Relationship of Thermodynamic Properties to Molecular Stru Heat Capacities and Heat Contents of
Hydrocarbon Vapors lMOTT SOUDERS, JR., C. S. MATTHEWS, AND C. 0. HURD Shell Development Company, San Francisco, Calif. Systematic correlation methods for the prediction of heat capacities and heat contents of hydrocarbons in the ideal vapor state have been developed on the basis of molecular structure. Values for the several structural groups necessary to the correlation method are tabulated for temperatures from -250' to 3000' F. Extensive tabulations of heat capacities and heat contents for many hydrocarbons in the ideal vapor state as calculated by this correlation are presented for temperatures from -250' to 3800 O F. Similar tabulations of the latest values for common gases are included for ready reference. Differences between heat capacities predicted by this correlation and modern experimental measurements are in general less than 3%. Comparisons with heat capacities and heat contents calculated by the methods of statistical mechanics show differences which in most instances are less than 2% at temperatures above SOo F.
tion method for a wide variety of hydrocarbons and are tabulated as values at zero pressure. Tables of heat capacity and heat content for oxygen, nitrogen, hydrogen, water, ammonia, sulfur dioxide, hydrogen sulfide, carbon dioxide, carbon monoxide, chlorine, hydrogen chloride, and hydrogen fluoride are also included for convenient reference (Tables I and 11). I n general, these values may be used directly in engineering work at 1 atmosphere. Where deviation from the ideal gas laws is appreciable, a correction for the effect of pressure should be applied (15). This work was completed in 1945. Since that time several excellent experimental determinations of heat capacity have been published. These later values are in such close agreement with the tabulations of this paper that no revisions have been undertaken, except for the cyclopentane homologs which have been coordinated with the latest data. EXPLANATION OF THE CORRELATION
I"
THE past few years many advances have been made in the calculation of heat capacities from spectroscopic data. Development of technique has also brought forth enough accurato measurements of heat capacity . t o confirm the validity of these calculations and t o orient new ones. It is still necessary, however, t o predict heat capacities, particularly for hydrocarbons TABLE I. of such complex structure that statistical calculations are impossible. The availTemp., o F. Ne Hn able correlations by Bennewitz and Rossner (6) and the modifications of this -250 6.96 5.64 correlation by Fugassi and Rudy (17), 6.96 6.01 -200 6.96 8.52 -100 Dobratz (14), and Stull and Mayfield 0 6 . 9 6 6.79 ( 4 6 ) do not satisfactorily reproduce the 100 6 . 9 6 6 . 9 1 200 6.97 6.96 modern heat capacity data and statis300 7.00 6.97 tical calculations. The correlation pro400 7 . 0 5 6 . 9 8 posed by Andersen, Beyer, and Watson 500 7 . 1 1 7.00 600 7.18 7.00 ( 8 )is also unsatisfactory, with the added 700 7.27 7.02 800 7.36 7.04 disadvantage that two or more results 900 7.45 7.06 may be obtained for the same compound 1000 7.53 7.08 depending upon which path is taken in 1100 7.62 7.12 1200 7.71 7.16 building up the heat capacity equation 1300 7.79 7.20 1400 7 . 8 7 7.25 corresponding t o a given molecular 1500 7.94 7.30 structure. 1600 8 . 0 2 7.35 A correlation method is presented here 1700 8.08 7.41 1800 8 . 1 3 7.47 which reproduces the modern experi1900 8.18 7.53 mental and statistical data accurately 2000 8.23 7 . 5 8 2200 8.31 7.70 and is believed t o give the best, available 2400 8 . 3 8 7.80 2600 8.45 7.90 approximation t o the heat capacities 2800 8.53 8.01 of the more complex molecules. Values 3000 8.59 8.10 of heat capacity and heat content 5 Units = B.t.u./lb. have been calculated by this correla-
According t o the quantum theory of heat capacity and the theorems of statistical mechanics, the molecules of a gas have definite amounts of translational, vibrational, rotational, and (when possible) internal rotational energy a t a given temperature.
HEATCAPACITIES OF COMMON GASESAT ZEROPRESSURED O2
H20 CO
7.96 6.96 6.96 7.96 7.97 6.96 6.98 7.98 8.04 7.03 8.12 7.13 7.25 8.23 8.37 7.37 8.50 7.51 7.65 8.65 7.78 8.80 8.96 7.89 9.12 8.00 8.08 9.29 9.47 8.17 9.64 8.24 8.31 9.80 9.97 8.38 8.43 10.15 8.48 10.32 8.53 10.48 8.58 10.63 8.62 10.79 8.65 10.94 8.72 11.21 8.79 11.47 8.85 11.72 8.91 11.94 8.98 12.13 mole-o F.
1037
6.95 6.96 6.96 6.96 6.96 6.98 7.03 7.09 7.17 7.26 7.36 7.46 7.55 7.65 7.74 7.83 7.91 7.98 8.05 8.11 8.16 8.22 8.28 8.32 8.40 8.48 8.54 8.59 8.63
C02
Clz
HC1
HF
NHa
H2S
7.03 7.18 7.73 8.38 9.02 9.58 10.08 10.52 10.91 11.25 11.57 11.86 12.12 12.36 12.57 12.76 12.94 13.10 13.24 13.37 13.50 13.61 13.71 13.80 13.97 14.11 14.24 14.36 14.43
7.08 7.24 7.57 7.89 8.16 8.35 8.49 8.60 8.67 8.74 8.79 8.83 8.86 8.90 8.93 8.95 8.97 8.99 9.01 9.02 9.04 9.05 9.07 9.09 9.11 9.14 9.16 9.18 9.19
6.95 6.95 6.95 6.96 6.96 6.96 6.97 6.99 7.02 7.06 7.11 7.17 7.24 7.30 7.38 7.46 7.54 7.61 7.68 7.76 7.83 7.89 7.96 8.03 8.13 8.22 8.31 8.39 8.45
6.95 6.95 6.95 6.96 6.96 6.96 6.97 6.97 6.98 6.99 7.00 7.01 7.04 7.08 7.12 7.16 7.20 7.25 7.30 7.35 7.41 7.46 7.52 7.57 7.68 7.79 7.90 8.00 8.09
7.96 7.97 8.05 8.26 8.57 8.93 9.33 9.73 10.16 10.58 10.98 11.38 11.75 12.13 12.50 12.85 13.18 13.50 13.81 14.11 14.38 14.65 14.90 15.14 15.59 15.98 16.34 16.65 16.93
7.95 7.95 7.97 8.03 8.14 8.31 8.61 8.71 8.94 9.18 9.43 9.67 9.90 10.13 10.35 10.57 10.77 10.95 11.13 11.30 11.46 11.61 11.75 11.88 12.09 12.28 12.45 12.59 12.72
C, Graph-
901 Solid ite 8.11 8.28 8.67 9.14 9.62 10.08 10.52 10.93 11.29 11.61 11.88 12.11 12.30 12.47 12.62 12.75 12.86 12.95 13.03 13.10 13.17 13.23 13.28 13.32 13.40 13.46 13.52 13.57 13.60
0.52 0.72 1.19 1.68 2.17 2.62 3.01 3.36 3.67 3.94 4.19 4.41 4.60 4.75 4.89 5.02 5.12 5.20 5.27 5.33 5.39 5.45 5.50 5.56 5.66 5.74 5.83 5.91 5.98
INDUSTRIAL AND ENGINEERING CHEMISTRY
1038
TABLE 11. HEATCONTENTS Temp.,
F.
Hz (18,2 9 )
N2 (E$) 1,457.7 1,805.7 2,501.7 3,197.7 3,893.8 4,590.7 5,289.7 5,992.3 6,700.1 7,414.6 8,137.0
1,576.9 1,823.3 2,448.8 3,115.8 0 3,801.8 100 4,495.7 200 5,192.6 300 5,891.0 400 6,589.9 500 7,289.3 600 7,990.6 700 8,694.2 8,868.2 800 0,609.0 9,399.7 900 0,359 10,107 1000 10,817 1,117 1100 1,884 11,531 1200 2,659 12,249 1300 3,444 12,972 1400 13,699 1500 14,233 15,032 14,433 1600 15,169 15,834 1700 16,646 15,914 1800 17,461 16,662 1900 17,418 2000 18,282 18,944 19,937 2200 21,607 20,495 2400 23,295 22,074 2600 23,659 2800 24,987 25,281 3000 26,701 Heat content = 0 a t 0' R.;
-250 -200 -100
O F COXUOP: GASES AT ZERO PRESSUREa
Ha0 (20) CO (29)
COz (24) Clz (43') HCl ( 4 3 ) 1.666.3 1,457.0 1,461.3 1,447.6 1,462.8 1,457.4 1,795.6 2,064.3 1,803.8 1,815.3 1,819.3 1,804.9 2,499.2 2,491.6 2,860.7 2,561.0 2,558.3 2,499.9 3,661.0 3,194.8 3,370.1 3,188.3 3,332.8 3,195.6 3,887.4 4,467.2 3,890.9 4,241.6 4,136.5 3,891.6 4,595.3 5,283.7 4,590.3 5,172.8 4,962.4 4,587.7 5,314.6 6,106.5 5,291.2 6,150.3 0,804.3 5,284.5 6,046.7 6,937.2 5,995.5 7,185.5 6,658.5 5,982.7 6,791.6 7,779.2 6,708.9 8,256.1 7,521.7 6683.2 7,549.4 8,634.1 7,430.3 9,363.5 8,391.9 7:387.2 9,504.3 8,161.0 10,504 8,320.2 9,267.9 8,098.4 8,900.9 11,675 9,103.1 10,392 10,148 8,808.9 9,896.6 11,300 9,652.1 12,875 11,033 9,529.4 10,700 12,224 10,412 14,100 11,941 10,257 13,163 11,182 11,615 15,347 12,903 10,991 12,336 14,121 11,960 16,614 13,796 11,734 13,164 15,093 12,746 17,898 14,692 12,483 14,000 16,088 13,542 19,204 15,591 13,243 17,092 14,839 14,341 . 20,519 16,490 14,007 18,119 16,151 21,853 15,686 17,392 14,780 19,153 15,964 23,191 18,294 16,535 15,557 17,392 20,206 16,786 24,551 19,200 16,346 18,251 21,265 17,611 25,914 20,107 17,137 17,938 22,351 18,442 27,292 19,115 21,015 24,562 20,115 30,069 20,853 22,835 19,553 22,603 26,828 21,801 32,878 24,660 21,187 24,377 29,165 23,006 35,723 26,491 22,847 38,576 28,324 24,512 26,154 31,516 25,215 33,924 26,942 41,462 30,161 26,203 27,946 units = B.t.u./lb. mole. b Graphite, solid. Oz (23)
An exact calculation of the heat capacity, heat. content, and ot'her thermodynamic properties may be made if the amounts of each type of energy are known. Generally this knowledge is deduced from infrared and Raman spectra, and from statistical mechanical theory. However, this is almost impossible for complex molecules. This correlation presents a method for calculation of bhe heat capacity of such molecules. The method is based on the premise that molecular structural groups have the same contribution to heat capacity, no matter what molecule they appear in. These contributions may be determined from the rigorously calculable heat capacities of the simpler molecules. Once determined they may be applied tmomore complex molecules. In accordance with theory, it was found necessary to consider heat capacity contributions of three separat,e types: translational and external rotational contributions of the molecule as a whole; vibrational contributions of structural groups such as CH3-, -CH,-, -CH=, etc., and internal rotational contributions required by rotation of these structural groups about internal bonds. The heat capacity of any molecule then may be evaluated as the sum of that arising from each of these three types of contributions. The method of assigning contributions t o structural groups is explained below.
c&-
i:i H and -A-i
groups were similarly deter-
STATISTICdL CALCULATIOXS
Compound Methane Ethane Propane Isobutane
n-Butane Neopentane
Ethylene Propylene
cis-2-butene
Allene Acetylene Methylacetylene Dimethylacetylene
Frequency Assignment, Lit. Cm.-l Cited Dennison Stitt Pitailr
Barner, Cal./ Mole
i7iO 3300 3400
%6Yui38(2), 799 925(2) 964(8), 1150($), 1170: 1328(6),1380(5), 1460 (6),2950(10) Pitzer 331(2), 415(3), 730, 900 ( 8 ) 926(8) 1050(5) 12&(5), 13?0(4), 1466 ( S ) , 2950(12) Burcilr, Eyster, and Yost
:
...
... 5.18
2000
1399,1416, 1448, 1472, 1647,2950(6') Scott, Ferguson, and Brickwedde Gershinoivitz and Vvil-
1040
2 666 4.51 5.06
4366
...
