EUQENEM, HOLLERAN AND GARYJ. GERARDI
528 Table IV: The Unit Compressibility Law for the CH4-CFr System"
Mole fraction of CH1
r
1.00
d, M b
1 2 3 4 5 6 7 8 9 10 11 12
T
494.61 480.85 466.69 452.30 437.88 423 53 409.23 395 05 380.88 366.66 352.49 338.44 I
I
A X 104
-7.0 2.6 4.5 1.9 -1.4 -3.4 -4.4 -2.9 -1.3 -0.6 1.o 4.9
1
0.50
0.75
0.00 c
0.25
T
A X 104
T
A X 104
T
A X 104
T
A x 104
475.34 460.67 445.72 430.77 415.81 400.88 385.91 371.14 356.21 341.35 326.38 311.46
-0.6 2.2 0.9 0.0 -0.9 -1.4 -2.6 0.5 0.2 1.4 0.5 0.4
477 09 461.07 445.07 428 95 412.93 396.89 380.99 365.06 349 IO9 332.99 316.88 300.72
-0.5 -0.3 0.1 -1.8 -1.7 -2.1 0.5 2.3 3.5 1.9 0.2 -2.4
487.69 469.79 452.35 434.93 417 59 400.20 382.89 365.49 348.07 330.45 312.75 294.94
3.8 -4.9 -4.3 -3.3 -0.8 $0.8 4.0 5.4 6.2 3.2 -1.2 -8.0
502.15 483.13 464.35 445.66 426.93 408 16 389.49 370.61 351.59 332.33 312.92 293.22
3.8 -2.6 -1.7 -0.3 +0.8 1.1 3.5 2.0 -2.1 -11.3 -23.0 -40.1
I
I
I
I
a The data are due to Douslin, Harrison, and Moore, ref 2. Twenty-four points at half-integer density intervals were used in the oalcuIations, except as noted below. The six density points above 9.5 M were not used in determining the constants for this gas because of the large highdensity deviations. A = T/TB d/do - 1.
+
for CF4, or an unsuspected high-density error in the measurements for this gas. Considering the range of the data, the results shown in Table IV represent the most accurate adherence to the unit compressibility law that has yet been observed. For the three mixtures taken together, the average absolute deviation from linearity over the entire experimental density range is only about two parts in ten thousand. Results such as these strengthen the view that the unit compressibility law is an exact law of nature, and again raise the question of a theoretical
explanation. The fact that the law can be obcyed by mixtures as well as pure gases provides the new information that the presence of three different pairwise molecular interaction potentials in one system does not interfere with its operation beyond affecting the constants. The T's and d's of the states for which the effects of the attractive and repulsive forces on 2 are balanced continue to be related by eq 1. It would seem that behavior of this generality should follow rather directly from the fundamental laws of mechanics and known molecular interactions.
Corresponding States of CH *,CF 4, and Their Mixtures by Eugene M. Holleran and Gary J. Gerardi Department of Chemistry, St. John's University, Jamaica, New York
ll4SB
(Reeetved August 5 , 1968)
An excellent correlation of the compressibilities of CHI, CF4, and their mixtures is obtained in the threeconstant system of corresponding states based on the unit compressibility law. The compressibility factors, 2 = PV/RT, of the two pure gases and two mixtures are calculated from the data for the 50-50 mixture with an average discrepancy of about 5 parts in 10,000. The reduced equation of state is given in the form, 2 = 1 BY, where Y is a function of reduced temperature, T/TB,and reduced density, d/do. A table is given for Y , from which 2 can be calculated from a knowledge of the three constants, TB,do, and k ~ .
+
Introduction The purpose of this paper is to report the correspond, ence found for the compressibility factors of C H ~CR, and their mixtures in the three-constant system of corresponding states based on the unit compressibility law (UCL). In this system the two UCL constants, The Journal of Physical Chemistry
T B and do, are used to reduce temperature and density. The Boyle temperature, TB,and the characteristic densib', do, are defined by the unit compressibility law'
TI/TB
+ &/do
=1
(1)E. M.Holleran, J . mem. Phys., 47,631s (1967).
