Thermodynamic Properties of Paraffins and Olefins
RAYMOND H. EWELL
Purdue University, Lafayette, Ind.
By extrapolation of experimental data on the entropies and heats of formation of the lower hydrocarbons,a set of rules is deduced for estimating the entropy and heat of formation of any paraffin or olefin hydrocarbon at 25" C. These properties are tabulated for all paraffins through the octanes and for all olefins through the hexenes. These values can be used to calculate the approximate state of equilibrium in any hydrocarbon reaction. The equilibrium proportions of 2,3-dimethyl-l-butene, 3,3dimethyl-1-butene, and 2,3-dimethyl-2-butene at 300" C. are calculated to be 25.4: 2.2:72.4, compared to Whitmore's experimental ratio of 31:3:61. Equilibrium calculations for the paraffins show that in the temperature range 150' to 175' C. all the isomers in any group of isomers have approximately the same free energy. The more highly branched isomers are more stable below this temperature range, and the straight-chain and less highly branched ones are more stable above this temperature range.
the others. If this heat of formation of butane is lowered 0.07 kcal. per mole, both these points come into line with the others. This change is approximately half the probable error (0.15 kcal. per mole) assigned by Rossini to the heat of combustion of butane, and the suggested change represents merely a mathematical "smoothing" operation, implying nothing as to the accuracy of the original experimental data. The writer has therefore taken the liberty of changing Rossini's figure of 29.72 to 29.65 kcal. per mole for the heat of formation of n-butane. These figures and all others in this paper are based on graphite as the standard state of carbon (26) and on the following heats of formation a t 25" C.: carbon dioxide (gas), 94.03 kcal. per mole; water (liquid), 68.32. Heats of formation based on graphite as the standard state of carbon can be changed t o heats of formation based on diamond by adding 0.45 kcal. per mole per carbon atom (25). The entropies of the first three normal paraffins in the gaseous state were determined accurately by means of heat capacities to liquid hydrogen temperatures and the use of the third law of thermodynamics. These are methane by Kelley (8), whose result agrees with that calculated statistically by MacDougall (16) and by Villars (ZQ),ethane by Witt and Kemp (51), and propane by Kemp and Egan (9). Their values are given in Tables I and 11. The entropies of the normal paraffins from butane to dodecane in the liquid state a t 25" C. were determined by Parks and co-workers (5, 6, 17, 13) by the third law, but their heat capacity data go only to liquid air temperatures which involve extrapolations to 0" K. amounting to 12 to 25 E. U. (entropy units) per mole. In a later article Parks, Shomate, Kennedy, and Crawford (19) reconsidered the method of extrapolation and recommended that the originally published values be increased by 10 per cent of the extrapolated portion. These corrections are as follows: butane 1.2, pentane 1.4, hexane 1.5, heptane 1.7, octane 1.8, nonane 2.0, decane 2.2, undecane 2.4, dodecane 2.5 E. U. per mole. The entropies of the liquids a t 25" C. corrected in this way are given in column 2 of Table 11. These liquid entropies are converted to the standard-state by the relation vapor entropies, S,",,,
T
HE desirability of having a complete set of data on the thermodynamic properties of hydrocarbons is selfevident. Provided such data were sufficiently precise, calculations of the equilibrium state could be made for many important reactions such as cracking, polymerization, alkylation, isomerization, cyclization, hydrogenation, etc. This paper presents a critical correlative study of the data available on the entropy and heat of formation, particularly at 25" C., of the paraffin and olefin hydrocarbons. By extrapolation of the experimental data on the lower members of these two series of hydrocarbons, a set of rules is deduced for estimating the entropy and heat of formation of any paraffin or olefin hydrocarbon a t 25" C.
where
= heat of vaporization t o saturated vapor at 25' C. P~ga = vapor pressure at 25" C., atm. T o = critical temperature, K. P, = critical pressure, atm.