"""l~~"pio"3"6f1?~?; K:+,
RPdiirecl Monientl G. Sq. Cm. x
4 .'236
700
5.02
1900
5.01
Using five
-b=
of these together with a paraffin CHZ- group, the (aromatic) group was calculated by difference from toluene. The -CH2groups in the cycloparaffins were determined by taking
252;'380, 432, 512, 804, 890, 992. 1021, 1064, 1160(2). 1278, 1370 ($1, 1414, 1460(4), 1664. 295018) Linnett and Aver, Stitt Crawford
2750
5.027
Crawford
I . .
...
... (8)
Free rotation
230(2), 460(2), 488(8), ... 644, 708(2), 2024, 2183, 3350(2) T'inylacetylene 219, 309, 635, 625, 678, ... 738, 926, 974, 1091, 1240, 1285, 1396, 1600,2098,2950,3010, 3096,,3300 Kilpatrick, Pitzer, and f , . . Cyclopentane Spitzer ... Aston, Szasz. and Fink Cyclohexane ,.. Pitzer and Scott Benzene Pitzer and Scott ... Toluene a Values derived froin unpublished data and calculations. Diacetylene
mined by subtract,ing the correct number of CHI- groups from the total vibrational contributions t o the heat capacities of isobutane and neopentane, respectively. From the statistically calculated vibrational lieat capacity of benzene the HA= (aromatic) group was evaluated.
Cb, ( 2 2 , $9, SO2 ( 1 1 ) 32, 6fj 1,673.5 44.3 2,081.7 73.6 2,927.9 167.5 3,815.4 312.7 4,753.3 006.1 5,736.1 745, 9 6,765.2 1,027.2 7,837.3 1,345.4 8,947.5 1,696.1 10,092 2,072.1 11,265 2,476.4 12,464 2,905.2 13,685 3,357.6 14,924 3,825.6 16,179 4,307,8 17,448 4,803.2 19,728 5,309.9 20,021 5,827.7 21,319 6,349.7 22,627 6,881.3 23,938 7,415.3 25,260 7,959.2 26,584 8,605,2 27,915 9,059.2 30,586 10,181.2 33,274 11,320.3 35,978 12,483.0 38,680 14,843,8 13,660.8 41,396
snn
Evaluation of the group Contributions for vibrational heat capacity was very simple. The CHa- group was taken as one half the statistically calculated vibrational contribution t o heat group, the -CHgroup capacity in ethane. Using this was determined by difference from the vibrational heat capacity of -
NH3 (49) HIS (10) 1,437.4 1,667.8 1,667.1 1,804.9 2,065.7 2,064.6 2,499.9 2,866.8 2,860.5 3,193.6 3,682.9 3,661.2 3,891.6 4,525.2 4,470.8 4,587.7 5,401.1 5,294.0 5,284.3 6,314.8 6,135.1 5,981.3 7.267.9 6,996.6 6678.7 8,261.9 7,879.5 7:376.8 9,297.3 8,785.2 8,076.2 10,374 9,714.7 8,776.5 11,490 10,668 9,479.2 12,648 11,648 10,185 13,844 12,650 10,896 15,076 13,675 11,609 16,344 14,722 12,327 17,645 15,789 13,051 18,988 16,880 13,777 20,348 17,982 14,210 21,761 19,107 15,246 23,164 20,238 15,992 24,624 21,397 16,740 26,094 22,560 17,496 27,601 23,743 19,020 30,673 26,137 20,568 33,828 28,566 22.145 37,084 31,049 23,728 40,361 33,543 25,342 43,734 36,081
ASSIGNUENTSAND BARRIERS USED IN TABLE 111. FREQUENCY
Isobutylene
The
HF ( 8 1 )
one fifth and one sixth, respectively, of the vibrational contributions t o heat capacity in cyclopeiitane and cyclohexane. The acetylenic groups mere determined from acetylene and group by methylacetylene, using a CH3- group t o get the --C=
tvans-2-butene
CONSTRL'CTION OF THE CORRELATIOS
propane.
Vol. 41, No. 5
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1949
TABLEIV.
HEATCONTENT AT ZERO PRESSURE^ Vibrational Group Contributions
Paraffinic Temp., O F .
-250 -200 - 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
I600
1700 1800 1900 2000 2200 2400 2600 2800 3000
CHa-
,. .
2.3 14.9 66.8 177.3 364.3 641.5 1,012 1,459 1,985 2,585 3,256 3,995 4,795 5,652 6 560 7:519 8,519 9,564 10,647 11,767 12,923 14,112 15,327 17,836 20,435 23,114 25,862 28,669
-CHz16.9 45.0 143.3 317.7 573.5 925.6 1,375 1,908 2,522 3,208 3,962 4,776 5,655 6,583 7,555 8,568 9,622 10,711 11,832 12,983 14,161 15,367 16,593 17,830 20,388 23,012 25 695 28:429 31,204
-&H
I
44:l 99.5 322.9 678.6 1,146 1,706 2,355 3,082 3,881 4,744 5,663 6,631 7,647 8,702 9,790 10,909 12,056 13,227 14421 15:635 16,868 18,119 19,384 20,663 23,260 25,901 28,579 31,288 34,024
Cycloparaffinic -CHz-CHa-
-&104.9 238.1 688.0 1,338 2,121 3,004 3,970 5,000 6,085 7213 8’377 9:571 10,790 12,030 13,287 14,559 15843 17:138 18442 19:755 21 074 22:399 23,729
1039
56.5 79.3 152.2 286.1 499.7 804.9 1,202 1,685 2,251 2890 3:598 4,366 5,190 6,065 6 987 7’950 8:954 9,995 11 067 12’171 13:301 14,469 15,639 16,844 19 311 21:850 24,447 27 099 29:796 Cyclopentane type
39.2 72.5 181.1 356.9 627.5 986.4 1,452 2,003 2,636 3 347 4’122 4:959 5,858 6,809 7,807 8,845 9,922 11,034 12,179 13,353 14,555 15 783 17:032 18,302 20 899 23’561 26:276 29 040 31:846 Cyclohexane type
Aromatic
-
Acetylenic
Olefinic
I
‘ U
Liquid range 190.4 364.0 605.7 916.2 1,287 1,708 2 176 2’683 3:227 3,808 4,421 5,060 5,724 6,410 7,117 7,842 8,583 9,338 10,113 10,897
891.4 1,363 1883 2,’448 3,056 3,699 4372 5:073 5,800 6,545 7,307 8,085 8,875 9,676 10,486 11,302 12,125 12,953 13,784 14,619
I
0.8 5.3 57.4 164.7 329.4 540.5 793.1 1,078 1,392 1726 2:078 2,446 2,834 3,239 3,657 4,090 4,536 4,998 5,468 5,954 6,444 6,954 7,466
.. , 60.3 127.4 0.9 342.0 13.3 629.1 62.6 964.8 168.7 1,327 338.0 1,732 579.6 2,144 891.2 2,577 1,257 3,024 1677 3,484 2:148 3,955 2,664 4,436 3,228 4,927 3,830 5,426 4,468 5,929 5,141 6,440 5,845 6,958 6,586 7,478 7,342 8,004 8,134 8,630 8,935 9,068 9,774 9,605 10,622 11,499 13 290 15:145 17 051 19:Olo 21,008
i
14.4 39.2 146.0 338.0 604.4 943.6 1,347 1,821 2,341 2,909 3,522 4,174 4,863 5,581 6,327 7,097 7,892 8,709 9,544 10,398 11,268 12,152 13,051
85.5 180.4 501.5
54.9 117.0 324.5
961.2 1,483 2,083 2,725 3,408 4,126 4,874 5,649 6,448 7.266 8,101 8,951 9,813 10,687 11,571 12,465 13,369 14,274 15,193 16,113
619.2 971.6 1370 1:794 2,241 2,705 3,184 3,674 4,172 4,681 5,197 5,721 6,251 6,787 7,330 7,874 8,426 8,978 9,537 10,095
Characteristic Internal Rotational Contributions
I11 Temp.
’ F.
-250 -200 - 100 0 100 200 300
400 500 600 700
800
900 $000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 1600 2800 3000
I
I1
-CHz-CHz173.9 261.0 491.6 779.0 1095 1399 1676 1932 2171 2393 2603 2798 2984 3160 3328 3490 3645 3793 3939 4080 4219 4352 4484 4612 4861 5100 5333 5565 5794 n-Butane
CHa--CHz71.1 128.3 282.5 468.9 674.8 888.6 1105 1318 1526 1727 1921 2105 2283 2454. 2620 2779 2937 3088 3234 3376 3517 3653 3788 3919 4177 4426 4668 4908 5141
R-AH
I
IV R-C-
78.5 139.5 298.7 488.3 695.8 912.1 1131 1347 1558 1763 1960 2149 2330 2505 2674 2837 2995 3147 3296 3440 3583 3721 3858 3991 4253 4507 4752 4995 5231 Isobutane
1
I
59.9 112.7 254.4 427.5 622.0 829.8 1046 1267 1489 1708 1924 2136 2340 2538 2731 2916 3096 3271 3443 3608 3771 3927 4081 4231 4524 4808 5078 5346 5603
VI V. Vb =CH-CH= R-CH= R-CH= 114.3 240.1 71.8 126.3 193.0 328.0 298.3 381.6 483.1 588.4 627.5 538.3 827.3 792.2 755.6 1146 986.8 876.6 1171 1471 992.6 1105 1344 1783 1509 1215 2078 1665 1323 2366 1814 1430 2619 1958 1535 2869 2096 1640 3108 2228 1744 3336 2357 1847 3554 2485 1950 3764 3967 2608 2053 2155 2728 4163 2848 2257 4353 2965 2359 4539 3081 2460 4719 4895 3194 2561 3307 2662 5067 3419 2763 5235 3640 2965 5557 3167 3859 5867 3368 4075 6166 3568 6455 4291 3768 6733 4505 Propylene 1, 3 - B ~ t a diene
Neopentane
Propane
cis-2butene
VI11
VI1
zC-c=
E-&=
59.0 90.5 165.4 252.9 344.1 430.7 508.1 575.7 634.6 686.5 732.8 774.2 811.2 845.9 880.6
95.9 164.2 337.7 539,5 753.0 968.2 1179 1382 1576 1761 1937 2105 2267 2424 2575
915.9 947.4 977.4 1007 1034 1061 1086 1111
2720 2861 2999 3135 3266 3396 3523 3649 3772 4013 4248 4477 4706 4930 Isobutylene
Diacetylene conj. fact.
IX CHa-CHa 55.0 104.0 247.5 429.7 628.3 832.0 1033 1228 1416 1597 1769 1935 2094 2247 2395 2539 2678 2814 2948 3079 3209 3334 3458 3580 3822 4055 4285 4513 4737
Ethane
X RT 208.3 258.0 357.3 456.6 555.9 655.2 754.6 853.9
4 RT 1,666.2 2,063.5 2.858.1 3,652.7 4.447.3 5,241.9 6,036.5 6,831.0
953.2 1052.5 1151.9 1251.2 1350.5 1448.7 1549.1 1648.5 1747.8 1847.1 1946.4 2046.7 2145.1 2244.3 2343.8 2443.0 2641.8 2840.4 3039.0 3237.6 3436.3 Free rotation
7,625.6 8,420.2 9,214.8 10,009.3 10,804.0 11,598.5 12,393 13,188 13,982 14,777 15,571 16,366 17,161 17,955 18,750 19,544 21,134 22,723 24,312 25,901 27,490
t/z
trans.
+
ext. rot.+ CpO
- C.”
Heat content = 0 a t Oo R.; units = B.t.u./lb. mole.
I
difference.
Olefinic groups were arrived a t in the same manner,
b
-b=
obtaining HzC= from ethylene, H d r o m propylene, from isoprene, and =C= from allene. The typical internal rotation contributions to heat capacity were taken directly from the statistically calculated values for the various molecules. Thus the CHs-CHt internal rotation contribution was taken from propane, the Rbutylene, the R-
hI - from neopentane, etc.
h= from iso-
I
The n-butane or CHZ-CH~ internal rotation contains a “steric” factor in addition to the ordinary barrier. This inernal rotation was evaluated by subtracting 4 R, 2CH8- group contributions, 2-CHZcontributions, and 2 propane internal rotational contributions from the calculated values for n-butane. The diacetylene conjugation factor is the difference necessary and 2 - C s groups agree with the t o make the sum of 2 H-C= statistically calculated heat capacity of diacetylene. The internal rotational contribution of butadiene also contains a difference of this kind. b’requency assignments, barriers, and reduced moments of
INDUSTRIAL AND ENGINEERING CHEMISTRY
1040
Vol. 41, No. 5
TABLE v. HEATCAP.4CITY
AT ZERO PRESSURE S'ibrational Group Contributions
Paraffinic I
Temp.
F.