(1)
CORRESPONDING STATESOF CH4, CF4,
AND
where T I and dl are the temperatures and densities of the states of the fluid in which the compressibility factor, 2 = PV/RT, equals unity. A good correspondence was found2 between the compressibility factors of Ar and Xe a t equal temperatures, 6, and reduced densities, 6, where 6
T / T B ; 6 = d/do
(2)
However, the extent of the agreement was made somewhat unclear by small uncertainties in the constants and the data. I n a more tractable temperature range, and with more reliable constants, the attainment of a good correlation of the compressibilities of Ar and CHI was found to require the introduction of a third constant.3 This constant was defined as the ratio of the deviations from ideality, ( 2 - l ) , of the two gases a t equal 6’s and 6’s. With this additional constant, the compressibility factor for CH4was calculated from the data for Ar with an average deviation of only four parts in ten thousand. The characteristic density do is related to the second and third virial coefficients, B and C, by the equation4 do = VB/CB
(3)
in which C g is C at T B , and V B is the Boyle volume, T B(dB/dT)T,. Using this relationship, the third constant mentioned above was identified6 as the ratio for the two gases of their constants Icg defined as = dovg = do2cB =
(4) Thus, the ( 2 - 1) ratio equals the k~ ratio, and according to this three-constant system of corresponding states, (Z - l ) / k g is taken as a universal function of 0 and 6. With this assumption, the compressibilities and related properties of fluids can be correlated accurately in terms of their three characteristic constants, T B ,do, and h B , with the effect of k~ given analytically. In order to obtain a correspondence as accurate as that found in ref 3, it is necessary to have reliable experimental values of these constants (at least Tg and do; k g can be found from the correlation). Uiifortunately such information is presently not yet available for most substances. However, the precise experimental data of Douslin, Harrison, and Moore6 for CH,, CF4, and three of their mixtures have provided accurate constants617 (Table I ) , and these gases and mixtures kg
529
THEIRMIXTURES
‘Vg2/cg
Table I: Constants for the Five Gases %OH4
TB.OK
do, mOl/l.
kg“
kb
k g ratio
100 75 50 25 0
509.2 490.5 493.1 505.0 521.0
35.73 32.87 30.77 28.91 27.70
1.94 2.22 2.43 2.62 2.88
0.7924 0.9038
0.80 0.91 1 .oo 1.08 1.19
1.0000
1.0903 1.2085
a Values found as V ~ d in o ref 5. b Optimum ratio of (Z given gas and 50-50 mixture at equal 0’s and 8’s.
- 1)’s of
therefore represent an excellent opportunity to apply this three-constant system of corresponding states. Compressibility Correlation. The basic correlation for two gases, 1 and 2, is given by
a t equal 0% and a’s, with the relative deviations from ideality determined by the k g ratio, k . From eq 5 the compressibility factors of four of the gases (the two pure gases, and the 75% and 25% CH, mixtures) were calculated from that of the 50-50 mixture taken as a reference standard. Assunling equal experimental accuracies for 2, and equally reliable constants, it can be seen from eq 5 that the best reference standard would be the gas with the largest I ~ B . I n this way, the ( Z 1)’s calculated for other gases from the reference would always be smaller than those of the reference, and experimental uncertainties would be minimized. The reverse calculation would magnify any errors in the data or in their empirical representation. For this reason argon, with its small k g , is not well suited as a reference standard, particularly for mixtures containing CFI, which