AH298
O
Normal Paraffins
and the superscript zeros refer to the standard state of unit activity (approximately one atmosphere pressure for a gas). These quantities were evaluated from the best data available and are given in Table 11. The experimental values of S & based on Parks' data are then given in column 6 which is the sum of columns 2 and 5. Figure 1shows a plot of these entropies as a function of n, the number of carbon atoms. From Table I1 and Figure 1, the standard-state entropies of the gaseous normal paraffins a t 25" C. appear to vary approximately linearly with n. Parks and co-workers (5) con-
The standard heats of formation of the gaseous normal paraffins at 25" C. were taken directly from Rossini (25), with the exception of n-butane. These values are given in Table I. If Rossini's heats of formation are plotted in the - &fn) us. n (the number of carbon atoms), form (&fn+, butane-propane and the pentane-butane points are out of line with the others. The former point is too high and the latter too low, which indicates that the heat of formation of butane given by Rossini is too high to be consistent with 778
JUNE, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
779
reasonable conclusion, since it is more probable that the DATAFOR GASEOUSPARAFFINS entropy of isolated gas molecules would be a linear function TABLEI. THERMODYNAMICS Q22008 sp8B of n than the entropy of a condensed phase where interKcal./mole E. U./mole molecular forces complicate the rotational and vibrational Methane 17.86 44 6 motions of the molecules. 20.19 54.8 Ethane 24.75 64.7 Propane In selecting a linear equation to represent the vapor enn-Butane 29.65 74.5 Isobutane 31.36 70.5 tropies, the line should be made to go through the point for n-Pentane 34. i 4 84 3 propane, the largest normal paraffin whose entropy is reIaopentane 36.67 80.3 liably known. The equation Neopentane 39.41 73.2 *Hexane 2-Methylpentane 3-Methylpentane 2 3-Dimethylbutane 2:2-Dimethylbutane n-Heptane 2-Methylhexane ) 3-Methylhexane 3-Ethylpentane 2 3-Dimethylpentane 2'4-Dimethylpentane 2'2-Dimethylpentane 3'3-Dimethylpentane 2:2,3-Trimethylbutane
f
1 1
.-
__
n-octanr , - ..-
2-Methylheptane 3-Methylheptane 4-Methylheptane 3-Ethylhexane I 2,3iDimethylhexane 2 &Dimethylhexane 2:j-Dimethylhexane 3 4-Dimethylhexane 2'2-Dimethylhexane 3:3-Dimethylhexane 2-Methyl-3-ethylpentane 3-Methy1-3-ethylpentane 2.24-Trlmethvloentane 2;2:3-Trimethylpentane 2,2,4-Trimethylpentane 2,3.3-Trimethylpentane
t1
2,2,3,3-Tetramethylbutane n-Nonane n-Decane
39.95 41.7 43.5 44.6 45.29
94.1 90.1 86.1 83.0 103.9
47.1
99.9
48.9
95.9
50.0 51.8 50.63
92.8 88.8 113.7
52.4
109.7
54.2
105.7
55.3 54.2 55.3 56.0
102.6 105.7 102.6 101.7
S& = 35.3
+ 9.8 n
fits butane to heptane quite well, while S& = 35.6
+ 9.7 n
fits octane to undecane quite well, and both pass through the propane point. The first equation is selected because 9.8 is nearer the propane-ethane difference of 9.9 and because we will be more interested in the smaller hydrocarbons. This line is shown in Figure 1 and the values calculated with this equation are given in column 7 of Table 11.
Branched Paraffins
57.1
98.6
60.0 55.97 61.31
91.5 123.5 133.3
cluded that the entropies of the liquid normal paraffins a t 25" C. varied linearly with n. Now AS&, the differences between the liquid and the standard-state vapor entropies, do not vary linearly with n but are strongly curved. There-
The standard heat of formation a t 25" C. (Table I) of isobutane is taken from Rossini (24), and those for isopentane and neopentane from Knowlton and Rossini (IS). These are the only reliable heat data available on the branched paraffins. The entropy of isobutane was determined by Parks, Shomate, Kennedy, and Crawford (19) from heat capacities to liquid air temperatures, and by Pitaer (21) from statistical calculations utilizing empirically determined restricting potentials for the internal rotations. These workers obtained AS& for the reaction, isobutane = n-butane, t o be 5.8 and 4.3 E. U., respectively. TABLE 11. EXTROPIES OF PARAFFINS SG8~ S S B 3rd From law Iateda Calcu7 -
Pa8
AHrrs
Sliqu>d 2PB
-E ._C._ _ Kcal. Methane Ethane Propane n-Butane n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Undecane n-Dodecane
mole
mole
Mm. Hg
... ... ...
...
.....
