 7.291 7.233 meniscus in the body of the tube, and not by 436.75 7.726 7.739 "moving out" (as Lorentzen calls it), is not con- 444.00 8.800 448.05 9.471 : fined to the critical volume, but this does not 453.30 10.43 10.40 necessarily prove that the nose of the curve of 458.85 11.45 11.41 orthobaric densities vs. temperature is horizontal. 463.70 12.38 12.36 469.55 13.61 13.58 In our previous paper (3), we obtained critical 475.75 14.95 14.98 densities by extrapolation of p, and pv plots 481.90 16.43 16.45 against (T, - T)'I3, with the result that our 487.55 17.86 17.91 493.10 19.39 19.43 values for the critical density are much lower than 498.45 21.02 21.01 those reported by other workers. The discrepancy 504.20 22.84 508.40 24.18 ~~:~~ is due, however, to the method of extrapolation, 513.15 25.82 25.79 and not to experimental inaccuracy. The values 516.25 26.94 26.90 for critical density which we now propose, based 520.70 28.62 524.60 30.06 : on the law of rectilinear diameter, agree very well 529.20 31.95 31.92 with literature values2. 532.75 33.48 33.42 Francis (6) has shown that the saturated den- 537.30 35.32 35 37 540.90 37.05 37:05 sity of the liquid phase (i.e. p, under its own vapor 544.50 38.72 38.75 pressure) as a function of t (temperature on the 547.95 40.41 550.10 41.52 : centigrade scale) can be expressed by the empirical 553.25 43.21 43.19 equation 554.70 44.06 43.99 'Standard deviation = 0.038 atrn. [I 1 pl = A + Bt + C/(E- t) tvalues were calculated from eq. [41 using the constants given in Table IV. In this equation, A is a constant, generally about 0.06 higher than the density at 20 "C; B is P ~ to (Tc - ~ T)"3. when P and if the ~ the slope ~ coefficient, ~ a little ~ lower than ~ the (T, - T)'I3 relation is obeyed, the slope of the ~ ~ curve, e.g., of orthobaric density vs. T, will be very slight in the neighborhood of the critical ZWe are greatly indebted to Dr. D. Ambrose, of the Division of Chemical Standards, National Physical Latemperature. l-he question then is, is the slope boratory, Teddington, England, who has processed our of the curve near T, less than that predicted by data for benzene. He says in a letter of ~uly 25, 1968, the (T, - T)lI3 relation? If it is, the existence of "We have processed your values for benzene by our standard program to obtain the critical density from the a On the curve, with all this implies, law of rectilinear diameters, and to fit equations for the might then be conceded. To settle the point variation in (p, + p,) and (p, - p,) as power series in experimentally, one requires materials of the (Tc- T) and (Tc- T)'I3 respectively. From this we find your results give us a critical volume (sic. obviously highest purity and a temperature control of great density is intended) of 0.306 glee, in very close agreement accuracy, e.g., f 0.001". Since our control was with the values of Young and of Bender, Furukawa, and Hyndman. In fact, the agreement throughout the whole only good to f0.030, we can draw no conclusion. range of your experiments with those of Young is very When our data are plotted in the form of ortho- good."

