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 1 V
benzene
1,3,5Trimethylbenzene . I .
... ...
...
7,873.3 11,315 15,399 20,137 25,466
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
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
...
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
H e a t 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).
(34) Pitzer, K. S., J . Am. ChPm. SOC.,62, 1224 (1940). (35) I b i d . , 63, 2413 (1941). (36) Pitzer, K. S., J . Chem. Phgs., 12, 310 (1944). (37) Pitser, K. S., and Gwinn, 11‘. D., Ibid., 10, 428 (1942). J Am. Chem. Soc., 63, 2419 (38) Pitzer, K. S., and Scott, D. W., (1941). ’ (39) Ibid., 65, 803 (1943). (40) Scott, R. B., Ferguson, W. J.. and Brickwedde, F. G., 6.Research N a t l . Bur. Standards, 33, 1 (1944). (41) Scott, R. B., and Mellors, J . JV., “Specific Heats of Gaseous 1,3-
Butadiene, Isobutene, Styrene, and Ethylbenzene,” Rept. to Office of Rubber Director (Sept. 13, 1944). (42) Sherman, J., and Ewell, R. B., J . Phys. Chem., 46, 641 (1942). (43) Spencer, H. hI., and Justice, J. L., J . Am. Chem. Soc., 56, 2311 (1934). (44) Stitt, F., J . Chem. Phys., 7, 297 (1939). (45) Zbid., 8, 56 (1940). (46) Stull, D. R., and Rlayfield, F. D., IND.ENG.CHEM., 35, 639 (1943). (47) Teifair, D., J. Chem. Phus., 10, 167 (1942). (48) Templeton, D. H., Davies, D. D., and Felsing, W.A , J . A m . Chem. S O C . ,66, 2033 (1944). (49) Thompson, H. T.,Trans. Faraday SOC., 3 7 , 3 4 4 (1941). (50) Wilson, E. B., Jr., and Vl’ells,A. J., J . Chem. P h y s . , 9, 319 (1941). (51) Worthing, A. G., P h y s . Ret., 12, 199 (1918). RECEIYED December 29,1947
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
INDUSTRIAL AND ENGINEERING CHEMISTRY
.May 1949
Systematic correlation methods for the prediction of entropies and heats of formation of hydrocarbon vapors have been developed on the basis of molecular structure. Values for the several structural groups necessary for the prediction of these thermodynamic properties i n the standard state and for the prediction o f their change with temperatures up to 2000' K. are tabulated. Standard state entropies of formation as predicted by this correlation method are believed to be within 11.0 entropy unit of the correct value, regardless of the complexity of the hydrocarbon molecule involved. Standard state heats of formation as predicted are believed to be within *0.5 kg,-cal. per mole. The effect of temperature on each of these thermodynamic functions is believed to be predicted with an uncertainty of less than 3%.
values to higher temperatures, however, requires a somewhat more complex system of correlation. Here, where heat capacity generalizations are involved, additional groups are required to account for variations in type of internal rotations. These additional factors are included in Type I1 groups which were developed from the preceding paper on heat capacities (49). EVALUATION OF TYPE I GROUPS
For compounds normally liquid at standard state conditions, heats of vaporization and vapor pressures are needed t o obtain entropy and heat of formation values for the ideal gas a t 1 atmosphere. Work at the Bureau of Standards (64) gave vapor pressures for a large number of compounds. When reliable experimental data for heats of vaporization were not available, they were calculated from reliable vapor pressure measurements by means of the Clapeyron equation. For this purpose the gas imperfection for the saturation vapor at 25" C. was assumed as: = 1 - 0.05P(atmosphere)
In the absence of reliable vapor pressure data these properties were estimated by Gordon's method (15) modified by use of several reference compounds. Critical properties were estimated. I n extrapolating experimental values t o 298.16' K. heat capacity values from ( 4 9 ) were used. I n a few instances early data were recalculated on the basis of the above vapor pressure, latent heat, and vapor heat capacity values. Values of the standard state entropy of formation (AS,") were calculated from the entropy a t 298.16" K. using the equation: A s ; = 8" - 1.36m - 15.615% = e.u. where m is the number of carbon atoms and n is the number of hydrogen atoms in the molecule. The value 1.36 is the entropy of solid graphite a t 298.16' K. (61) and 15.615 is one half the virtual entropy of hydrogen (IS). For statistical calculations the Einstein functions tabulated by Sherman and Ewe11 (48) and the hindered rotational contribution tables of Pitzer and Gwinn ( 3 7 ) were employed. The heat of formation of liquid water at 25' C. was taken as 68.318 kg.-cal. per mole (43). The standard state heat of formation of gaseous carbon dioxide mas taken as 94.052 kg.-cal. per mole (41). All entropy values listed are virtual. Physical constants listed by Birge ( 8 ) were used throughout. STANDARD STATE ENTROPY OF FORMATION