I
CHr-
-CH-
-c13
-c-I
I
I
-CHz-
Cycloparaffinic -CHr(61
(6)
Aromatic H -c-
I -c=
- 250 -200 - 100
0.02 0.06 0.29
0.33 0.66 1.35
0.86 1.51 2.97
2.12 3.42 5.38
0.39 0.63 1 00
0.57 0.80 1.40
0 100 200 300 400
0.77 1.47 2.33 3.20 4.06
2.14 3.04 3.96 4.87 5.76
4.10 5.10 6.05 6.89 7.66
7.10 8.36 9.28 10.01 10.61
1.71 2.58 3.50 4.41 5.23
2.18 3.11 4.09 5.05 5.93
1.41 2.10 2.76 3.38 3.96
4.37 4.93 5.43 5.88 6.26
500 600 700 800 900 1000 1100 1200 1300 1400
4.89 5.66 6.39 7.06 7.69 8.28 8.83 9.34 9.82 10.25
6.54 7.22 7.87 8.47 9.02
8.34 8.94 9.47 9.93 10.34 10.71 11.04 11.34 11.60 11.84
11.00 11.49 11.81 12. 08 12.30 12.49 12.64 12.78 12.90 13.00
6.74 7.46 8.11 8.70 9.24
4.46 4.90 5.28 5.64 5.96
9.74 10.18 10.58 10.9.5 11.30
1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
10.65 11.03 11.30 11.72 12.01 12.29 12.78 13.21 13.58 13.90 14.17
12.04 12.24 12.42 12.58 12.73 12.86 13.10 13.30 13.47 13.62 13.74
13 .09 13.16 13.22 13.28 13.33 13.38 13.45 13.51 13.57 13.61 13.64
6.02 6.74 7.38 7.97 8.50 8.99 9.43 9.84 10.22 10.57 10.89 11.18 11.45 11.80 11.93 12.14 12.52 12.85 13.14 13.38 13.59
11.61 11.89 12.15 12.38 12.60 12.80 13.15 13.46 13.71 13.93 14.11
9.60 9.93 10.33 10.71 11.08 11.37 11.66 11.93 12.18 12.40 12.61 12.97 13.28 13.55 13.78 13.96
Cyclopentan type
Cyclohexane tspe
Liquid range
Acetylenic
H
E
-C5
0
I
F." -CHCz-H---
I1 CHa--CI&-
-250 -200 - 100
1.60 1.99 2.64
1.03 1.33 1.74
1.10 1.68 2.58 3.13 3.53 3.83 4.07 4.26
6.60 6.90 7.15 7.36 7.55
1.37 1.90 2.33 2.67 2.96 3.20 3.42 3.61 3.79 3.95
4.42 4.56 4.67 4.77 4.86
0.74 1.38 2.06 2.74 3.37 3.94 4.47 4.96 5.41 5.82
6.26 6.52 6.75 6.97 7.16
7.71 7.84 7.96 8.06 8.14
4.11 4.26 4.40 4.63 4.66
7.34 7.50 7.66 7.79 7.92 8.04 8.26 8.45 8.59 8.71 8.82
8.20 8.26 8.30 8.34 8.38 8.41 8.47 8.53 8.59 8.65 8.69
4.78 4.89 5.00 5.11 5.20
4.94 n.O1 5.07 5.13 5.19 5.23 5.27 5.32 6.36 5.40 5.43 5 48 5.62 5.56 5.60 5.64
6.20 6.56 6.88 7.19 7.48 7.75 7.99 8 21 8.42 8.62 8.81 9.14 9.43 9.67 9.89 10.08
5.29 5.4n 5.60 6.72 5.83 5,93
0 100 200 300 400
3.08 3.17 2.90 2.65 2.46
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
0:04 0.27
i
--& =e=
0.33 0.69 1.50 2.30 3.03 3.74 4.36 4.94 5.46 6.92 6.34 6.71 7.03 7.32 7.58 7.83 8.06 8.27 8.46 8.63 8.78 8.91 9.04 9.16 9.37 9.55 9.69 9.81 9.92
1.66 2.46 3.94 4.98 5.68 6.20 6.64 7.02
1.01 1.61 2.58 3.27 3.77 4.12 4.37 4.56
7.34 7.63 7.88 8.09 8.27
4.72 4.88 4.95 5.04 5.12
8.43 8.56 8.68 8.79 8.80 8.98 9.0: 9.12 9.18 9.24
5.19 5.27 5.33 5.39 5.44 6.48 5.52 5.66 5.59 5.61
9.28 9.36 9.41 9.46 9.60 9.58
5.63 5.68 5.72 *5,74 E.76 3.78
IX
1
K-A=
0.99
1.80 1.69 1.48 1.34 1.24 1.18 1.14 1.11
0.84 1.34 2.09 2.70 3.07 3.27 3.21 3.03
0.60 0.67 0.81 0.91 0.91 0.83 0.72 0.63
1.24 1.54 1.91 2.10 2.16 2.14 2.07 1.98
0.87 1.20 1.66
2.30 2.15 2.02 1.90 1.80
1.98 2.11 2.17 2.16 2.10 2.05 1.9s 1.90 1.82 1.74
1.42 1.73 2.02 2.08 2.00 1.89 1.79 1.69 1.60 1.82 1.45 1.40 1.36
1.09 1.07 1.06 1.05 1.04
2.86 2.70 2.56 2.44 2.33
0.55 0.49 0.44 0.39 0.36
1.89 1.81 1.72 1.65 1.58
1.84 1.76 1.69 1.62 1.56
1.72 1.64 1.58 1.53 1.48
1.68 1.63 1.57 1.53 1.48
1.71 1.66 1.60 1.56 1.51
1.95 1.89 1.83 1.78 1.73
1.32 1.28 1.25 1.22 1.20
1.04 1.03 1.03 1.02 1.02
2.23 2.14 2.06 1.99 1.93
1.53 1.44 1 40 1.36
1.50 1.45 1.41 1.38 1.34
1.43 1.40 1.36 1.33 1.30
1.43 1.40 1.38 1.36 1.33
1.47 1.43 1.40 1.38 1.35
1.68 1.64 1.60 1.56 1.52
1.18 I .16 1.16 1.14 1.12
1.02 1.02 1.01 1.01 1.01
1.33 1.31 1.28 1.26 1.23
1.32 1.29 1.27 1.25 1.23
1.27 1.22 1.18 1.16 1.15 1.14
1.30 1.27 1.24 1.21 1.18 1.16
1.33 1.29 1.25 1.22 1.20 1.18
1.49 1.44 1.39 1.35 1.31 1.28
1.11 1.10 1.09 1.08 1.08 1.07
1.01 1.01 1.01 1.00 1.00 1.00
1.88 1.83 1.78 1.74 1.70 1.66 1.58 1.52 1.47 1.42 1.36
0.34 0.23 0.32 0.31 0.30 0.28 0.27 0.26 0.26 0.24 0.23 0.22 0.21 0.20 0.19 0.18
1.21 1.18 1.16 1.14 1.12 1.10
1.22 1.10 1.16 1.14
Propane
Propylene
Seopentane
inertia used in making these calculations are given in Table 111. The tables of Sherman and Ewe11 (4s) were used for the calculations of the vibrational contributions t o heat capacity, and Pitzer's tables (37)were used in calculating the internal rotational contributions. Heat content contributions were evaluated by graphically integrating the heat capacity functions over the temperature range from -250' to 3000" I?. More significant figures are carried than are warranted by the absolute accuracy of the values in order to preserve precision in subtractions between heat contents a t two temperature levels. The values a t -250" F. were taken from the statistically calculated values of the heat
cis-2-
butene
1,3-Butadiene
Diaoetylene eonj. fact.
1,48
.?
n
'/% R
0.93 1.21 1.60 1.85 2.02 2.13 2.20 2.22 2.22 2.18 2.13 2.08 2.02
Isobutane
Aliens tsw
CH-CI-Ia
1.39 1.76 2.00 2.13 2.19 2.18 2.14 2.08 2.01 1.93 1.85 1.76
n-Butane
-
Olefinic I
Id2=
VI11
I
R---CH
I. 12
H9C=
0.09 0.24 0.76
111
Temp
___._.
0
1 c
e
K E 42
3
u Y
n
fI.. ?1?1
Isobutylene Ethane
Free rotation
content function at that temperature. The compounds and general procedure were the same as those used for evaluating the contributions of the corresponding groups to heat capacit,y. USE OF THE CORRELATION
By this correlation method the contributions to heat capacity and to heat content of vibrational, internal rotational, and translational plus external rotational states are separately evaluated. To calculate a desired heat capacity or heat content, one evaluates each of these three contributions in turn; the sum gives the total heat capacity or heat content.
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1949
1041
OF HYDROCARBON VAPORSAT ZEROPRESSURE" TABLE VI. HEATCAPACITIES
Temp., O
F.
-250 -200 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
-
Temp., O
F.
-250 -200 - 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
Methane 7.95 7.95 7.99 8.21 8.67 9.30 10.04 10.82 11.61 12.39 13.14 13.88 14.56 15.22 15.84 16.43 16.99 17.50 17.99 18.44 18.88 19.26 19.64 19.98 20.59 21.13 21.56 21 * 9 8 22.33 stat. calcd. 2,3-Dimethylbutane 15.83 18.76 24.73 30.31 35.72 41.03 45.90 50.51 54.81 58.66 62.19 65.35 68.23 71.05 73.63 75.97 78.20 80.15 81.94 83.67 85.31 86.84 88.15 89.42 91.65 93.57 95.25 96.74 97.97
11
a
Ethane 8.86 9.27 10.19 11.42 12.92 14.65 16.34 17.99 19.57 21.03 22.42 23.69 24.89 26.01 27.06 28.04 28.97 29.79 30.57 31.30 32.00 32.64 33.20 33.75 34.70 35.53 36.25 36.87 37.40 1 IX
nHeptane 18.10 21.99 29.32 36.47 42.99 48.35 53.62 58.91 63.73 67.93 71.96 75.66 79.11 82.25 85.08 87.74 90.32 92.63 94.68 96.71 98.58 100.33 101.83 103.26 105.78 107.97 109 92 111.61 112.97 41 2 I1
4 111 Units B.t.u./lb. mole-o F.
I
Propane 10.38 11.39 13.36 15.59 18.15 20.91 23.54 26.03 28.37 30.45 32.40 34.18 35.83 37.37 38.80 40.10 41.36 42.47 43.48 44.47 45.42 46.29 47.03 47.74 49.02 50.13 51.08 51.89 52.57 2 I1
3-Et hylpentane 16.31 19.78 26.34 32.72 39.30 45.95 52.07 57.78 62.97 67.50 71.69 75.48 78.92 82.17 85.14 87.81 90.41 92.69 94.75 96.75 98.67 100.45 101.95 103.40 105.98 108.19 110.10 111.75 113.10 3 I1 3 I11
n-Butane 12.31 14.04 17.35 20.81 24.36 27.77 31.06 34.25 37.21 39.82 42.29 44.55 46.65 48.59 50.37 52.01 53.60 55.01 56.28 57.53 58.71 59.80 60.73 61.62 63.21 64.59 65.79 66.82 67.67 11 2 11
nOctane 20.03 24.64 33.31 41.69 49.20 55.21 61.14 67.13 72.57 77.30 81.85 86.03 89.93 93.47 96.65 99.65 102.56 105.17 107.48 109.77 111.87 113.84 115.53 117.14 119.97 122.43 124.63 126.54 128.07 51 2 I1
Isobutane 12.23 13.81 17.07 20.36 23,85 27.56 30.98 34.20 37.20 39.90 42.38 44.61 46.64 48.63 50.46 52.11 53.69 55.07 56.35 57.57 58.74 59.83 60.76 61.67 63.26 64.63 66.82 66.87 67.74 3 I11
Ison-Pentane 14.24 16.69 21.34 26.03 30.57 34.63 38.58 42.47 46.05 49.19 52.18 54.92 57.47 59.81 61.94 63.92 65.84 67.55 69.08 70.59 72.0D 73.31 74.43 75.50 77.40 79.05 80.50 81.75 82.77 21 2 I1
2,2,4,2,3,4,Trimethyl- Trimethylnpentane pentane Nonane 18.47 21.96 18.44 22.51 27.29 22.85 30.98 30.63 37.30 38.63 38.10 46.91 45.51 55.41 46.27 53.08 62.07 53.98 59.88 68.66 61.06 66.18 75.35 67.57 73.49 81.41 71.98 77.14 86.67 78.64 81.82 91.74 83.36 96.40 87.60 85.99 91.42 89.74 100.75 94.98 93.45 104.69 96.84 108.22 98.25 101.22 111.56 99.87 114.80 104.06 102.77 105.29 117.71 106.55 107.61 120.28 108.83 109.83 122.88 111.01 111.96 125.16 113.07 113.95 127.35 114.97 129.23 116.59 115.64 118.20 117.29 131.02 121,oo 120.18 134.16 123.40 122.65 136.89 125.50 124.80 139.34 127.30 126.71 141.47 128.80 128.28 143.17 3 I11 7 I11 6 I 4 IV 2 I1
TRANSLATIONAL PLUS EXTERNAL ROT.4TIONAL CONTRIBUTION. For nonlinear polyatomic molecules at temperatures above 100' K., this contribution t o th! constant pressure heat ca acity is 4 R or 7.95 B.t.u./lb. mole- R. This include: *//e R$r external rotation, R for translation and R for C, - C, For linear molecules -e.g , H-CGC-H, H C = C C = C H , but not H&-CrCH-the external rotation contribution is only R; hence, the additive constant decreases t o 3 '/z R or 6.95 B.t.u./ ih. mole-' R. - . ...- T h e additive quantities for heat content are similarly 4 RT and 3 '/2 RT. Values of 4 R T are tabulated in Table IV. VIBRATIONALCONTRIBUTIONS. Vibrational contributions t o heat capacity are given in Table V for the various groups, CHa-,
.