56.1 63.4 72.3 80.6 87.8 95.9 104.7 113.3 120.7
... ...
+
5.03 6.30 7.55 8.70 9.80 10.80 11.70 12.55 13.35
..... .....
1823 521 153 47.7 13.9 4.75 1.85 0.73 0.26
--E.
.. ..
18:s 20.6 22.3 23.7 25.1 26.2 27.3 28.3 29.1
U. per 44.6 54.8 64.7 75.0 84.0 94.6 104.3 112.9 122.1 132.0 141.6 149.8
mole-
... ...
64.7 74.5 84.3 94.1 103.9 113.7 123.5 133.3 143.1 152.9
a From S,",B = 35.3 9.8 n. New d a t a presented, after this paper was set in type, by Aston and by Pitser (Chern. Rev., to be published, 1940) indicate t h a t the value, = 37.8 9.1 n , will probably give more correct entropies for t h e gaseous normal p a r a 5 n a t h a n those given i n thia table and in Table I.
+
7
FIGURE1.
STASDARD-STATE EN-
TROPIES OF GASEOUS NORMAL PARAFFIXS AT 25" C. us. NUMBER OF CARBON ATOMSIN THE MOLECULE
fore the liquid entropies and vapor entropies cannot both be linear functions of n. I n the case of the heats of formation, Rossini (23) found that the standard heat of formation of the gaseous normal paraffins a t 25" C. was a linear function of n above five carbon atoms; Jessup ( 7 ) found that the heat of combustion (and therefore also the heat of formation) of the liquid normal paraffins a t 25" C. was a quadratic function of n. It is probable, therefore, that the standard-state entropy of the gaseous normal paraffins a t 25" C. is a linear function of n, but that the entropy of the liquids is not. This is a
Another estimation of the entropy difference between isobutane and n-butane can be obtained from the equilibrium studies of Montgomery, McAteer, and Franke (16). They obtained a ratio of n-butane to isobutane of 23 to 77 in the liquid a t 27" C. If this is multiplied by the ratio of vapor pressures a t 27" C., 23
2
KmO = 77 X 3- = 0.2
Using the heat difference between isobutane and n-butane from Table I,
- 300AS& 1710 - 3 0 0 h s &
AH&
= -RTln Ktwa = 4.575 X 300 X log A s & = 2.5
5
INDUSTRIAL AND ENGINEERING CHEMISTRY
780
From a consideration of these three values (5.8, 4.3, and 2.5 E. U.), 4.0 E. U. is selected as the entropy difference between 72- and isobutane; this gives most weight to Pitzer's statistical calculations. The entropy of neopentane was accurately determined by Aston and Messerly (1) from the third law and heat capacities to liquid hydrogen temperatures. Their value for the vapor at the boiling point, 9.5" C., is 71.7 E. U. Sage and Lacey (g7) gave the heat capacity of n-pentane a t 290' K. to be 28.5 calories per mole-degree, and from this the heat capacity neopentane a t 290' K. is estimated to be 27.5 calories per mole-degree. Using this value t o extrapolate the entropy of neopentane to 25' C., S& = 73.2, as given in Table I. The heat of formation and entropy data discussed so far yield the following rules which can be used to estimate these quantities for other branched paraffins: 1. For each simple chain branch: a. Add 1.8 kcal. t o &f& for n-paraffin of same number of
carbon atoms. b. Subtract 4.0 E. U. from S&for n-paraffin of same number of carbon atoms. 2. For each neopentyl rouping: a. Add 4.7 kcal. t o && for n-paraffin of same number of carbon atoms. b. Subtract 11.1 E. U. from SPS for n-paraffin of same number of carbon atoms.
It is worthy of note that the ratio of the two entropy terms, 11.1to 4.0, is approximately the same as the ratio of the two terms relating to the heat of formation, 4.7 to 1.8. This seems reasonable in view of the general principle that increased heat of formation, (i. e,, stronger bonds) is in general accompanied by a decrease in entropy (i. e., less freedom of motion).
-4 8
I
I
PO
22
FIGURE 2.
I
24
A $2.
I
26
VOL. 32, NO. 6
subject to large uncertainties on account of the long extrapolations involved. TABLE111. COMPARISON OF EXPERIMENTAL AND CALCULATED ENTROPIES OF HEFTANES AND OCTANES Sfiwid na
-
-E.