A satisfactory correlation was found t o be possible if values were assigned for the contribution of structural groups and symmetry to entropy. The contributions of -CHI, -CHZ-,
I
I
1
I
4 H , and -C-
groups were obtained from the more reliable
1049
entropy values for the paraffin hydrocarbons by the method of least squares. All the paraffin hydrocarbons from propane through the heptane isomers were used in this treatment. Also included were n-octane, 2,2,4trimethylpentane, and 2 , 3 , 4 trimethylpentane. Sources of the values were propane (64), n-butane ( 4 ) , 2-methylpropane (d), n-pentane (SO), 2-methylbutane (46), 2,2-&methylpropane ( S ) , n-heptane (35), 2,2,4trimethylpentane (35), and 2,3,4-trimethylpentane (88). All other values were taken from Pitzer's treatment (36). Symmetry contributions are given by the theoretical term -R In u, where u is the symmetry number. This symmetry number represents the total number of identical orientations that R molecule may assume by rigid rotations about any axis, or by rotations within the molecule. Symmetry numbers of some of the simpler hydrocarbons are: methane, (r = 12; ethane and the normal paraffins, u = 18; 2-methyIpropane, u = 81; 2methylbutane, u = 27. However, in evaluation of the -CHs group, the effect of symmetry was not removed, since every time a -CHI group appears, it has a symmetry number of 3. Thus, in evaluating symmetry number, methyl group rotations should not be considered. Therefore, the effective symmetry numbers are: methane, u = 12; ethane and the normal paraffins, u = 2; 2-methylpropane, u = 3; 2-methylbutane, u = 1. Sometimes it s difficult t o determine symmetry numberj from a twodimensional diagram. Molecular models, if available, should make the symmetry number clear. I n cases where optical isomers exist, such as in 3-methylhexane, the number of probable orientations is doubled. There is thus an additional contribution of R In 2 t o the entropy. The sign of this term is opposite that of the symmetry term, for it increases the number of probable orientations whereas symmetry decreases this number.
I
I
Values for the olefin groups H&=, HC=, and -C= were obtained by a least square treatment of the following olefin entropies: 1-butene (6$), cis-2-butene (46), isobutene (61), 3,3-dimethyl-l-butene (66), 1,4-pentadiene (S4), 2,4,+trimethyI2-pentene (34), and the entropy of the three isomerization reactions between 2-methyI-l-butene, 2-methyI-2-butene, and 3-methyl-1-butene (12). Heats of these three isomerization reactions were obtained from heats of hydrogenation of the olefins (11, $ 7 ) together with heats of formation of the corresponding paraffins (42). and -C-
l
The contributions of -CH,,
-CHz-,
I
-CH,
I
groups in these molecules were those determined from
I
I
the paraffin molecules. The value for a (HC=)trans group was determined from the experimental entropy of trans-2-butene (17). The =C== group was determined from the allene entropy (29). The conjugation contribution of
was evaluated from the entropies of 1,3-butadiene (47) and isoprene ( 7 ) . This contribution was the residual entropy remaining after the values for the various groups and symmetries had been deducted irom the experimental entropies of these two compounds. In the aromatic series the following values were used t o deter-
I
I
mine HC= and -C= groups: benzene (as), toluene (as), m- and p-xylene (39),mesitylene (39),and ethylbenzene (16, 18). The average effect of adjacent groups on the ring in lowering entropy was found by consideration of o-xylene (39) 1,2,4 trimethylbenzene (19), 1,2,3,4-tetramethylbenzene (19), 1,2,3,5tetramethylbenzene ( 1Q), 1,2,4,5-tetramethylbenzene(19)' pentamethylbenzene (19), and hexamethylbenzene (20). The conjugation contribution of a double bond once removed from a benzene ring was determined from the entropy of styrene (18). In the cyclohexane series experimental entropies of cyclohexane