L
pentane 13.59 15.80 20.16 24.48 29.00 33.69 38.01 42.06 45.79 49.10 52.15 54.90 57.40 59.81 62.02 64.01 65.93 67.61' 69.15 70.63 72.05 73.37 74.49 75.58 77.50 79.16 80.58 81.83 82.86 1 I1 3 I11
-CHs-, H -, HC=, etc. The total vibrational heat capacity i~ evaluated by adding together the contribution of all the groups in the molecule. Heat content contributions may be found in Table IV.
Neopentane 13.87 16.45 21.09 25.62 30.27 35.07 39.56 43.68 47.48 50.79 53.84 56.59 59.09 61.36 63.47 65.41 67.25 68.87 70.96 71.79 73.13 74.35 75.40 76.45 78.28 79.86 81.24 82.40 83.39 4IV'
nDecane 23.89 29.94 41.29 52.13 61.62 68.93 76.18 83.57 90.25 96.04 101.63 106.77 111.57 115.91 119.79 123.47 127.04 130.25 133.08 136.89 138.45 140.86 142.93 144.90 148.35 151.35 154.05 156.40 158.27 7 1 2 I1
Neo-
n-Hexane 16.17 19.34 25.33 31.25 36.78 41.49 46.10 50.69 54.89 58.56 62.07 65.29 68.29 71.03 73.51 75.83 78.08 80.09 81.88 83.65 85.29 86.82 88.13 89.38 91.59 93.51 95.21 96.68 97.87 3 1 2 I1 A per -CH*-
group
1.93 2.65 3.79 5.22 6.21 6.86 7.52 8.22 8.84 9.37 9.89 10.37 10.82 11.22 11.57 11.91 12.24 12.54 12.80 13.06 13.29 13.51 13.70 13.88 14.19 14.46 14.71 14.93 15.10
11
hexane 15.23 18.44 24.18 29.74 35.42 41.20 46.59 51.54 56.07 59.99 63.61 66.88 69.85 72.54 .75.03 77.31 79.49 81.41 83.16 84.85 86.44 87.89 89.13 90.36 92.52 94.38 96.00 97,36 98.51 1 I1 4 IV
Ethylene 7.95 8.03 8.49 9.43 10.71 12.07 13.43 14.69 15.83 16.89 17.87 18.77 19.59 20.35 21.07 21.71 22.33 22.91 23.45 23.93 24.37 24.79 25.19 25.57 26.23 26.81 27.29 27.73 28.11
'
2Methylpentane 15.52 18.45 24.15 29.70 31.21 40.55 45.53 50.28 54.63 58.47 62.04 65.27 68.22 70.03 73.59 75.92 78.17 80.18 81.95 83.69 85.34 86.88 88.19 89.47 91.69 93.61 95.29 96,76 97.96
11
1 I1 3 I11
Propylene 9.74 10.47 12.03 13.84 15.83 17.97 20.04 22.01 23.84 25.52 27.09 28.53 29.85 31.07 32.20 33.25 34.24 35.15 35.99 36.76 37.48 38.14 38.74 39.32 40.34 41.23 41.97 42.63 43.19
1v
3Methylpentane 14.95 17.79 23.25 28.60 34.15 39.82 45.04 49.92 54.38 58.30 61 92 65.19 68.16 70.99 73.58 75.91 78.17 80.15 81.95 83.69 85.36 86.91 88.22 89 49 91.74 93.67 95.34 96.79 97.98 2 I1 3 111
1-Butene 11.26 12.72 15.74 18.96 22.15 25.11 27.93 30.64 33.13 35.35 37.43 39.32 41.05 42.65 44.12 45.48 46.79 47.97 49.04 50.06 51.00 51.87 52.65 53.39 54.70 55.84 56.81 57.66 58.38
11
1 I1 (Continued on page 104s)
The presence of a conjugated double or triple bond in a molecule alters the vibrational contribution of these groups. Differences between conjugated and nonconjugated contributions have been included in the internal rotational contribution in each case (VI and VI1 in Tables IV and V). For the case of the triple bonds the entire contribution listed in the tables is due t o the conjugation effect, the internal rotational contribution being zero. INTERNAL ROTATIONAL CONTRIBUTIONS. Rotation about any single bond in which the groups on both ends of the bond have lateral extension requires energy. The rate of acquisition of this energy is governed by the moments of inertia of both groups, the number of potential minima, and the potential barrier hindering the rotation. The contributions of characteristic rotators t o heat capacity are given in Table V ; Table IV contains the corresponding contributions t o heat cohtent. The user should attem t t o choose from these the internal rotations most like those in t i e molecule under consideration. No two rotations in different molecules will give exactly the same contribution, but it is felt that the "charac-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1042
Vol. 41, No. 5
TABLE VI. ITEAT CAPACIT~ES OF HYDROCARBON VAPORSAT ZERO PRESSURE^ (Concluded) Temp., F. -250 - 200 - 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
Temp.,
F.
-250 - 200 - 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000 a
t?’QnS-2Butene 12.87 14.07 16.45 18.87 21.50 24.28 26.91 29.47 31.92 34.25 36.38 38.42 40.34 42.08 43.68 45.10 46.35 47.46 48.51 49.50 50.42 51.30 52.15 52.96 54.57 55.86 56.83 57.65 58.42 Stat. calod. Methylcyclopentane 11.51 13.03 16.97 21.66 26.97 32.62 37.86 42.80 47.34 51.52 55.26 58.67 61.74 64.61 67.20 69.59 71.81 73.83 75.67 27.37 18.96 80.83 81 .76 82.99 85.20 87.11 88.78 90.19 91.40 1111
ris-2Butene 12.42 13.17 14.90 17.13 19.83 22.77 25.70 28.52 31.06 33.48 35.72 37.74 39.62 41.33 42.93 44.39 45.76 47.02 48.18 49.26 50.25 51.17 52.02 52.80 53.18 55.45 56.48 57.30 58.05 Stat. oalod. Cyclohexane 11.37 12.75 16.35 21.03 26.61 32.49 38.25 43.53 48.39 52.71 56.61 60.15 63.39 66.39 69.03 71.43 73.65 15.75 77.61 79.29 80.85 82.23 83.55 84.75 86.85 88 71 90.21 91.53 92.61
Iso-
butylene 10.79 13.65 16.56 19.41 22.27 25.15 27.87 30.42 32.79 34.99 37.01 38.87 40.58 ,42.20 43.69 45.07 46.37 47.54 48.64 49.67 50.62 51.51 52.29 53.04 54.37 55, 53 56.52 57.38 58.12 2 VI11 Methylcyolohexane 12.80 14.91 19.97 25.72 32.20 38.97 45.47 51.45 56.96 61.86 66.29 i o . 29 73.94 77.35 80.38 83.13 85.68 88.05 90.16 92.10 93.91 95.53 97.04 98.43 100.87 103,Ol 104.77 106.32 107.59 1 I11
Acetylene 7.13 7.43 8.47 9.69 10.75 11.61 12.29 12.87 13.35 13.79 14.17 14.53 14,85 15,17 15.47 15.75 16.01 16.27 16.51 16.73 16.95 17.17 17.35 17.53 17.85 18.15 18.39 18.61 18.81
CJ,olapentane 9.78 10.92 13.95 17.68 21.75 25.93 29.90 33.58 36.93 40.01 42.77 45.28 47.51 49.56 51.40 53.13 54.73 56.20 57.54 58.75 59.86 61.17 61.82 62.69 64.25 65.60 66.75 67.71 68.56
Methylacetylene 9 16 9.93 11.58 13.22 14.85 16.44 17.89 19.23 20.46 21.58 22.62 23.57 24.45 25.28 26.05 26.76 27.43 28.05 28.61 29.14 29.66 30.14 30.56 30.96 31.66 32.28 32.81 33.28 33.69
Cyclohexene 10.89 12.53 16.55 21.27 26.45 31.75 36.87 41.55 45.83 49.63 53.07 56.17 58.97 61.55 63.83 65.93 67.87 09.69 71.31 72.77 74.11 75.29 76.43 17.47 19.29 80.89 82.17 83.29 84.23
Dimethylacetylene 12.06 13.15 15.10 17.02 19.11 21.29 23.46 25.54 27.48 29.31 31 . O O 32.58 34.03 35.37 36.63 37.79 38.66 39.84 40.77 41.61 42.43 43.13 43.82 44.43 45.55 46.51 47.29 48.04 48.65 Stat. calod.
Vinylaoetylene 9.98 10.90 12.94 15.16 17.34 19.40 21.28 22.98 24.51 25.88 27.12 21.26 29.28 30.24 31.11 31.91 32.66 33.33 33.98 34.56 35.12 35.61 36.08 36.51 37.29 37.95 38.50 39.02 39.44 Stat. calcd.
Diacetylene 9.93 11 46 14.44 16 86 18.72 20.10 21.15 22.02 22.74 23.38 23.95 24,46 24.93
25.39 25.82 26.21 26.58 26.95 27.25 27.54 27.85 28.14 28.39 28.62 89.03 29.40 29.71 30.00 30.27 1 7711
Benzene
Toluene
...
...
...
... ...
t . .
16.41 20.55 24.51 28.23 31.71 34.71 37.35 39.63 41.79 43.71 45.51 47.07 48.45 49.77 50.91 51.99 52.96 53.85 54.69 55.47 56.19 57.51 58.65 59.49 60.21 60.87
o-Xylene
...
...
...
411ene 8.96 9.64 11.07 12. 70 14.48 16.19 17.80 19.25 20.5; 21.74 22.82 23.81 24.71 25.54 26.34 27.04 27.72 28.35 28.93 29.45 29.93 30,38 30.80 31.20 31.91 32 53 33.03 33 49 33.89
21.13 26.84 30.50 34.92 39.06 42.73 46.00 48.88 51.56 53.98 56,23 58.21 59.99 61.67 63.13 64.49 65.73 66.88 67.95 68.93 69.84 71.49 72.93 74.06 75.04 75.90 1X
28.03 33.15 38.29 43.21 47.81 51.97 55.71 59.05 62.15 64.99 67.61 69.93 72.05 74.03 75.77 77.37 78.85 80.23 81.51 82.65 83.73 85.69 87.41 88.81 90.05 91.09 2 vo
13-Budadiene 9.45 10.75 13.58 16.73 19.84 22.82 25.36 27.60 29.61 31.43 33.11 34.63 35.98 37.29 38.37 39.43 40.44 41.38 42.25 43 02 43.71 44.35 44.97 45.55 46.55 47.43 48.14 48.77 49.31 1 VI
m- OT
1 “I
Isoprene 11.04 14.12 18.22 22.28 26.12 29.75 32.91 35.72 38.27 40.61 42.76 44.72 46.49 48.14 49.66 51.06 52.39 53.61 54.75 55.78 56.72 57,60 58.41 59.17 60.50 61.66 62.63 63.48 64.21 1 VI 1 VI11
Ethylbenzene
RIeuitylene
1 Va
... ...
25.85 31.13 36.49
41.61
46.41 50.75 54.65 58.13 61.33 64.25 66.95 69.35 71.53 73.57 75.35 76.99 78.51 79.91 81.21 82.39 83.49 85.47 87.21 88.63 89.87 90.93 2 x
Cyolopentane 9.90 10.60 12.95 16.50 20.85 25.45 30.00 34.20 38.05 41.65 44.85 47.80 50.45 52.90 56.15 57.15 59.05 60.85 62.45 63.86 65.25 66.95 67.60 68.65 i o . 55 72.20 73.65 74.85 75.90
Styrene
..