Octanes n-Octane 2,2,4-Trimethyipentane
LIQUID AND STANDARDSTATEVAPORENTROPIES, FOR NORMAL PARAFFINS us. THEIRNORM.4L BOILING POINTS
A test of these rules for entropies can be made with the entropy data of Parks and eo-workers ( 6 , 18) on the nine isomeric heptanes and three of the isomeric octanes (Table 111). Column 2 of Table I11 gives the experimental liquid entropies corrected by adding 10 per cent of the extrapolated portion. The entropies of vaporization t o the ideal vapors a t 1 atmosphere pressure (AS&) in column 3 were obtained by interpolation on a curve of AS& vs. boiling point for the normal paraffins, shown in Figure 2. This is a rough approximation based by analogy on the observation that the entropies of aliphatic hydrocarbons are roughly in the same order as their boiling points. The remainder of Table 111 is self-explanatory. The agreement between the last two columns is as good as could be expected. These experimental entropies are
-
U. per mole-
23.7 23.2 23.3 23.4 23.2 22.8 22.7 23.0 22.8
104.3 100.2 99.0 99.6 98.1 94.1 92.3 94.5 89.0
0 4.1 5.3 4.7 6.2 10.2 12.0 9.8 15.3
0 4.0 4.0 4.0 8.0 8.0 10.5 10.5 14.5
87.8 76.8
25.2 23.7 24.1
113.0 100.5 91.0
0 12.5 22.0
0 14.5 21.0
2,2.3,3-Tetramethylbutane 6 6 . 9
Normal 1-Olefins The standard heats of formation of the gaseous normal 1olefins a t 25' C. were taken directly from Rossini and Knowlton (26). These values are given in Table IV. TABLEIV. THERMODYNAMIC DATAFOR GASEOUSOLEFINS
&fa Kcal./mole Ethylene Propylene 1-Butene 2-&-Butene 2-trans-Butene Isobutene
I
BETWEEN THE
Difference from nPars511 3rd law Calcd.
80.6 77.0 75.7 76.2 74.9 71.3 09.6 71.5 66.2
28
As&, THE DIFFERENCE
S2orS (3rd law)
A&
1-Heptene I-Octene 2,4,4-Trimethyl-l-pentene 2,4,4-Trirnethyl-Z-pentene 1-Nonene 1-Decene
--
SGa
E . U./mole
-12.56 4.87 0.29 1.33 2.28 3.22
52.5 64.7 74.5 72.7 72.1 70.5
4.95 6.42 7.37 8.43 6.58 10.00 10.16 11.7 12.7 11.7 12.7 13.6 11.9
84.3 82.5 81.9 80.3 80.3 78.5 94.1 92.3 91.7 92.3 91.7 90.1 90.1
15.2
88.3
13.5 14.5 13.6 15.7 14.5 17.1
88.3 87.7 90.1 86.1 83.0 85.9
15.50 20.84 29.1 30.7 26.19 31.53
103.9 113.7 98.6 96.8 123.5 133.3
The entropy of ethylene was determined by Egan and Kemp (4)from low-temperature heat capacities t o be S& = 54.5 E. U.per mole, The data of Parks and eo-workers (6) give S& = 64.3 E. U. for propylene, subject to the uncertainty already mentioned. From statistical calculations Pitzer (21) gives Si, = 65.1 E. U. for propylene, or 64.9 E. U.if a correction for restricted rotation of the methyl group is applied. The recent calculation by Powell and Giauque (22) contains an error, and their result should be the same as Pitzer's. Pitzer gives S& = 75.4 E. U. for 1-butene (compared to his value of 75.1 E. U. for n-butane). From the data of Parks, Todd, and Shomate (20), the writer calculated S& = 103.4 E. U. for l-heptene, using themethods described in connection with Table 111.
JUNE, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
The conclusion drawn from these data is that the entropies of 1-olefins (except ethylene) differ from those of the corresponding normal paraffins by less than the probable errors, and therefore the entropies of the 1-olefins are taken to be the same as those of the corresponding normal paraffins (Table IV).
Branched and Nonterminal Olefins
TABLE V. HEATOF FORMATIOX OF BRANCHED OLEFINS
2-czs-Butene 2-trans-Butene Isobutene 2-Methyl-1-butene 3-Methyl-1-butene 2-Methyl-1-butene 2.3-Dimethyl-1-butene 3,3-Dimethyl-l-butene 2,3-Dimethyl-Z-butene
7 -
Q f i s --.