INDUSTRIAL AND ENGINEERING CHEMISTRY
1050
Vol. 41, No. 5
available on 5- and 6-mcmbcred rings fell on a smooth curve. The other curves were drawn in by analogy, and values for 5and 6-niem.bered rings read off. STANDARD S T A T E HEA'l' OF FORMATION
Foi the correlation of heat of formation, it was found necessary to include more additive constants t o a l l o ~for the effect of adjacent groups. Such adjacent groups raise the heat of formation of one compound above that of another having the samc groups placed nonadjacently. Symmetry does not enter into the calculation of heat of formation. Values for the contribution of the paraffin groups --CHI, I
I
-CH2--,
-CH,
and -C-
and for the five paraffin adjacency
,
1
factors
NUMBER OF CARBON ATOMS
IN
were derived by a least squares trcahient of the dat,a collected by Prosen and Rossini ( 4 2 ) . All the paraffin hydrocarbons from Ca through CS were used with the exception of 2,2,i-trimethylpentane and 2,3-d methylhesane. The heat of formittion given for these two compounds w d d not correlate well. T-dues for n-nonane and n-decane were also used in the t,reatnient,.
RING
E f f e c t of R i n g Size on Group Cont r i b u t i o n s to E n t r o p y of Formation
Figure 1.
~
(6, 44 j, and methylcyclohexane (33) were available. From hydrogenation equilibrium measurements (53), heats of hydrogenation (11), and aromatic entropies, the entropies of methylcyclohexane, ethylcyclohexane, and n-propylcyclohexane TT-ere obt,ained. Contributions were evaluated by t,he least squares
method on these four compounds for -CH2-I
I
and -CH
I
groups
in the ring. The contribution of a HC= group in a &membered nonaromatic ring was evaluated from the entropy of cyclohexene (33). A better correlation resulted in the cyclopentane series if this ring was considered to be planar, having u = 10. This is not to be construed as an argument that cyclopentane is a planar molecule, but simply t,hat, t,his empirical correlation n-orlrs better if it is considered as planar in evaluating the -C,H2group. Experimental entropies of cyclopentane ( 6 ) methylcyclopentane ( 1 9 ) , and ethylcyclopentane (52) t,ogether with an entropy value for methylcyclopentane derived from equilibrium measurements ( 1 4 ) were used in a least square treatment to obtain contributions of -CX-
I
and -CH i
groups in the ring.
The heat of the equilibrium reactions \;-as obtained from the heats of combustion of cyclohexane and methylcyclopentane (3'1 j. The ent,ropy of cyclohexane was taken from the work of Aston et al. (6). I n the acetylene series, entropies of acetylene ( j O ) , methylacetylene (IO), dimethylacetylenc (56), and vinylacetylene (49j were used in determining values for HC= and -C= groups. A conjugation contribut,ion for diacetylenes was determined by finding the difference between the entropy of diacetylcne ( 4 8 ) and that calculated from its structura,l groups. I I Values for the contribution of -Cand -C= groups in 5-
I I
and 6-membered rings and of HC= in &membered rings were estimated from a plot of group contributions versus the number of carbon atoms in the ring shown in Figure 1. Data were available on the 2-membered rings (olefins) and on the straight-chain members for all groups. The group contributions ~ ~ h i cwere h
I
The olefin group contributions HX=, HC=, -C= were derived by a least square treatment. of the heats of formation of the following compounds : 1-butene ' 2 6 ) , cis-2-butene (26), 2-methy propene (2?6), cis-2-pentene ( 2 7 ) , 2-methyl 1-butene (27 j , 3-methyl-1-butene (11), 2-methyl-2-butene ( 2 7 ) 2 3dimethyl-1 butene ( 2 7 ) , 3,3-dimethyl-l-butene ( 1 1 ) 1-heptene (27), 1,4-pentadiene (28), and 1,S-hesadiene (28). Heats of formation of the paraffin hydroc,arbons given by Prosen and Rossini (4.2) were used to convert hydrogenation heats to heats of 1 formation. The value for the group (HC=)lians was obtained from heats of formation of irans-2-butene ($6) and trane-2pentene ( 2 7 ) . The group contribution for =C= was obt,ained from the heat of hydrogenation of allene (28). Only one ad-
I
I
jacency factor was needed in this series. This value for -C-=C--. was obtained from the heat of hydrogenation of 2,3-dimethyl2-butene ( 2 7 ) . Three conjugation contributions werc dcrived :
H H I
!