has a very large k g . For the present calculations, the 50-50 mixture with its intermediate k g was a compromise choice as the reference gas because its data fit the unitcompressibility law better’ than 75% or 100% CF4, and its UCL constants are therefore more reliably known. The compressibility data used in the present correlation are those of ref G adjusted as in ref 7. The adjustment consisted of multiplying Z by a factor of (1 e ) , with the values of e X lo6used being 8, -7, -19, -29, -40 for the gases containing 100, 75, 50, 25, 0% CTT,, respectively. These constant overall adjustments for each gas were made in order to provide the best fit of the unit compressibility law and hence the most reliable T B and do values. For the most part, the adjustments are well within experimental error. They modify 2 by a few parts in ten thousand at most and so do not change the order of magnitude of the correlation found here. The compressibility factor for each gas (2) was calculated from the reference gas (1) by
-
+
2 2
= (1 - I C )
+ kZ,
(6)
in the region of 0 and 6 in which the two sets of data overlap. 21for the 50-50 reference mixture was interpolated from its tabulated data by the following two steps. First, for the density interpolation, the Z1 data a t each constant experimental temperature were fit by
(2) E.M.Holleran, J . Phys. Chem., 72, 1230 (1968). (3)E. M.Holleran and G . J . Gerardf, ibtd., 72, 3559 (1968). (4) E. M. Holleran, J . Chem. Phys., 49, 39 (1968). (5) E. M.Holleran, J . Phys. Chem., 73, 167 (1969). (6) D. R. Douslin, R . H. Harrison, and R. T. Moore, ibid., 71, 3477 (1967). (7) E. M. Holleran and G . J. Gerardi, {bid., 73, 525 (1969). Volume 7t? Number J March 1600
EUGENEM. HOLLERAN AND GARYJ. GERARDI
530 least squares to a polynomial in the density. It was found that polynomials of the fourth to seventh degree, depending on the temperature, were sufficient to reproduce the data points to within two or three parts per ten thousand. The coefficients of these polynomials are listed in Table I1 which has been deposited with NAPS.* Because they were not intended for extrapolation below the smallest experimental density of 0.75 mol/l., the first coefficients, co, were not constrained to unity, and the c1 values are not very good representations of the second virial coefficient, B. On each of these isotherms, 21 was interpolated at the densities for which 61 = 62, that is, a t the densities given by dl = dz(dol/doz),where the dz values are the tabulated experimental densities for gas ( 2 ) . Second, for the temperature interpolation, these isochoric compressibilities were then fit to an empirical equation quadratic in 1/T. At every density these equations reproduced the input values with a maximum deviation of two or three parts per ten thousand. On each of these isochores, 21 was calculated at the temperatures for which O1 = 02, that is, a t the temperatures given by T I = T S ( T B ~ / T Bwhere ~ ) , T z are the experimental temperatures. In calculating Zzfrom Z1 by eq G , the values of k used finally were those which gave the smallest sum of absolute deviations, A = 22 - 21. The values of k~ for these gases found in ref 3 as doT7B and listed in Table I are probably accurate to within 1%) and their ratios were taken as the first estimates of k . Then by varying k slightly the optimum value was easily found for each gas. These IC’s are also listed in Table I along with the ratio of the ~ B ’ s , and the agreement is seen to be good. The k g values and their ratios are approximately linear in mole fraction, and in fact the ratios for the five gases are not far from the simple series, 0.8, 0.9, 1.0, 1.1, 1.2. The experimental compressibilities, 2, (adjusted by the factor ( 1 E ) , as noted earlier), and the differences between these and the calculated values, ( 2 - 2 2 ) X lo4, are listed in Tables I11 to VI for the 100, 75, 23, and 0% CHI systems. (Tables IV, T’, VI h‘ave been deposited with NAPS.)