Compound TABLE In Statistical analysis of the coe5cients of eq. [I]* Coefficients and standard deviations Multiple correlation Standard error of A B C E coe5cient estimate (x 10') Acetonet 0.840081-0.961206~10-~ -9.04112 269.0 0.999894 0.141144 (0.0) (0.186739 x (0.124244) (0.0) 0 Benzene? 0.934348-0.102571 x lo-' -8.52229 323.0 0.999920 0.132441 (0.0) (0.958163 x (0.0914741) (0.0) Chlorofomt 1.87908-0.324651 x lod2-0.125809 x lo2 297.0 0.999875 0.374888 1 (0.0) (0.406807 x (0.337744) (0.0) F 2: Carbon tetrachloride 1.69534-0.191825 x lo-' -0.145197 x lo2 317.0 0.999907 0.267937 (0.0) (0.189715 x 10-3 (0.169265) (0.0) *Standard deviations in parentheses.?data from ref. 3. TABLE IV Statistical analysis of the coefficients of eq. [4]* 5 < Coefficients and standard deviations Multiple correlation Standard error Compound A B C D coefficient of estimate -2 Acetonet 0.261062 x lo2-0.269100 x lo4-7.14004 1007.0 0.999897 0.427330 x lo-' (0.0) (0.948664 x 10') (0.497585) (0.0) Benzene? 0.131489 x lo2-0.195618 x lo4-2.96899 1200.0 0.999933 0.416288 x (0.0) (0.494399 x lo2) (0.248025) (0.0) Chloroformt 0.220199 x lo2-0.24567 x lo4-5.82143 1001.0 0.999997 0.756441 x (0.0) (0.137857 x lo2) (0.0706142) (0.0) Carbon tetrachloride 0.182145 x lo2 (0.01-0.226846 x lo4 (0.794815 x lo2) -4.61431 (0.3976081 1260.0 (0.0) 0.999842 0.646184 x lo-' *Standard deviations in parentheses.?data from ref. 3. B t 0 I w

CAMPBELL AND CHATTERJEE: CRITICAL CONSTANTS AND ORTHOBARIC DENSITIES 3897 expansion coefficient at ordinary temperature; C is an integer, generally between 6 and 10; and E is a number generally 34" above the critical temperature. We evaluated the 4 constants, for all 4 liquids, with the aid of an IBM 360165 computer, using a multiple regression method of analysis. The values of the constants, together with the multiple correlation coefficients, and the standard error of estimate, are given in Table 111. Using these constants, we calculated the liquid densities for all our experimental points. The agreement, is very good; the calculated liquid densities are within 0.0010 g/cc of the experimental values. Waring (7) has suggested a criterion, which need not be dealt with here, for the suitability of the various vapor-pressure equations. Recently, Ambrose et al. (8) have chosen the equations of Cox (9), Cragoe (lo), and Frost- Kalkwarf (1 1) as possibly the best. These are [2] Cox log P = A(1 - (T,/T)) [3] Cragoe log P = A + BT + CT + D T~ [4] Frost-Kalkwarf logp= A+ BIT+ ClogT+ DP/T~ In addition to these equations, Ambrose et al. (8) have used a 7-constant equation to represent their vapor-pressure data, but they find that this equati'on is only slightly better than the Frost- Kalkwarf equation over the whole temperature range, except for the range TR = 0.95 to 1.00 (TR = reduced temperature), where the7-constant equation gave a markedly better fit. We therefore chose to fit our data to the Frost-Kalkwarf equation. In this semi-theoretical equation, the slight reverse curvature in the plot of log P vs. l/t is explained on the basis of the non-ideal behavior of the vapor, together with the change in the heat of vaporization with temperature. If it is assumed that AH is linear in T and that the van der Waals a/v2 term is a first approximation to the deviation from ideality, the Frost-Kalkwarf equation is obtained by integration of the Clapeyron- Clausius equation. The constant D is related to the van der Waals "a" as follows so that D = 27Tc2/(64 x 2.303P,) The remaining constants were obtained by multiple regression analysis. The statistical analysis of the coefficients is given in Table IV, which lists the values of the constants, the standard deviation in their estimation, the values of the multiple correlation coefficient, etc. We have calculated the vapor pressures corresponding to each experimental point. The agreement with the observed values is fairly good for benzene, acetone, and carbon tetrachloride. The chloroform results scatter, especially at high temperatures. This is probably due to decomposition of this compound near the critical temperature and, therefore, we have not attempted to fit the data for chloroform to either the Cox or Cragoe equations. The constants3 obtained are shown in Table V. As we stated in our previous communication (3), we used the van der Waals equation to obtain the equilibrium pressure in our air manometer. Thus, at a temperature 0.45" below the critical temperature of benzene, the van der Waals equation gave a pressure of 3636.7 cm Hg. Had we used the Beattie-Bridgman equation we should have obtained a value of 3651.2 cm Hg, while the experimental value of Bender, Furukawa, and Hyndman (14) is 3641.0. The discrepancy is about 0.3% and this is about the same as the discrepancies between the observed vapor pressures and those calculated by the Cox and by the Cragoe equations. TABLE V Constants obtained by fitting vapor pressure data for benzene and carbon tetrachloride to the Cox and the Cragoe equations Constant Benzene Carbon tetrachloride log A,* 0.6408 0.6475 E* - 0.2445 0.1719 *Constant obtained for Cox equation (ref. 9).?Constant obtained for Cragoe equation (ref. 10). According to Thodos (12) 3We are indebted to Dr. J. F. Counsel1 (13) of the National Physical Laboratory, Teddington, for an analysis of our benzene and carbon tetrachloride data, using the equations of Cox and of Cragoe.