=C-C=
R H
1 1 from 1,3-butadiene (&?), =C-C= R R
1
(22) and =C-C=from
from isoprene
2,3-dimethg-1-1,3-butadienr (11) .
I n the acetylene series, heats of hydrogenation (9) of acetylene, methylacetylene, and dimet'hylacetylene together with heats of formation of the paraffin hydrocarbons ( 4 2 ) werc used t o cvaluate the contribution of H C z and - C r groups. Accurate heat of combustion data are available for 14 alkyl benzenes (23,40) in the liquid state. Latent heats were obtained from vapor pressure measurement (54) and from correlation values (15). Assuming the alkyl branches to have the same contributions as those determined from the paraffin hydrocar-
I
-A=
bons, values for HC= and contributions and for the ortho adjacency contribution were determined by a leaat squares treatment of these data. The conjugation contribution of a double bond once removed from the ring was evaluated from the heat of formation of styrene. This value was a mean of the values from combustion (40j and hydrogenation (11 ) which differed by only 0.2 kg.-cal. per,mole.
INDUSTRIAL AND ENGINEERING CHEMISTRY
M a y 1949
~
~
1051
~~~~~
triple bonds, if present, and by the adjacency effect of ( T y p e I groups) any carbon chains in the ortho position (to each other) AS,?, Cal./Mole-' K. AH', Kg.-Cal./Molei n a r o m a t i c hydrocarbons. SixFived x FiveAlicarbon carbon Alicarbon carbon Lastly the effect of symmetry hatic naphnaphArophatic naphnaphAroand optical isomerism must gydrothenic thenlc matic hydrotlienic thenic matic be included. The entropy of Structural Group carbon ring ring ring carbon ring ring ring formation is obtained simply -CHI - 1 9 66 . . . -10.05 ... by summing the contribu-CH2-23:37 -io.'og -ii.'ss ... - 4.95 -'4.'91 -'3.'68 , .. tions of structural groups, I c o n j u g a t i o n s , adjacencies, -CH (2nd carbon)a -30.19 -26.08 -24.71 , ,. - 1.57 -1.53 -1.63 1 (3rd o r h ~ g h e r ) ~- 3 0 . 1 9 ... ... ... - 0.88 , . . ... symmetry, and optical isomerism. These values are pre-C(2nd carbon)a -37.17 (-32.82) (-30.80) .. .. .. 0.85 (0.85) (0.85) ... sented in TabIes I and 11. ... ... 1 (3rd or higher)a - 3 7 . 1 7 2.45 .., ... ... HE~T OF FORMATION. The -5.05 ... ... ... 5.80 ... HzC= h e a t of f o r m a t i o n j n t h e standard state is calculated in I HC= b -8.61 -3.93 (-1.80) -5.43 9.28 9.20 9.67 3.33 a very similar manner. From ... ... HC=(trans) -9.28 , .. 8.70 ,,, ... ... consideration of the structural formula the contributions of -c=1 -14.55 (-9.00) (-6.50) -9.49 10.84 (10.75) (11.10) 5.48 the various structural groups =C= 4.51 ... ... ... 34.09 ... ... ... arc listed. Additional contri... ... ... ... HCG 7.64 27.04 ... ... butions are made by conju-c=. . . . . . . . . . . . 4.68 27.65 ... ... gated double bonds, and by the adjacency effects, if either a Indicates position of group in t h e longest chain of a n aliphatic hydrocarbon (measured from shortest end). b To be used when groups are i n the adjacent (cis) position or when there is no cis-trans effect. or both are present. Symmetry number and the number of optical isomers are not used in the calculation of heat of formation. However, In the cyclohexane series heats of formation for cyclohexane, there are many more adjacency contributions to be considered methylcyclohexane and ethylcyclohexane were obtained from than in the case of entropy. The heat of formation is obtained hydrogenation heats ( 1 1 , 28), and heats of formation of the simply by summing the contributions of structural groups, conbenzene homologs (40). Toluene was assumed t o have the same jugations, and adjacencies. All