* The data for all these gases cover the same range of T and d , but because of the differences in TB and do, the ranges of 0 and 6 do not exactly overlap with the 50% reference. The data points outside the overlap region were not included in Tables I11 to VI because the calculated Zzwould require extrapolation rather than interpolation with the empirical equations. The compressibility correlation obtained in this way is seen in the tables to be excellent. The average absolute differences are 4.9,3.2,4.4, and 8.4 units in the fourth decimal place (roughly parts per ten thousand) for the 100,75,25, and 0% systems, respectively. Pure CF4 correlates least well, and this is consistent with the fact that its data also give the poorest fit of the unit compressibility law.’ For all the gases, the worst agree-
+
The Journal of Phgsical Chemistry
ment occurs generally a t the highest densities and temperatures, that is, near the limiting experimental conditions. Omission of some of these peripheral values would permit an improved overall correlation, and would also change the k values slightly. The four decimals given for k in Table I therefore simply represent the values used in the present calculations and do not indicate the absolute accuracy of the ICB ratios, which is still probably not better than f0.5%. It should also be noted that since CH4 and Ar correlate very well,3we can expect that the compressibility of Ar can also be calculated accurately from the 50-50 (or other) CH4-CF4 mixture, although the reverse would be somewhat less accurate as discussed earlier. Generalized Equation of State. The above results demonstrate the correspondence of the quantity (2 - 1) / k for ~ these five gases a t equal reduced temperatures and densities. As shown in ref 3, this implies a similar correspondence of the reduced residual thermodynamic properties divided by k ~ .It also implies the correspondence of B / V B and C/CB at equal reduced temperatures, and these implications appear to be borne out a t ordinary temperatures by both experimental measurements and theoretical calculations, as discussed in ref 5. If this behavior proves to be general, then the properties of any gas can be found from a knowledge of its three constants, T B , do, k B , and a tabulation of the reduced properties as functions of e and 6. In particular, the equation of state can be given in generalized form by 2 = 1 k B x Y(6,6) (7)
+
where Y(O,6) can be tabulated from accurately known measurements of ( 2 - 1)/LB for one or several reference gases. In Table T’II are listed the values of Y as derived from the 50-50 mixture data at small enough intervals of 0 (0.02) and 6 (0.01) to permit easy interpolation. The value of k g was taken as 2.430, and if this should later prove to be in error, Y will have to be corrected accordingly. The unit-2 line can be seen running diagonally through Table VII. Given T B ,do, and k g , the conipressibility factor can be found from Table VI1 for (as we assume) any gas a t m y temperature and density in this range by interpolating Y at e = T / T B and 6 = d/do, and applying eq 7. For example, spot checks with CHI, CF4, and the three mixtures show that this procedure will quickly give 2 accurate to the third decimal in most cases, (i.e., within about O . l ~ o ) . Calculations for Ar also give good results, as might be expected. For N,, using the constants given in ref 5 and 7, a few test calculations show somewhat greater discrepancies, but this could (8) For Tables 11, I V , V, and VI, order NAPS Document 00164 from ASIS, National Auxiliary Publications Service c/o C C M Information Sciences, Inc., 22 West 34th Street, N R WYork. N. Y. 10001,remitting $1.00for microflchs or $3.00 for photocopies.