..I
Units B.t.u./lb. mole-” F.
teristic” rotat,ions given afford a choice wide enough to give adequate accuracy in all practical cases. A simple schematic group drawing of t h e molecule under consideration will usually indicate which characteristic rotation should be chosen. As a furt,her guide, the internal rotation types used in calculating the values in Tables VI and VI1 are listed at the bottom of each column. The Roman numerals there refer t o the internal rotation type (in Tables I1 or I V ) and the Arabic digit t,o the number of internal rotations of that type. When the potential barrier restricting int’eriial rotation is very low (500 calories per mole or less), the contribut,ion to heat capacity of a n internal rotation is very nearly l/z IZT a t all temperatures above 0”F. The methyl group rotation in toluene is of this type, as is also the rotation in dimethylacetylene (example 3). Because the restrictive forces are low, due to wide separation of the rotating groups, this type of rotation is called “free,” to distinguish it from other “restricted” rotations. One internal rotational contribution will be made by each carbon-carbon single bond unless there is no lateral extension a t either end of the bond. Thus -C=H gives no contribution, but
p-
Xylene
trans1,3-Pentadiene 11.24 13.19 17.12 21.14 24.96 28.72 31.97 34.92 37.62 40.06 42.33 44.39 46.24 47.94 49.50 50.97 52.35 53.62 54.79 55.86 56.82 57.70 58.52 59.30 60.66 61.85 62.82 63.67 64.39
26.29 31.92 37.40 42.58 47.44 51.72 55.51 58.90 62.06 64.93 67.56 69.88 71.99 73.99 75.74 77.37 78.85 80.24 81.53 82.69 83.79 85.76 87.47 88.84 90.03 91.05 1 \’a 1 IX
80.58
36.43 4L.49 48 31 53.77 58.78 63.31 67.39 71.11 74.53 77.68 80.50 83.08 85.48 87.58 89.50 91.30 92.95 94.48 95.86 97.15 59.46 101.50 103.21 104.71 105.97 3 x
2d.11 30.86 3(j , 2 5 41.04 45.35 49.11 52.44 55.36 68.07 60,48 62.71 64.67 06.43 68.10 69.57 70.94 72.16 73.27 74.31 75.29 76.19 77.81 79 23 80.32 81.21 82.10 1 VI
H -C-H/ does. These considerations should bc made clear by the \ H following examples: Example 1 . Calculate the heat capacity of 2-methylpentane a t 300” F. The molecule contains three CHa- groups, two
I I
-CHt-
groups, and one -CH
group. An analysis of the interI
nal rotations shows three groups on the -hH
group. This is
analogous t o the isobutane molecule, and we Amy thus t>akrthree isobutane (or R d H ) type rotations. The rotation between the
I
CH, and the CH? group is like that in propane, and the
I
I
CH2-CH2 internal rotation is counterclockwise, analogous to that occurring in n-butane. Picking these contributions from Table V:
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1949
TABLE VII. HEATCONTENTS Temp.,
F.
Methane 1,666.2 2,063.5 2,860.4 3,670.0 4,512.1 5,406.9 6,374.0 7,417.5 8,542.9 9,741.3 11,016 . 12,364 13,789 15,280 16,835 18,450 20,122 21,859 23,625 25,457 27,306 29,228 31,163 33,151 37,204 41,374 45,674 50,002 54,454 Stat. Calcd.
- 250 - 200
- 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
Temp.,
3-Methylpentane -250 2,121.8 2,935.0 -200 4,973.4 - 100 7,569.8 10,709 14,405 18,669 23,442 28,654 34,278 40,279 46,617 53,302 1000 60,275 1100 67,511 1200 74,982 1300 82,098 1400 90,600 98,704 106,980 115,335 124,046 132,806 2000 141,659 2200 159 791 2400 178:326 197,215 2600 2800 216,434 3000 235,904 2 I1 3 I11 a Heat content = 0 a t O
F.
Group 3 CH32 -CHz-
Ethane 1,721.2 2,172.1 3,135.4 4,216.0 5,430.2 6,802.5 8352.5 101083 11 960 13:987 16,154 18,456 20,888 23,436 26,092 28,847 31,698 34,629 37 647 40:739 43 904 47:135 50,432 53,778 60,628 67,648 74,825 82,138 89,565 1I X
Propane 1,825.3 2,369.7 3,596.2 5,041.8 6,725.0 8,673.3 10,905 13,399 16,118 19,052 22,189 25,507 29,015 32,680 36,492 40,434 44,516 48,702 52,999 57,395 61 890 66,'474 71,143 75,866 85 548 95:457 105,571 115,870 126,314 2 I1
2,2-Dimethylbutane 2,098.7 2,934.9 5,049.1 7,754.8 11,014 14,836 19,237 24,173 29,551 35,340 41,511 48,029 54,872 61 998 69'387 76:998 84 844 92:874 101,107 109,500 118,065 126,774 135,632 144,590 162 887 181:578 200,595 219,941 239,518 1 I1 4 IV Oo R.; units
n-Butane 2,016.1 2,675.7 4,231.1 6 138.5 d393.5 10,998 13,956 17,239 20,811 24,653 28,754 33,081 37,654 42,423 47,375 52 492 57:783 63,206 68,770 74,458 80,270 86,193 92,220 98,308 110,797 123,569 136,599 149,864 163,312
11
2 I1
2,3-Dimethyln-Heptane butane 2 242 3 2,588.2 3:090:7 3 593 7 6:135:8 5,249.9 9,428.6 8,009.3 11,327 13,399 17 972 15,159 23:109 19,513 24,363 28,759 29,627 34,890 35,293 41,456 41,324 48,449 47,689 55,803 54,382 63,571 61,363 71,652 68,005 80,024 76 084 88,666 83:795 97,584 91,688 106,718 116,083 99,792 108,084 125,647 135,410 116,516 145,350 125,121 155,451 133,882 142,754 165,634 160 871 186,544 179:393 207,905 229 683 190,267 217,470 251:846 236,932 274,306 11 41 4 I11 2 I1 = B.t.u./lb. mole.
OF
HYDROCARBON VAPORS AT ZERO
Isobutane 1,945.8 2,588.4 4,121.8 5,996.6 8,212.6 10,777 13,709 16,990 20,558 24,408 28,513 32,855 37,426 42,201 47,161 52 288 57:580 63,002 68 572 74:262 80.079 86,006 92,044 98,161 110,661 123,450 136,489 149,760 163,214 3 I11
3-Ethylpentane 2,209.8 3,108.3 5,399.2 8,356.4 11,958 16 219 2i.149 26,068 32 702 39:213 46,162 53,498 61,240 69,312 77,686 86,329 95,257 104,399 113,770 123 339 133:113 143,066 153,187 163,408 184,356 205,764 227,578 249,771 272,249 3 I1 3 111
Contribution to Heat Capacity a t 300' F. 3 X 3.20 = 9.60 2 X 4.87 = 9.74
3 II? internal rotation 1 I1 internal rotation 1 I internal rotation Translation plus external rotation plus (CpO - C V " ) Total heat capacity a t 300° F.
.
n-Octane 2,779.2 3 899 7 6:770: 7 10,525 15,068 20,296 26,160 32,599 39,583 47,057 55,014 63,377 72,210 81,395 90,907 100,724 110,851 121,222 131,854 142,710 153,790 165,069 176,528 188 076 211:793 236,017 260,711 285,840 311,304 51 2 I1
1 --Ti=
=
7.95
2,2,4-Trimethyl pentane
2 3 4-Tri&thylpentane
2,307.2 3.326.9 6,000.5 9,495.9 13,750 18 755 24:521 30,990 38,039 45 631 53'718 62:258 71,221 80,556 90,231 100,199 110,467 120,973 131,746 142,726 153,942 165,326 176,914 188,634 212,565 237 009 261:876 287 168 312:763 3 I11 4 IV
2,348.0 3,350.0 5,992.2 9,440.6 13,642 18,566 24,226 30,566 37,470 44,918 52,849 61,225 70,030 79,215 88,741 98,574 108,710 119,082 129,726 146,586 151,681 162,974 174,468 186,105 209 865 234:150 258,883 284,040 309,524 7 I11
n-Hexane 2397 7 3:287:7 5,500.9 8,331. 9 11,731 15,647 20,058 24,919 30,197 35,855 41,884 48,229 54,932 61,909 69,141 76,608 84,317 92,214 100,312 108,584 117,030 125,631 134,374 ''143,192 161,295 179,793 198,655 217,852 237,308 3 1 2 I1
n-Nonane 2,970.1 4,205.7 7,405.6 11,822 16,736 22,621 29,211 36,439 44,276 52,658 61,579 70,951 80,849 91,138 101,790 112,782 124,118 135,726 147,625 159,773 172,170 184,788 197,605 210,518 237,042 264,129 291,739 319,834 348,302 6 1 2 I1 (Continued
2-Methylpentane 2,224.6 3,067.7 5,182.5 7,879 . 9 11,129 14,919 19,240 24,056 29,299 34,944 40,961 47,310 54,003 60,981 68,219 75,693 83,406 91.305 99,409 107,684 116,137 124,745 133,502 142,352 160,475 179,000 197,880 217,091 236,557
11 111
3 I11
n-Decane 3 160 8 4'511'7 8:040:5 12,719 18,405 24,946 32 262 40:279
Contribution t o Heat Content a t 1000° F. = 4,795 = 3,830
Group
3 X 2.18 = 6.54 1 X 2.16 = 2.16 1 X 2 . 6 5 = 2.65 = 45.63B.t.~./mole-~ F.
Neopentane 2,010.7 2,761.6 4,623.3 6,967.9 9,765.5 1 3 022 16'757 20:947 25 503 30:405 35,628 41,148 46,934 52,961 59,212 65 651 72:285 79,075 86,041 93,141 100 387 107,'754 115,251 122,841 138,322 154,140 170,232 186,604 203,173 4 IV
CH3CHz=
I X 6.89 = 6.89
4R
Isopentane 2,033.8 2,761.7 4,547.6 6,783.2 9,460.9 12,591 16,189 20,216 24.606 29,343 34,396 39,736 45.364 51.238 57,336 63 635 70'139 76:601 83,638 90,621 97,757 105,026 112,425 119,910 135.226 150,888 166,852 183.097 199,559 1 I1 3 111
PRESSURE'
these rotations and the group vibrational contribution from Table IV, one has: 1 1
Example 9. Calculate the heat content of 2-methylbutene-1yne-3 a t 1000° F. (Table IV has a datum level of zero heat content a t 0 R.) If the -C=CH group were replaced by a hydrogen atom, the molecule would become propylene. Thus for the =C-CHa rotation contribution one takes the propylene (Va) value. As explained above the other carbon-carbon single bond has zero internal rotational contribution. There is no conjugation contribution between a double and triple bond. Picking O
n-Pentane 2,206.9 2,981.7 4,866.0 7,235.2 10,062 13,323 17,007 21,079 25 504 30:254 35,319 40,655 46,293 52,166 58 258 64'550 71:050 77,710 84,541 91,521 98,650 105,912 113,297 120,750 136,046 151,681 167,627 183,858 200,310 21 2 I1
1043
-I i -G
+
[UD-
8,101 4,927 3,239 2,228 4 R T = 11,599 =
1 IICE 1 Va, internal rotation external rotation Trans.
-
+
= = =
VV')
Total heat content a t io000 F.
=
38,719 B.t.u./mole
Example 8. Calculate the heat content a t 800' F. of hexadiyne2,4. For the urposes of internal rotation, one could consider the molecule as geing CHI-CHI. Thus there would be one internal rotational contribution. Because of the extreme separation of the two rotating groups, the molecule exhibits free rotation-i.e., the contribution to heat content is the classical value RT.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1044
TABLEVII. HEATCONTENTS OF HYDROCARBON VAPOR6
AT ZERO PRESSUREa
Vol. 41, No. 5
(Continued)
A per
-CHzGroup 190.8 306.0 634.9 1,096.7 1,668.5 2,324.6 3,051 3,840 4.693 5,601 6,565 7,574 8,639 9,743 10,883 12,068 13,267 14,504 15,771 17,063 18,380 18,719 21,077 22,442 26,249 28,112 31,028 33,994 36,098 11
Temp. F. -250 -200 100 0 100 200 300 400 ,500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
-
3-31ethyl1-butene
Te trip,, 0
v.