3898 CANADIAN JOURNAL OF CHEMISTRY. VOL. 47, 1969 Chebyshev (15) has discussed the use of poly- of pure liquids very often used to give other nomials of an orthogonal system in the solution thermodynamic functions. of the problem of the best approximation of continuous functions. Thus T log P can be fitted 1. A. N. CAMPBELL, E. M. KARTZMARK, and R. M. CHATTERJEE. Can. J. Chem. 44, 1183 (1966). to an series in and the constants 2. M. M. ABBO~. Ph.D. Thesis, Rensselaer Polyrearranged so that Tlog P is expressed as a technic Inst., Troy, New York. 1965. Chebyshev series. It is then possible to write 3. A. N. CAMPBELL and R. M. ~HAT-ERJEE. Can. J. Chem. 46, 575 (1968). T log P as 4. M. A. WEINBERGER and W. G. SCHNEIDER. Can. J. Chern. 30, 422 (1952); A. N. CAMPBELL and E. M. Tlog P = 112 a, + a,c, (x) + a,c, (x) + -. KARTZMARK. Can. J. Chern. 45, 2433 (1967); E. A. GUGGENHEIM. J. Chern. Phys. 13, 253 (1945); D. A. where a,, a,, a,,. - - are constants and c,(x), GOLDHAMMER. Z. Phys. Chern. 71, 577 (1910); H. VON JUpTNER. c,(x),... are Chebyshev polynomials. Truncation Z. 'hys. Chern. 85, 1 (1913); H. H. LOWRY and W. R. ERICKSON. J. Arner. Chern. Soc. may occur wherever desired by the size of the 49, 2729 (1927); D. COOK. Trans. Faraday Soc. 49, residuals and smoothness of fit4, and x is defined 716 (1953). 5. H. L. LORENTZEN. Acta Chern. Scand. 7, 1335 by (1953). = - (Tmax- Tmin)ll(Tmax - Tmin) 6. A. W. FRANCIS. Ind. Eng. Chern. 49,1779 (1957). 7. W. WARING. Ind. Eng. Chern. 46, 762 (19%). 8. D. AMBROSE, B. E. BRODERICK, and R. TOWNSEND. We think, however, that these extensive tables J, chern. sot. A 633 (1967). are of no interest to the general reader; they can 9. E. R. Cox. Ind. Eng. Chern. 28, 613 (1936). always be obtained directly from us. ~l~~~ and 10. C. S. CRAGOE. International critical tables. Vol. 111. McGraw-Hill Book Co., Inc., New York. 1928. Van Ness (16) have recently advocated the use of *. 228. orthogonal polynomials for representing thermo- 11. A. A. FROST and D. R. ULKWARF. J. Chern. Phys. 21, 264 (1953). dynamic excess functions and, in view of this, 12. G. THODOS. Ind. Eng. C-,ern. 42, 1514 (1950). we thought it worthwhile to mention their 13. J. F. COUNSELL. Private communication. application to vapor pressure data, as suggested 14. p- BENDER, G. T. FURUKAWA~ and J. R- H~~MAN. by ~ounsell, since vapor pressure is a property Ind Eng Chern 44 387 (1952) IS. L. A, LASER& and A. R. YANPOL~SKII. Mathematical analysis. The Pergarnon Press, Ltd., New York. 1965. 4Again, we are indebted to Dr. Counsel1 for carrying 16. R. L. KLAUS and H. C. VAN NESS. Chern. Eng. out the fits for the 4 compounds. Progr. Syrnp. Ser. 81, 63, 88 (1967).