53 1
CORRESPONDIKG STATESOF CHI, CF4, AND THEIRMIXTURES Table 111: Correspondence of Pure CHa with the 50% Mixture" Density, mol/l.--
_ _ _ . I
1.0
1.5
2.0
2.5
3.0
3.5
4.0
25
0.9596 0 0.9615 0 0.9680 -1 0.9750 -1 0,9809 -1 0.9859 -2 0.9903 -1 0.9941 0 0.9974 0 1.0004 0 1.0031 1 1.0054 1 1.0075 1 1.0094 2 1.0112 2
0.9412 -1 0.9439 -1 0.9536 -3 0.9640 -3 0,9728 -3 0.9803 -2 0.9868 -1 0.9924 -1 0.9974 0 1.0017 0 1.0057 1 1.0091 1 1.0122 1 1.0151 1 1.0177 3
0.9240 -2 0.9275 -2 0.9404 -3 0.9540 -5 0.9657 -3 0.9755 -4 0.9842 -2 0.9916
0.9079 -3 0.9124 -3 0.9282 -5 0.9451 -5 0.9596 -3 0.9717 -5 0.9825 -2 0.9917 -1 0.9999 1 1.0071 1 1.0135 2 1,0193 3 1.0243 2 1.0290 3 1.0335 6
0.8932 -4 0.8986 -2 0.9172 -6 0.9373 -6 0.9545 -4 0.9690 -4 0.9817 -2 0.9927
0.8796 -5 0.8859 -2 0.9074 -6 0.9307 -6 0.9505 -4 0.9673 -3 0.9821 -1 0.9948 -1 1.0061 0 1.0161 2 1.0250 3 1.0329 3 1.0401 3 1.0466 4 1.0528 7
0.8673 -6 0.8743 -3 0.8988 -6 0.9250 -7 0.9475 -4 0.9667 -2 0.9833 -2 0.9980 1 1.0106 1 1.0220 2 1.0322 3 1.0413
8.0
8.5
9.0
9.5
0.8163 6 0.8297 7 0.8789 8 0.9316 10 0.9762 4 1.0156 6 1.0488 -4 1.0791 -3 1.1050 -13 1 1285 -17
0.8179 10 0.8321 10 0.8841 14 0.9396 12 0.9865 3 1.0278 1 1.0633 -8 1.0952 -9 1.1229 -17
0.8214 14 0.8358 10 0.8909 16 0.9493 13 0.9992 7 1.0426 3 1.0794 -13 1.1134 - 12
30 50 75 100 125 150 175 200 225 250 275 300 325 350
-1
0.9982 0 1.0040 1 1.0092 2 1.0139 3 1.0179 2 1.0217 3 1.0252 4
-1
1.0026 1 1.0111 1 1.0187 2 1.0257 3 1.0317 2 1.0375 4 1.0425 5
2 , O C
25 30 50
75 100 125 150 175 200 225 250 275
4 1.0494 3 1.0568
300 325
4
1.0638 6
350
11.0
t.OC
0.8424 18 0.8596 19 0.9222 16 0.9895 6 1.0470 -5 1.0972 -14
25
Density, mol/l. L,"C
25 30 50 75 100 125 150 175 200 225 250 0
0.8163 4 0.8290 4 0.8754 6 0.9252 6 0.9674 2 1.0046 6 1,0362 0 1.0647 0 1.0895 -4 1.1114 -10 1.1311 - 14
10.0
10.5
0.8263 15 0.8416 12 0.8991 15 0.9607 12 1.0130 2 1.0588 -2 1.0977 -21
0.8335 19 0.8495 16 0.9096 16 0.9740 10 1.0287 -4 1.0769 -11
--
r
F
t,oc
30 50 75 100
Density, mol/l.---
4.5
6.0
6.5
6.0
6.6
7.0
7.6
0,8563 -6 0,8641 -3 0.8915 -4 0.9207 -5 0.9456 -4 0.9673 -1 0,9856 -2 1.0021 1 1.0163 1 1.0291 3 1.0404 4 1.0508 5 1.0597 3 1.0680 3 1.0759 6
0.8465 -6 0.8550 -3 0.8853 -4 0.9175 -4 0.9450 -3 0.9688 0 0.9891 -1 1.0070 -1 1.0229 0 1.0373 5 1.0499 5 1.0611 5 1.0712
0.8381 -4 0.8473 -3 0.8800 -6 0.9156 -2 0.9455 -3 0.9716 1 0.9937 -1 1.0136 2 1.0309 2 1.0464 3 1.0602 4 1.0726 4 1.0836 2 1.0937 1 1.1033 3
0.8310 -3 0.8409 -2 0.8764 -4 0.9150 0 0.9472 -2 0.9753 0 0.9996 0 1.0211 2 1.0397 0 1.0567 3 1.0719 4 1.0855 5 1.0975 2 1.1083 -1 1.1186 0
0.8251 -3 0.8358 -1 0.8744 1 0.9153 -1 0.9501 -2 0.9807 3 1.0067 0 1.0299 3 1.0503 3 1.0683 1 1.OS46 1 1.0992 1 1.1123 -1 1.1239 -6 1.1352 -3
0.8208 -1 0.8322 1 0.8732 1 0.9174 4 0.9548 3 0.9870 2 1.0151
0.8179 2 0.8295 -1 0.8733 1 0.9204 4 0.9603 3 0.9951 5 1.0248 0 1.0515 0 1.0747 -4 1.0956
4
1.0803 2 1.0891
5
---
1
1.0399 1 1.0617 0 1.0814 0 -5 1.0988 1.1142 -2 -7 1.1145 1 1309 -3 -11 1 1282 - 10 1 1404 - 19 I
I
I
Den sity , mol/l-.
11.5
12.0
12.6
0.8541 22 0.8712 15 0.9372 15 1,0068 -3 1.0676 -11
0.8672 19 0.8858 17 0.9540 6 1.0269 -23 1.0904 -45
0.8837 19 0.9023 9 0,9737 -2 1.0503 -26
I
The compressibility Z, and [Z
- Z(calcd)]
X 10'.