- 250 - 200
Ethylene 1,666.2 2,065,2 2,884.7 3,777.9 4,784.7 5,917.9 7,195.7 8,613.4 10,140 11,774 13.511 15,337 17,260 19,259 21,329 23,470 25,672 27,949 30,255 32,634 3.5,031 37.503 39,994 42,542 . 47,714 53,013 58,414 63,921 69,506
Propylene 1,794.9 2,298.9 3,413.9 4,708.5 6,189.9 7,874.6 9,775.6 11,899 14,199 16,656 19,284 22,061 24,986
1-Butene 1,942.5 2,540.2 3,949.7 5,686.7 7,741.0 10,101 12,760 15,713 18,902 22,319 25,956 29,782 33,812 38,002 42,343 46,823 51,442 56,183
44,869 48,503 52,212
61.020
$3,977 11,028 76,170 81,400 86,602 97.500 108,610 110,800 131.255 142,860 I1 1 I1
25,098
~9,842
1V 2-AIethyl2-butene
1-liexene
Acetylene 1,460.5 1,816.1 2,615.6 3,525.5 4,550.2 5,667.7 6,868.1 8,133.1 9,456.4 10,820 12,219 13,650 15,121 16,628 18,158 19,719 21,306 22,926 24,561 26,228 27,904 29,619 31,338 33,085 36,622 40,221 43,873 47,575 51.318
2.072.2 2,324.1 3,152 , 2 2,811.4 5,219.3 4,607.3 0 6.819.7 7,879.1 100 11,078 9,364.8 200 12,285 14,751 300 15,862 18,863 400 19,204 23,393 500 23,131 28,288 600 27,345 33,521 700 31,828 39,080 800 36,567 44,930 900 51,090 41,648 IO00 46,742 57,488 1100 52,134 64,109 1200 57.703 20,939 1300 63,448 (7,976 1400 69,340 85,191 1,500 75,390 92,568 1600 100,103 81,571 1700 107,788 87,877 1800 115,614 94,309 1900 123,554 100,855 2000 107,489 132,676 2200 121,025 147,998 2400 134,867 164,170 2600 148,979 181,856 2800 163,334 190,243 moo 177,886 216.856 3 1 1. v 2 VIIS 1 I1 a Heat content = 0 a t Oo R.; units = B.t.u./lb. mole. 1,960.2 2,626,2 4,266.2 6,330.4 8,808.4 11,694 14,894 18,690 22,697 27,009 31,598 36,437 41,522 46,817 02,304 57,966 63,798 69,778 75,804 82,147 88.515 95,009 101,605 108,294 121,929 135,864 150,053 164,488 179,107 3 111
- 100
lletllylacetylene 1,727.3 2,198.5 3,272.4 4,513.3 5,918.8 7,473.7 9,203.1 11,065 13,064 15.156 17,362 19,666 22,069 24,560 27,127 29,767 32,477 35,252 38,081 40,971 43,902 46,900 49,933 23,010 69,274 65,666 72,172 78,782 85,478
Conjugation of the triple bond also contributes t o heat content, and its effect is added as shown below (Data taken from Table IV) : Group 2 CHI4 -CE Triple bond conj. (VII) 1 free rotation (X) Trans. external rotation (CnO
+ -
+
CoIitribution t u Heat Content a t 800' I 2 X 3,256 = 6,512 4 x 3,955 = 15,820 1 x 774.2 = 774.2 RT = 1,251.2 4 RT = 10,009.3
C V O )
Totai beat rontent a t 800° F.
=
cis-2Butene 2,206 2,843 4,244 6,840 7,706 9,847 12,287 14,997 17,970 21,195 24,651 28,314 32,190 36,239 40,439 44,833 49,342 54,015 58,754 63,654 68,594 73 694 is:s23 84,073 94,735 105,711 116,000 128,288 139,877 Star. Calcd.
trans-2Butene 2,044 2,714 4,242 6,015 8,038 10,329 12,888 15,708 18,777 22,021 25,531 29,257 33,208 37,366 41,663 46,113 50,661 55,305 60,023 64,898 69,814 74,905 80,039 85,351 96,338 107,406 118.730 130,189 141,804 Stat. Cdlcd.
34,366.7 B.t.u./mole
Irobutylene 1,943.5 2,577.8 4,078.1 5,889.1 7,959,6 1.0.32s 12,982 15,918 19,079 22,463 26,056 29,843 33,822 37,968 42,266 46,702 51,275 55.970 60,776 65,695 70,696 75,814 81,007 86,281 07,025 108,014 119,214 127,627 142,166 2 VI11
Dimethylacetylene 1.995.1 2,580.9 3,929.2 3,501.1 7,287.4 9,278.7 11,538 13,997 16,651 19,491 22,505 25,762 29,017 32,492 36,096 39,815 43,648 47,578 61,601 55,714 59,900 64,181 68,528 72,935 81,926 91,111 100,471 109,989 119,638
1X
Ethylacetylene 1,799.2 2,347.5 3,663.2 5,260.8 7,129.6 9,231.3 11,611 14,201 16,692 19,960 23,093 26,317 29,818 33,390 37,077 40,874 44,777 48,777 52,861 57,033 61,272 65,801 69,984 74,420 83,484 92,733 102,152 111,724 121,419 1 IX
2-Methyl1-butene
truns-2-
1-Pentene 2,133 . 3 2,846.2 4,594.6 6,782.4 9.409.5 12.420 14,768 19,553 23,595 27,92 0 32.521 37,356 42,451 47,743 53,226 58,881 64,709 70,687 76,797 83,040 89,408 9539.5 102,477 109,134 122.749 136,658 150,828 165,249 179,868 21 I I1
Pentene 2,071.2 2,773.8 4,478.9 6,616.3 9,146.2 12,058 15,341 18,999 22,934 27,201 31,720 36,506 41,538 46,'776 52,211 57.824 63,610 69,533 75,640 81,860 88,205) 94,671 101,248 107,900 121,500
2,109.5 2,847.9 4,657.8 6,915.2 9,549 .Q 12,573 15,959 19,694 '23,722 28,030 82,005 37,417 42.477 47,741 53,194 3S,819 04,617 70,563 76,646 82,868 89,197 95,663 102,229
135,3HB
149,565
163,978
178,,580 11 1 11
11 I I1 I VI11
tr
Methylcthylacetylene 2,067.0 2,729.9 4,320.0 6,248.5 8,489.2 11,037 13,946 17,133 20,490 24,296 28,236 32,393 36,766 41,322 46,046 50,922 55,948 61,103 66,381 71,776 77,270 82,882 88,579 94,345 106,136 118,178 130,451 142,931 i65,579 1 IX I X
n-I'ropylacetylene 1,832.2 2,545.1 4,124.0 6,080. 5 8,415.4 11,102 14,163 17,517 21,150 23,025 20,128 33,428 37.945 42,634 47,477 52.461 57,592 62,880 68,213 73,689 79.238 84,940 90,695 96,508 108,404 120,542 132.898 145,456 158,l68 2
TI
1301)ro~ylametylenc
1,842.4 2,256.6 4,175.2 6,196.5 8.291 .? 11,320 14,410 17,795 21,446 25,338 29,462 33.763 38,277
2 SI
(Continued on page 1046:
St the present time few reliable data are available €or evaluation of the contribution of a --AIS group in a ring, and thus a I I paraffin -CH contribution is ukd. On the other hand, the --CE- rikg contribution has been evaluated; in this case the cyclopentane -CHsgroup should be chosen. From Table IV,
.,..-
nno ha-.
Group
Contribution t o Heat Content at 600' F. 1 X 1,985 = 1,985 2 X 3,208 = 6,416
Example 4. Calculate the heat content of n-propylcyclopentane at 600" F. T h e groups in the ring structure are unable to rotate and thus make no rotational contribution to heat content. Of the other rotations, that between the --CH2- group in the
1
chain, and the -AH
4 X 2,890 ~ ~ ~ ~ ~ n a l ( r O ~ ~ ~ ~ ~ ~ ~1 X t a2,393 n e 1 X 1727 1 I1 internal rotation 1 X 1:763 1 111 internal rotation 4 RT TrT6:' rotatLon -t
= 11,560 = =
2,393 1727 1:763 8,420
Total heat content a t 600' F
=
39,008
group in the ring is most analogous t o the
isobutane type of' internal rotation. The CHB-CH2 rotation and the CHs-CHs rotation are readily seen t o be analogous to the rotations in propane and n-butane. rcspectively.
CHs--
-cHz-
.-LHI
(paraffin)
(paraRnj
2 :tFnal
1
x
4,744 = 4,744 = ) =
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1949
TABLE VII.
HEATCONTENTS O F HYDROCARBON VAPORS AT ZERO PRESSURE" (COnt'hUed) trane-
TEmZ., -250 -200 - 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
Allene 1,721.1 2,182.3 3,209.2 4,397.1 5,756.3 7,287.9 8,989.7 10,854 12,846 14,958 17,185 19,509 21,941 24,456 27,050 29,721 32.459 35,279 38,129 41,060 44,009 47,040 50,089 53,200 59.503 65.942 72,488 79,146 85,886
1,2-Butadiene 1,849.8 2,415.9 3,738.4 5 327.7 7:161.5 9,244.6 11,570 14,140 16,897 19,840 22,958 26,233 29,667 33,230 36,918 40,722 44,633 48,649 52,743 56,936 61,190 65,535 69,937 74,408 83,503 92,795 102,253 111,869 121,606 1 Va
T e nip, 0
v.
- 250 - 200 - 100 0 100 200 300 401) 500
coo
IO0 8(10 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
1-Pentene4-yne 1,872.9 2,474.3 3,941.7 5,753 2 7,880.3 10,303 13,034 16,017 19,224 22,629 26,223 29.982 33,916 37,987 42,182 46,498 30,925 55,467 60,083 64,804 69 580 74:464 79,392 84.392 94,570 104,951 115,5i)d 126,230 137,080 1 Va
a Heat content = 0
2-Methyll-butene3-yne 1,926 0 2,572 8 4,168 8 6,128 5 8,362 7 10,882 13,679 16,708 19,946 23,371 26,973 30,736 34,659 38,719 42,903 46,206 51,617 56,137 60,736 65,439 70,192 76.061 79,975 84.968 85,107 105,450 115,967 126,647 137,461 1 Va
1045
1,3-Butadiene 1,766.8 2,270.0 3,475.0 4,992.2 6,820.8 8,951.4 11,361 14,038 16,900 19,948 23,174 26,554 30,094 33,757 37,537 41,428 45,423 49,530 63,696 57,969 62,286 66,702 71,163 75,699 84,899 94,288 103,834 113,536 123,347 1 VI
13-Pen&diene 1.895.5 2,503.6 4,004.2 5,922.8 8,226.0 10,908 13,941 17,324 20,952 24,830 28,947 33,218 37,820 42,631 47,405 52,429 57,597 62,900 68,310 73,845 79,467 85,197 91,011 96,907 108,899 121,141 133,699 146,259 169,067 1 vs 1VI
1.4-Pentadiene 1940 5 2:574: 7 4,083.2 5,948.4 8,151.4 10,704 13,607 16,851 20,362 24,130 28,145 32,377 36,833 41,460 46 252 51:202 56.294 61,534 66,871 72,343 77,890 83,662 89,303 95,132 107,010 119,151 131,513 144,092 156,828 2 Va
Diacetylene 1,589.1 2,161.4 3,465.0 5,036.6 6,823.9 8,752.4 10,840 12,997 15,243 17,554 19,920 22,334 24,804 27,328 29,889 32,493 35,133 37,819 40,524 43,270 46,025 48,841 51,659 54,514 60,281 66,124 72,030 78,006 84,033 1 VI1
1,3-PeIItadiyne 1,906 9 2,543.8 4,121.8 6,024 4 8,192.5 10,568 13,173 15,929 18,842 21,890 25,063 28,350 31,752 35,260 38,858 42,541 46,304 60,146 54,044 58,013 62,023 66,122 70,254 74,439 82,933 91,369 100,329 109 213 118:193 1 VI1
1,4-Pentsdiyne 1,805.3 2,373.9 3,800.2 5,558.0 7,609.2 9,902.5 12,462 15,183 18,086 21,128 24,301 27,587 30,999 34,514 38,107 41,794 45,556 49,400 53.295 57,265 61,262 65,366 69,485 73,652 82,080 90,751 99,499 108 368 117:332
a t O0 R.; units = B.t.u./lb. mole.