values needed for this calcuheat of hydrogenation a t 355" K. as ethylbenzene. A value for lation are presented in Tables I and 11. I the heat of combustion of cyclohexane (31) was also available. The user should note the two HC= groups given. The first is These values were used t o determine the contribution of -CHsl to be used whenever a molecule contains groups in the adjacent (cis) position, as cis-2-butene or trans-3-methyl-2-pentene. It is and -CH groups in the ring again by the least squares proalso to be used when there is no cis-trans effect. This group, then, I is t o be used whenever the following structures appear: cedure. Heats of hydrogenation of cyclohexene ( 2 7 ) and 1,3cyclohexadiene (28) gave values for the contribution of an R R R It H R 1 HC= group and for the conjugation contribution in the 6membered ring. Heats of combustion are available for methyl- and ethylTO ENTROPY OF FORMATION AND HEATOF FORMATION TABLEI. GROUPCONTRIBUTIONS
- --
7 -
cyclopentane (51). Values for --CH2--
7
I
and-CH
I ring group contributions were derived from these data. Heats of hydrogenation of cyclopentene ( 1 1 ) and cyclopentadiene (28) yielded values for the
TABLE11. CONJUGATION AND ADJACENCY CONTRIBUTIONS TO EXTROPY OF FORMATION AND HEATOF FORMATIOP
I HC= group and the conjugation contribution in the %membered ring Approximate values for the contribution of -C-
l
-C-C_=
-3.38
I H =C-C=
(aliphatios)
- 4 45
(aliphatios)
-2.10
-2.05 Each pair ortho groups in aromatics
and -C= groups in 5- and &membered rings were obtained by analogy with the straightchain values. As seen from the tables, values in the 6-carbon naphthenic ring differ only slightly from straight-chain values. Values for the 5carbon ring differ only slightly more. Tables I and I1 summarize the values of the contribution of the above factors t o entropy of formation and heat of formation a t the standard state.
-0.8
I
=(!-C= H H =C-C=
Group
(5-member naphthenic ring)
AH/"
-2.88
Symmetry Contributions
USE OF TYPE I GROUPS
ENTROPY OF FORMATION. For entropy of formation in the standard state, the first step in the calculation is to write the structural formula. Then the contributions of the various structural groups are listed. Additional contributions are made by conjugated double or
(aliphatics)
-8.83
I I
( T y p e I groups) AS; €1 H -3.73 =C-C=
Q
-RInv
2
-1.38
3 4
-2.18 -2.76
5
-3.20
6
-3.56
10
-4.57
Each pair ortho groups in aromatics E t h y l side chain (aliphatics) I
0.69
0.88
1
-H ~H A -
0.75
- LHA -I
2.39
2.30
-A-bI I - L c -I
4.61
2 61 12 -4.94 T o be added t o t h e group contributions whenever these 'molecular groups appear. The symbol indicates a C-C bond; R indicates either H or C. a
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1052
where R is an alkyl group. The group (HA=)tr.,. only when the structure below appears.
R
\
These three examples given in detail plus the calculated entries in Table I11 should permit the reader t o become familiar Kith the use of this part of the correlation.
I1
C=C
/
EXAMPLE OF USE OF
is to be used
/
EVALUATION OF TYPE I1 GROUPS
\
This type of group was evaluated in order to extend the range of entropy and heat of formation values from 298.16’ IC‘.to higher temperatures. The following equations show how this is done:
H R TYPEI GROUPS. Calculation of the en-
tropy of formation and heat of formation of 3-methyl-1-pentyne at 298.16’ 42. (ideal gas, 1 atmosphere). The symmetry number is one (u = 1)and there are two optical isomers (i = 2). ASf 7.64
1H C S
27.04
-cs
4 68
1-cz
2 i . 63
I I
1 -&I
1 -CH
-30.19
1 --CH*-
-23.37
2i8.16
2