easily be due to the present uncertainties in the values of the constants. As far as can be seen a t the present time, this threeconstant system of corresponding states is very prom-
ising. It has the advantage of requiring only one graph or table (such as Table VII) to represent the compressibilities of substances with different values of the third constant, kg. In this respect it is superior to the sysVolume 78, Number 8 March 1060
EUGENEM. HOLLERAN AND GARYJ. GERARDI
532
Table VII: Generalized Compressibility. The Quantity lo4@ 8
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39
0.66
0.57
0.60
-264 -345 -423 -497 -568 -635 -699 -759 -816 -869 -919 -966 -1009 - 1048 - 1084 -1117 -1116 -1171 -1192 -1209 -1223 - 1232 -1238 - 1239 -1236 -1228 -1215 -1196 -1172 -1142 -1105 -1062 - 1012 -953 -886 -810 -725
-241 -314 -384 -451 -515 -575 -632 -685 -735 -782 -826 -866 -903 -936 -966 -993 -1015 - 1035 - 1050 - 1061 - 1069 - 1073 - 1072 - 1067 - 1057 - 1043 - 1024 -999 -968 -931 -888 -838 -780 -714 -641 -558 466
-219 -285 -349 -409 -466 -520 -570 -618 -662 -703 -740 -774 -805 -833 -857 -878 -895 -909 -918 -924 -927 -925 -918 -908 -892 -872 -846 -816 -779 -736 -686 -629 -565 -492 -413 -323 -223
-
- l)/lc~as a Function of Reduced Temperature and Density
0.61
0.63
0.65
- 199 -259
- 180 -235 -286 -334 -379 -422 -461 -497 -530 -560 -587 -611 -632 -649 -663 -673 -680 -683 -683 -679 -671 -659 -642 -621 595 -564 -527 -486 -437 -383 -322 -253 - 176 -92 0 103 215
-163
-316 -370 -421 -469 -513 -555 -593 -629 -661 -690 -715 -738 -756 -772 -784 -792 -797 -797 -794 -787 -775 -759 -738 -712 -681 -645 -602 -553 -498 -434 -364 -285 -200 - 105
-
0
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23
0
89 189 297 414
0.69
0.71
- 148
- 133 - 172
- 154
-191 -232 -270 -305 -338 -367 -394 -417 -438 -456 -470
-482 -490 -494 -496 -494 -488 -479 -466 -448 -427 -401 -371 -335 -294 -248 - 196 - 138 -72 0
78 164 259 366 479 601
0.75
-94
-121 -145
0.77
0.79
-83 - 106
-72 -92 - 109
- 126
- 166 -144 -185 - 159 -201 -214 -225 -233 -238 -240 -239 -235 -228 -218 -204 - 186 - 165 - 141 -113 -80
- 172 -182 - 189 - 194 -195 - 194 - 190 -183 - 172 - 168 -141 - 121 -96 -69 -37
The Journal of Physical Chemiatry
0
- 123 - 135 - 145 - 151 - 155 - 157 - 155 - 151 - 143 - 133 -119 - 102 -82 -58 -31 0 35 74
0.81
-62 -79
-92 - 104 -113 -119 - 122 - 123 - 122 -117 -110 -99 -86 -69 -50 -26 0 31 65 103 146
0.73
- 106 - 137
-119
-208 -241
- 164 -189
-185 -215 -241 -265 -286 -304 -319 -331 -341 -347 -350 -351 -347 -341 -330 -317 -300 -278 -253 -223 - 189 - 150 - 106 -56 0 60 126 200 281 368 464 569 692
-272 -300
-325 -347 -367 -383 -396 -407 -414 -418 -418 -416 -409 -400 -386 -369 -348 -322 -292 -257 -217 - 172 -121 -64 0
68 144 227 318 418 533 651 778
------e
7
s
-212 -258 -301 -341 -378 -412 -444 -472 -497 -519 -538 -554 -566 -576 -581 -584 -582 -578 -569 -556 -539 -518 -492 -461 -425 -383 -336 -283 -223 -157 -83
0.67
-212 -232 -249 -263 -275 -283 -289 -291 -291 -287 -280 -270 -256 -239 -218 - 193 - 164 - 131 -92 -49 0
52 111 176 247 325 410 501
~
0.83
,085
0.87
0.80
0.91
0.93
0.05
0.07
0.99
-53 - 66 -77
-44 -54 -62 -68
-36 -43 -49 -51
-28 -33
- 20 -23 -23 -21 - 16 - 10
- 13 - 13 - 11
-6 -4
0
-7
6 15 27 41 57 76
6 12 21 31 44 60 78 98 121 147 176 208 242 280 321 366 414 466 523 584 648
-85 -91 -94 -95 -93 -89 -81 -71 -58 -42 -22 0
26 56 89 126 168 213
-71 -71 -69 65 57 -47 -34 -19
-
0
22 48 77 109 145 185 229 277
-52
-50 - 45
-38 -28 - 15 0
19 40 65 93 124 159 lQ8 240 287 338
-35 -36 -34 -29 -22 - 12 0 15 33 54 78 105 136 169 207 248 293 342 396
0
12 27 44 65 88 114 144 176 213 252 296 343 395 451
0