COMPARISONS WITH DATA AND OTHER CORRELATIONS
A comparison of experimental heat capacities as reported by several investigators (3,16, 87, SO, 34, 35, 58,41, 43, 48)with those calculated from the correlation has been made for all hydrocarbons and at all temperatures reported by these investigators. I n general, the agreement is excellent. The differences rarely exceed 3% and average only 1.3% with the positive deviations approximately equal t o the negative deviations. Inclusion of the experimental data published since 1945 does not substantially alter these results. A systematic comparison of heat capacities as calculated by the methods of statistical mechanics using the frequencies and potential barriers given as Table I11 has been made with those calculated from the correlation between 200' and 2000" K. for all the hydrocarbons listed in Table 111. In general, the
Isoprene 1,933.8 2,577.7 4,183.1 6,222.7 8,629.7 11,423 14,559 18,019 21,720 25,659 29,823 34,189 38,759 43,495 48,388 53.424 58,598 63,910 69,316 74,853 80,455 86,189 91,986 97,877 109,837 122,047 134,467 147,088 159,862 1 VI 1 VI11 1,3-Hexadiyne 1,978.8 2,692.8 4,512.6 6,771.8 9,394.3 12,315 15,583 19,065 22,780 26,695 30,794 35,001 39,501 44,090 48,808 53,648 58,604 63,670 68,824 74,075 79,393 84,823 90,305 95.849 107,143 118,636 130,579 142,158 154,134 1 VI1 1 IX
%Methyl1,3-pentadiene 2,062.5 2,811.3 4,712.3 7,152.3 10,034 13,380 17,139 21,305 25,772 30,541 35,596 40,913 46,485 52,269 58,256 64,425 70,772 77,280 83,930 90,729 97,636 104,684 111,834 119,085 133,837 148,900 164,232 179,811 195,582 1 Va 1VI 1 VI11 1,4-Hexsdiyne 2,073.1 2,756.3 4,457.0 6,545.8 8,977.8 11,709 14,797 18,115 21,683 25,464 29,444 33,603 37,947 42,446 47,081 51,842 56,727 61,726 66,815 72,008 77,268 82,647 88,080 93,577 104,732 116,196 127,798 139,575 151.492 1 x
1,3,5-Hexatriene 1,867.4 2,474.7 4,065.3 6,206.5 8,856.9 11,985 15,626 19,463 23,660 28,122 32,837 37,771 42,928 48,254 53,745 59,386 65,174 71,111 77,137 83,304 89,541 95,901 102,332 108,856 122,084 135,563 149,254 161,156 175,133 2 VI
Vinylacetylene 1,741.7 2,236.3 3,416.8 4,847.1 6,514.6 8,391.0 10,488 12,765 15,193 17,786 20,447 23,248 26,165 29,176 32,270 35,445 38,695 42,028 46,403 48,856 52,338 55,903 59,492 63,143 70,542 78,080 88,736 93,510 101,371
],&Hexadiyne 1,877.2 2,522.9 4,191.0 6,305.4 8,811.0 11,660 14,870 18,319 22,024 25,933 30,032 34,298 38,748 43,344 48 057 52:901 57,856 62,925 68,075 73,327 78,623 84,067 89,536 95.062 106,190 117,818 129,479 141,310 153,273 1 IX
2,4-Hexadiyne 2,174.7 2,926.2 4,778.6 7,012.2 9,561.1 12,364 15,510 18,861 22.440 26,226 30,206 34,366 38,700 43,192 , 47,827 52,589 57,475 62,471 67,564 72,756 78,021 x3.403 88,849 94.36? 105,580 117,014 128,628 140,420 152,353 1 VI1 1 x
1-Pentene3-yne 2,009.5 2,618.7 4,073.6 5,834.9 7,883.2 10,197 12,823 15,697 18,790 22,092 26,590 29,264 33,113 37,108 41,239 45,493 49,866 54,354 58,919 63,599 68,336 73,184 78,089 83,068 93,194 103,525 114,035 124,717 135,531
1x Cyclopentane 1948 7 2:460:0 3,619.1 5083 2 6:945 :8 9,266.4 12,046 15,256 18,881 22,870 27,205 31,839 36,754 41,924 47,328 52,938 58,752 64,752 70,906 77,221 83,666 90.260 96,945 103,764 117,689 131,973 146,547 161,396 176,470
(Continued on p a g e 1046)
agr:eement is excellent. Differences rarely exceeded 3% and the few cases where the differences exceed 3% are all a t temperatures below 50" F. Excluding those compounds which were used in building up the correlation, which naturally are in exact agreement, the average differences were only 1.0% and the positive deviations were approximately equal t o the negative deviations. The results of this correlation have been compared in detail with the compilations published by A.P.I. Research Project 44 ( 1 ) . The general agreement is excellent. I n heat capacity the agreement is as good as t h a t found in comparisons with calculations from spectroscopic data. The largest discrepancies with the A.P.I. tables are in the numerical values for heat content which include an integrated value from absolute zero that is not identical. T h e principal cause of discrepancy lies in the treatment of restricted internal rotation. All treatments of restricted
1046
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
I
Vol. 41, No. 5
TABLE VII. HEATCOXTENTS OF HYDROCARBON VAPORSAT ZERO PRESSURE^ (Continued) Methyloyclopentane 2,014.8 2,622 . 0 4,103.4 6,030.8 8,465.2 11,444 14,972 19,012 23,528 28,472 33,815 39,509 45,536 51,861 58,457 65 294 72:368 79,650 87,120 94,772 102,583 110,554 118,660 126,901 143,727 160,966 178,545 196,442 214,598 1 I11
Temp.
F.
O
-250 200 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
-
cis- or trans-l,2dimethylcyclohexane 2,068,2 2,836.1 4,855.5 7,547.7 10 996 15:152 20,100 25,725 31,966 38,792 46,119 53,917 62,180 70,839 79,853 89,180 98,810 108,699 118,849 129,222 139,817 150,613 161,586 172,714 195,428 218,653 242,306 266,351 290,722 2 I11
Temp.,
F.,
-- 200 250 - 100
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
a Heat content = 0 a t 0' ~
~
Ethylcyolopentane 2,102.8 2,795.3 4,529.2 6,817.4 9,713 5 13,258 17,452 22,238 27,576 33,407 39,698 46.390 53,474 60,898 68,632 76,641 84,927 93,449 102,186 111,131 120,261 129,574 139,041 148,650 168,292 188,404 208,908 229,779 250,943 1 I1 1 111
n-Propylcyclohexane 2,263.6 3,146.6 5,460.8 8,554.2 12 521 17:294 22,955 29,353 36,445 44,183 52,481 61 295 70:643 80,426 90,602 101,124 111,988 123,143 134 584 1461275 158,212 170,372 182,722 195,206 220.7 92 246 921 273:528 300,577 327,987 11
111 1111
1,l-Dimethylcyclopentane 2,116.9 2,848.8 4,693.5 7,123.7 10,165 13,864 18,190 23,129 28,611 34,579 41,002 47,828 55,024 62,555 70,394 78,499 86,871 95,475 104,295 113,315 122,515 131,890 141,421 151,101 170,846 191,054 211,636 232,584 253,813 2 IV
cis- or trans-l,2dimethylcyclopentane 2,080.9 2,784,O 4,587.7 6,978.4 9,984.6 i3,ezi 17,898 22,768 28,175 34 074 40:425 47,179 54,318 61,798 69,586 77,650 85,984 94,548 103,334 112 323 12 1:a00 130,858 140,375 150,038 169,765 189,959 210,543 231,488 252,726 2 I11
Isopropylcyclohexane 2,185.9 3,048.1 5,335.3 8,392.9 12 319 17:051 22,683 29,075 36,160 43,902 52,201 61,025 70,368 80,153 90,334 100,862 111,727 122,880 134,324 146,015 157,955 170,117 182,476 195,007 220,580 246,721 273,334 300,386 327,799 3 I11
n-Propylcyclopentane 2,293.6 3,101.3 5,164.1 7,914.1 11,382 16,583 20,503 26,078 32,269 39,008 46,263 53,964 62,113 70,641 79,515 88,699 98,194 107,953 117,957 128,194 138 707 149:293 160,118 171,092 193,541 216,516 239,936 263,773 287,941 11 1 I1 1 I11
Cyclopentene 1,864.5 2,379.8 3,606.7 5,187.0 7,157.0 9,543.8 12,336 15,528 19,061 22,908 27,053 31,455 36,100 40,956 46,008 51,232 56,628 62,180 67,860 73 675 79:600 85,636 91,769 97,998 109,795 123,681 136,907 150,358 163,986
Isopropylcyclopentane 2,215.9 3,002.8 5,038.6 7,752.8 11,180 15,338 20,231 25,800 31,984 38,727 45,983 53,694 61,838 70.368 79,247 88,437 97,933 107,690 117,697 127,934 138,384 149,038 159,872 170,873 193,329 216,316 239,742 263,582 287,753 3 I11
1-Methylcyclopentene 2,031.5 2,687.5 4,314.8 6,416.5 8,964.1 12,016 15,535 19,509 23,881 28,619 33,702 39,090 44,765 50,695 56,859 63,228 69,803 76,560 83,480 90,559 97,769 105,123 112,592 120,176 135,633 161,440 167,540 183,910 200,501 1 VI11
Cyclohexane 1,901.4 2,498.5 3,944.7 5,794.1 8,212.3 11,160 14,749 18,849 23,442 28,502 33,947 39,763 45,952 52,453 59,235 66,258 73,514 80,987 88,645 96,484 104,491 112,653 120,942 129,356 146,528 164,089 181,978 200,147 218,566
3-Methylcyclopentene 1,930.6 2,541.8 4,091 .O 6,134.6 8,674.6 11,721 15.262 19,284 23,708 28,508 83,663 39 125 44:882 50,893 57,137 63,588 70,244 77,078 84,074 95,226 98,517 105 940 113:484 121,135 136,733 152,674 168,905 185,404 202,114 1 I11
Methylcyclo-
hexane 1,984.8 2,667.3 4,400.1 6,670.9 9,603.9 13,155 17,424 22,287 27,704 33,647 40,033 46,840 54,066 61,646 69,544 77.719 86,162 94,840 103,747 112,853 122,154 131,633 141,264 151,035 170,978 191,371 212,137 233,246 254,644 1 I11
1-Ethylcyclopentene 2,103.4 2,836.5 4,705.6 7,163.9 10,166 13,773 17,943 22,645 27,819 33,424 39,433 45,801 52,514 59,525 66,968 74 335 82: 103 90,085 98,260 106,621 115,139 123,824 132,643 141,586 159,843 178,507 197,5?0 216,802 236,442 1 VI11 1IX
Ethylcyclohexane 2,072.8 2,840.6 4,825.9 7,457.5 10,852 14,969 19,904 25,513 31,752 38,582 45,916 53.721 62,004 70,683 79.719 89,066 98,721 108,639 118,813 129,212 139,832 150,653 161,645 172,784 195,543 218,809 242,500 266,583 290,989 1 I1 1 I11
1,Z-Dimethylcyclopentene 2,198.5 2,995.2 5,022.9 7,646.0 10,773 14,488 18,734 23,490 28,701 34,330 40,351 46,725 53,430 60 434 67:710 75 224 82:978 90,939 99 100 107:443 115,918 124,610 133,415 142,354 160,571 179,199 198 173 217:462 237,016 2 VI11
R.; units = B.t.u./lb. mole.
1 1-Di;ethylcyclohexane 2,086.9 2,894.1 4,990.2 7,763.8 11,284 15,566 20,642 26,404 32,787 39,754 47,220 55,159 63,554 72,340 81,481 90,924 100,665 110,665 120,922 131,396 142,086 152,969 164,025 175,235 198,097 22 1,459 245,228 269,388 293,859 2 IV
1,5-Dimethylcyclopentene 2,097.6 2,849.5 4,799.1 7,364.1 10,483 14,193 18,461 23,265 28,528 34 221 40:312 46,760 53,547 60,632 67,988 75,584 83,419 91,458 99,694 108,110 116,686 125,427 134,307 143,313 161,671 180,433 199,532 218,956 238,629 1 I11 1 VI11
( C o n t i n u e d o n page 1047)
~~
internal rotation are uncertain at low temperatures and because the approximation used in this correlation differs from that used for the A.P.I. tables, values obtained by integration through the low temperature range will not correspond numerically. Enthalpy differences between any two temperatures above 60' F., however, show good agreement with the A.P.I. tables, the discrepancy rarely exceeding 2% for temperature intervals of 500" F. or more. Although a systematic comparison with other heat capacity correlations (8, 6, 14, 17, 46) has not been attempted, a, large number of random comparisons show the earlier correlations t o be less satisfactory than the correlation proposed in this paper.
CONCLUSION
-4correlation with chemical structure has been developed for hydrocarbons which gives reliable values for heat capacity and heat content in the ideal vapor state above 50' F. Although i t is advisable t o take full advantage of the convenient tabulations of A.P.I. Project 44, the correlations here provided furnish a useful source of information for compounds not elsewhere tabulated. ACKNOWLEDGMENT
The authors thank Shell Development Company for permission to publish this paper.
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1949
1047
TABLE VII. HEATCONTENTS O F HYDROCARBON VAPORS AT ZERO PRESSURE" ( C O n k k U e d ) Temp.,
F.
-250 -200 100
-
0 100
200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
Temp.,
' F.
-250 -200 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
-
1-n-Propylcyclopentene 2,207.5 3034 1 5:166:4 7,989.7 11,461 15,644 20,495 25,961 31 977 38:579 45,488 54,852 60,641 68,769 77,368 85,922 94,921 104,158 113 612 123:277 133,125 143,163 153,354 163,674 184,763 206,316 227,866 250 584 273:191 2 I1 1 VI11 1 3 - c clodexa&ene 1802 2 2:365:3 3,804.3 5,718.5 8,119.9 10,QSB 14 329 18:121 22 262 26:750 31,547 36,623 41,972 47 547 53:315 59,266 65,394 71,681 78,105 84,664 91,343 98,129 105,018 111,992 126,188 140,661 155 372 170'301 185:398
Cyclohexene 1,851.8 2431 9 3:874: 5 5,756.3 8,166.1 11,075 14 539 18:485 22.862 27,626 32,747 38,193 43,962 49,997 56,275 62,762 69,454 76,331 83,375 90,574 97,917 105,391 112,980 120,674 136,358 162,375 168,670 185,221 201,988 2-Me thyl-
:2:li%;
1,969.2 2,673.0 4,426.4 6,948.0 9,928.8 13,461 17,527 22,102 27,082 32,461 38 196 441258 50,637 57,280 64,166 71,262 78,569 86,061 93,725 101,548 109,512 117,616 125,841 134,170 151,126 168,420 186,005 203,853 221,913 1 VI11
1-Methyloyclohexene 2,018.8 2,739.6 4,582.6 6,985.8 9,975.0 13,547 17,737 22,466 27,672 33,337 39,396 45 828 52:627 59 736 67'126 74:758 82,629 90,711 98,995 107,458 116 086 124'878 133:803 142,852 161,296 180,134 199 303 218,'773 238,497 1 VI11 5-Methyl1,3-0yOlohexadiene 1,885.6 2,534.1 4,259.7 6,595.3 9,611.5 12,967 17,004 21,559 26,624 31,895 37 633 43:700 50,086 56,734 63,624 70,727 78 042 853540 93,207 101,033 109 006 117:109 125,340 133,671 150 638 167'943 1851547 203,406 221,476 1 I11
1-Et hylcyclohexene 2,090.7 2,888.6 4,973.4 7,733.2 11,186 15,304 20,145 25,602 31,610 38 142 45:127 52,639 60,376 68,666 77,076 85,865 94 929 104:236 113,775 123 520 133:456 143 579 163:854 164,262 185,506 207,201 229,283 251,715 274,438 1 VI11 1 IX
3-Methylcyolohexene 1935.2 2:600.7 4,329.9 6633 1 9:557 :7 13,071 17,214 21,923 27 114 32:771 38,833 45,270 52,076 59,190 66,584 74,223 82,102 90,190 98 477 106'943 115:580 124,371 133,302 142.353 160,808 179,657 198,839 218,326 238,560 1 I11
Benzene
Toluene
. ..., .... ..
1,2-Dimethylcyclohexene 2,185.8 3,047.3 6,290.7 8,215.5 11,784 16,019 20,936 26,447 32,492 39,048 46 046 53:463 61,292 69,475 77 977 86:754 95,804 105,091 114,615 124,342 134,255 144,365 154,626 165,030 186 234 207h93 229,936 252,325 275,012 2 VI11 p-
or m-
Xylene
....
.... 6,019.5 8,363.5 11,172 14,462 18,188 22,277 26,710 31,440 36,451 41,735 47,255 52,979 58,892 64,975 71,214 77,693 84 099 90:716 97,471 104,310 111,252 125,395 139,841 154,566 169,465 184,562 1 x
(Conjugation was ignored in these compounds because of the approximation made in inserting
l-nPropyloyclohexene 2,194.8 3,086.2 5,434.2 8,559.0 12 472 17:175 22,697 28,918 35,768 43,207 51,162 59,590 68,503 77,810 87,476 97,452 107,747 118,309 129,127 140,176 151,442 162 918 174:565 186,350 210,426 235,010 260,029 285,447 311,187 2 I1 1 VI11
o-Xylene
Ethylbenzene
.
....
4,795.1 6 631.3 8:876.1 11,534 14,553 17,874 21,476 25,313 29,371 33,652 38,125 42,753 47,532 52,442 57,479 62.623 67,864 73,189 78,633 84,132 89,720 101,096 112,717 124,560 136,517 148,630
1,5-Dimethylcyclohexene 2,102.2 2,908.4 5,038.0 7,862.6 11.367 15,543 20,413 25,904 31,934 38,482 45,482 52,905 60,741 68 929 78:435 86,219 95,277 104.570 114,097 123 827 133:749 143,858 154,125 164,531 185,746 207 416 229:472 261,878 274,575 1 I11 1 VI11
7,243.9 10,096 13,470 17,390 21,823 26,680 31,943 37,567 43,531 49,817 56,385 63,205 70,251 77,508 . 84,949 92,564 100,334 108,243 116 309 124:488 132.784 149,694 166,965 184,573 202,413 220,494 2 x
.
. .
7,507.5 10 568 14:133 18,224 22,803 27,792 33,168 38.891 44,945 51,308 57,943 64.821 71 924 79'228 86:711 94,367 102,172 110,115 118,209 126,414 134,736 151,690 169,003 186,644 204,519 222,632 2 Ve
6,898.3 9,801.6 13,261 17,286 21,814 26 771 32'127 37:833 43,869 50,229 56,864 63.737 70 835 78:135 85,620 93,275 101,080 109 022 117:122 125.324 133,638 150 603 167:927 185,582 203,460 221,572 1vs 1IX
-A=;
a
groups.) olefin =AB and Heat content = 0 a t O o R.; units = B.t.u./lb. mole.
(Concluded on p a g e 1048)
NOMENCLATURE
molal units as above
K. = absolute temperature on Centigrade scale ( ' C. R. = absolute temperature on Fahrenheit scale ( ' F. R = gas constant 1.98646 B.:.u./lb. mole-" R. T = absolute temperature, R.
Andersen, J. W., Beyer, G. H., and Watson, K. M., Natl. Petroleum News, 36, R-476 (1944). Aston, J . G., Moessen, G. W., Hardy, H. C., and Saase, G. J., J . Chem. Phys., 12,458 (1944). Aston, J. G., Schumann, S. C., Fink, H. L., and Doty, P. M., J . Am. Chem. Soc., 63,2029 (1941). Aston, J. G., Szasz, G. J., and Fink, H. L., Ibid.,65, 1135 (1943). Bennewitz, K., and Rossner, W., Z . physak. Chem., 39B, 126 (1938). Burcik, E. J., Eyster, E. H., and Yost, D. M., J . Chem. Phus., 9, 118 (1941). Crawford, B. L., Jr., Ibid.,7, 555 (1939). Ibid.,8, 526 (1940). cioj Cross, P. C., Ibid.,3, 168 (1935). (11) Ibid.,3, 825 (1935). (12) Davis, C. O., and Johnston, H. L., J. Am. Chem. Soc., 56, 1045 (1934). 12
C$ = constant pressure heat capacity at infinite attenuation, in molal units (cal./g. mole OK. or B.t.u./lb. mole-" F.) Cz = constant volume heat capacity at infinite attenuation, in
++ 273.16) 459.69)
I n statistical calculations the second radiation constant, hc/k, was taken as 1.4384 cm.-O K.; the ice point as 273.16" K.; and Avogadro's number as 6.0228 X LITERATURE CITED (1) Am. Petroleum Inst. Research Project 44, "Selected Values of Properties of Hydrocarbons," Tables of SeriesU and V.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1048
Vol. 41, No. 5
TABLE VII. HEATCOSTEXTSOF HYDROCARBON VAPORS AT ZERO PRESSLJRE~ (Concluded) Temp., I)
F.
- 250
-200 - 100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000
a
n-Propylbenzene
Isopropyl-
...
...
7,724.1 11,096 15,132 19,838 25,130 30,929 37,192 43,868 50,920 58,356 66,108 74,137 82,422 90,953 99,693 108,627 117,736 127,008 136,461 146,035 155,726 175,523 195,736 216,328 237,192 268,321 2 I1 1V
benzene
1,3,5Trimethylbenzene . I .
... ...
...
7,873.3 11,315 15,399 20,137 25,466 31,289 37,577 44,270 51,343 08,782 66,541 74,577 82,871 91,400 100,135 109,072 118,180 127,453 136,906 146,485 156,200 175,995 196,210 216,799 237,658 258,786 2 I11 1 V
8,468.3 11,828 15,767 20,317 25,458 31,083 37,177 43,694 50,611 57,900 65,514 73,431 81,611 90,040 98,684 107,534 116,568 125,770 135,148 144,665 154,316 173,992 194,090 214,578 235,360 256,427
...
3x
1,2,4Trimethylbenzene , . , .
..
8,731.9 12,301 16,430 21,150 26,438 32,195 38,402 45,018 52,025 59,391 87,073 75,047 83,284 91,761 100,446 109,337 118,407 127 642 137:047 146,592 156,268 175,989 196,127 216,650 237,467 258,564 2v 1x
1-Methyl2-et hylbenzene
l-hlethglðylbcnzene
...
... ... ...
...
8,123.1 11.525 15,559 20,214 25,449 31,174 37,361 43,960 50,949 58,311 65,994 73,963 82,194 90,668 99,355 108,246 117,314 126,549 135,960 145,502 155,170 174,904 195,062 215,588 237,642 257,504 1T’ I IX I X
8,820.8 12,765 17,456 22.889 28,970 35,622 42,793 50,433 58,494 66,995 75,851 85,020 94,480 104,220 114,197 124,398 134,799 145,388 156,180 167,112 178,168 200,772 223,848 247,356 27 1,186 295,319 11 2 11
...
...
8 284.9 11,770 15,890 20,630 25,939 31,730 37,973 44,622 51,656 59,857 66,773 74,767 83,031 91,528 100,236 109,147 118,234 127,485 136,910 146,465 156,146 175,902 196,070 216.624 237,461 258,573 2 5’ 1 IX
n-Butylbenzene
...
...
S tyrerie 1
.
... I..
6,435 0 9,230.7 12,581 16,463 20,817 25,541 30,614 35,992 41,651 47,588 53,7:s 60,127 66,685 73,412 80,300 87,322 94,477 101,726 109,125 116,594 124,177 139,578 165,282 171,257 187,410 203,752 1 VI
IV
Heat content = 0 a t 0’ R . ; units = B.t.u./lb. mole.
(13) Dennison, D. AI., Rev. iModern Phys., 12, 175 (1940). ESG.CHEU.,33, 759 (1941). (14) Dobrats, C. J., IND. (15) Edmister, W. C., Ibid., 30, 352 (1938). (16) Eucken, A., and Sarstedt, B , 2. phystk. Chem., B50, 143 (1941). (17) Fugassi, P., and Rudy, C. E., Jr., IND.ESG. CHEU.,30, 1029 (1938). (18) Gershinowitz, H., and \Tiisoil, E. B., Jr., J . Chem. Phys., 6, 247 (1938). (19) Giauque, W.F., J. Am. Chem. Soc., 52, 4816 (1930). (20) Gordon, A. R . , J . Chem. Phys., 2, 65,549 (1934). (21) Jacobs, C. J., and Parks, G. S., J . A m . Chem. SOC.,56, 1513 (1934). (22) Johnston, H. L., and Davis, C. O.,Ibzd., 56, 271 (1934). 123) Johnston, H. L., and Walker, &I. K., Ibid., 55, 172 (1933); 57, 682 (1935). (24) Kassel, L. S., Ibid., 56, 1838 (1934). (25) Kilpatriok, J. E., Pitzer, K. S., and Spitzer, R., Ibid., 69, 2483 (1947). (26) Kistiakowsky, G. B., Lacher, J. K., and Stitt, F., J . Chem. Phys., 7, 289 (1939). (27) Kistiakowsky, G. B., and Rice, W.W., Ibid.,8, 610 (1940). (28) Linnett, J. W., and Awry W. H., Ibid., 6, 686 (1938). (29) Magnus, A,, Ann. Physik (4), 70, 303 (1923). (30) Montgomery, J. B., and DeVries, T., J. Am. Chem. Soc., 64, 2375 (1942). (31) Murphy, G . M., and Vance, J. E., J . Chem. P h y s , 7 , 8 0 6 (1939). (32) Nernst W., Ann. Physik (4), 36, 395 (1911). (33) Pitzer, K. S., IVD. ENG.CHEW.,36, 829 (1944).
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Entropy and Heat of Formation of Hydrocarbon Vapors RIOTT SOCDERS, JR., C. S. IIIATTHEVS, AND C. 0. HURD Shell Development Company, Sun Francisco, Calif.
T
HIS paper presents a systematic correlation of entropy and heat of formation over the temperature range from 298.16” to 2000’ K. This correlation method is based on the premise that thermodynamic functions within a molecule are additive, and thus the values for the whole molecule can be built u p from
an assignment of definite contributions t o the various groups which make up the molecule under consideration. Two types of groups are presented. For values a t the standard state, calculations are made with Type I groups which depend only on structural constants. Extension of standard state