9 21 35 52 72 94 120 148 180 215 254 296 341 391 446 504
0
98
123 151 181 215 252 293 337 385 437 494 554
4 11 19 30 44 60 78 99 123 150 180 212 248 288 330 376 426 481 540 602
CORRESPOKDING STATESOF CHI, CF,,
AND
THEIRMIXTURES
Table VII (Continued) 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34
-43 0 45 97 154 217 287 362 444 533 627
40 85 135 191 251 318 391 470 556
118 167 220 279 343 413 490 573 662
192 244 301 363 430 503 584 670 763
263 318 377 442 513 589 674 762
330 387 450 518 591 670 759 851
393 454 519 590
454 517 585 659
512 577 648 724
567 635 708
620 690 765
670 743 820
719 793 873
6
1.01
1.03
1.05
1.07
1.09
1.11
1.13
1.15
1.17
1.19
1.21
1.23
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26
12 20 30 43 58 75 95 117 142 170 201 234 271 311 354 400 450 504 563 626 693 765 842 923
18 28 40 54 71 90 111 136 162 192 224 260 298 340 385 433 485 541 601 666 735 809
23 35 49 65 83 104 127 153 182 213 247 284 324 368 414 464 518 576 638 706 776 852
28 42 57 75 95 117 142 170 200 233 269 308 349 394 443 495 550 609 674 743
33 48 65 85 106 130 157 186 218 252 290 330 374 420 470 523 581 641 708 778
38 54 73 94 117 143 171 201 235 271 310 352 397 445 496 551 610
42 60 80 103 127 144 184 216 251 289 329 372 419 469 522 578
47 66 88 111 137 166 197 231 267 306 348 392 440 49 1 546 604
51 72 95 120 147 177 209 244 282 322 365 412 461 513 569 629
55 77 101 128 156 188 221 257 296 338 383 430 481 535 592 653
59 82 108 135 165 198 233 270 310 353 399 448 500 555 614 676
63 87 114 143 174 207 244 282 324 368 415 465 518 574 635
tems which use as the third constant the critical compressibility factor,9J0 or the acentricity factor of Pitzer.11-16 However, because of experimental limitations on the range of the data used, Table VI1 does not represent extreme deviations from ideality. For CF4, with the relatively large k~ of 2.88, the 2 values extend from 0.69 to 1.21. Also, the system has not been tested forgreatly dissimilar compounds. Although CF4 and CH, differ considerably in k B , so that (2 - 1) for CF, is always about 50% greater than for CHI, the difference appears to be due mainly to molecular size. It would be interesting to test polar compounds, but unfortunately their Boyle temperatures are relatively high, and good quality PVT data are usually in a region of e and 6 which does not permit direct evaluation of the constants T B and do by eq 1, and in large part does not overlap Table VII. Further application of this system will depend on (a) its general validity, (b) the accurate determination of
characteristic constants for additional gases, (e) the extension of Table VI1 to wider ranges of 0 and 6, and (d) the preparation of similar tables for other properties.
Acknowledgment. Although the experimental data are cited in the text, the authors wish to acknowledge a special indebtedness to D. R. Douslin, R. H. Harrison, and R. T. Moore, without whose careful measurements the present work would have been impossible. (9)H. P. Meissner and R. Seferian, Chem. Eng. Progr., 47, 579 (1951). (10) A. L. Lydersen, R. A. Greenkorn, and 0. A. Hougen, College
of Engineering, University of Wisconsin, Engineering Experimental Station Report 4, Madison, Wis., Oct 1955. (11)K. S. Pitzer, J . Amer. Chem. SOC.,77, 3427 (1955). (12) K. 9. Pitzer, D. Z. Lippmann. R . F. Curl, 0.M. Huggins, and D. E. Petersen, #btd., 77, 3433 (1955). (13) K. 9. Pitzer and R. F. Curl, Conference on Thermodynamics and Transport Properties of Fluids, London, July 1957. (14)W. C.Edmister, Petrol. Refiner. 37, 173 (1958). (15)N. Satter, N. Abdus, and J . M. Campbell, SOC.Petrol. Eng. J., 333 (1963).
Volume 75,Number 9 March 1969