Para5n 29.65 29.65 31.36 36.67 36.67 36.67 4 3 . .5 44.6 43.5
Olefin 1.33 2.28 3.22 5.43 6.58 10.00 15.7 14.5 17.1
The only entropy data on these olefins in the literature concern 2-butene (cis and trans) and isobutene. Todd and Parks (28) measured these entropies experimentally, and Pitzer (2.2) calculated them statistically. Their results for the statistical entropies at 25" C. compare as follows (including also Pitzer's value for 1-butene) : Parks 1-Butene 2-cis-Butene 2-trans-Butene Isobutene Differences between cis and trans
74:2 72.2 70.1 2.0
VI.
RULESFOR ESTIMATIOIV~
s?%
Q/&
Structural Change
Kcnl./mule
E . U./mole
+1.8 - 4.0 +4 7 -10.5 4.0 +3.5 f1.6 - 1.8 f2.6 2 4 Use rule 4 -1.6 1.6 a Amount to add to gaseous normal paraffin o r n o r m a l 1-olefin of same number of carbon atoms. 1.
S i m d e chain branch
-
+
The heats of formation of the other three butenes, of three branched pentenes, and of three branched hexenes can be calculated from the accurate heats of hydrogenation of Kistiakowsky and co-workers (3, 11, 12). This calculation is shown in Table V where column 4 is obtained by subtraction of column 3 from column 2. These heats of formation are included in Table ITr. The heats of hydrogenation were all converted from 82" to 25' C. by subtracting 0.25 kcal. The data of Beeck ( 2 ) and of Sage and Lacey (273, combined with C, = 7 calories per mole-degree for hydrogen, yield AC, values of 4.4calories per mole-degree for the hydrogenation of propylene and 4.2 for 1-butene, both a t 53" C.
Heat of Hydrogenation at 298' K. (Kistiakowsky) 28.32 27.37 28.14 28.24 30.09 26.67 27.75 30.09 26.38
TABLE
781
Pitzer 75.4 73.6 73.0 71.3 0.6
Pitzer considers this good agreement, but exception might be taken. I n view of the uncertainty in the experimental values, it seems preferable to use Pitzer's differences from 1-butene. Therefore, we shall use 1-Butene-2-cis-butene = 1.8 E. U. 1-Butene-2-trans-butene = 2.4 E. U. 1-Butene-isobutene = 4.0E. U. The last figure is taken the same as the n-butane-isobutane difference instead of Pitzer's value of 4.1 E. U. These considerations of the heats of formation and entropies of olefins yield some further rules for estimation which are combined in Table VI with those already stated for the paraffins. The remainder of the values given in Table 1%were calculated by these rules. In estimating bhe effect of moving a double bond out of the terminal position, the rule for either cis or for truns will be used when there are two substituents on the double bond. When there are three or four substituents, it seems reasonable to use the cis rule in all cases since there are bound to be two alkyl groups in the cis position to each other. A test of this latter assumption is given in Table VI1 comparing the experimental heats of formation of some branched olefins with those calculated by the rules in Table VI. The
TABLE
VII.
EXPERIMENTAL AND CALCULATED HEATSO F FORMATION
COMPARISON OF
Olefins 2-Methyl-1-butene 3-Methyl-1-butene 2-hlethyl-%butene 2,3-Dimethyl-l-butene 3,3-Dimethyl-l-butene 2,3-Dimethyl-Z-butene
-Qf& Kcal./MoleExptl. Calcd. 8.43 6.58 10.00 10.0 15.7 l5,6 14.3 14.8 17.1 18.7
Difference
:.;
0.0 -0.1 0 .0 +O. 1 -0.3 -1.6
calculated heats of formation agree with the experimental ones, except in the one case where there are four substituents on the double bond. Apparently the rules interfere with one another when there are four substituents, and 1.6 kcal. should be subtracted from the calculated heat of formation in such cases. Table VI shows that for each rule concerning olefins the change in the heat of formation expressed in kcal. per mole is practically the same as the change in entropy expressed in E. U. per mole. Therefore we assume that this applies to the correction to be applied when there are four substituents on the double bond, and that 1.6 E. U. should be added to the entropy of such olefins after applying rules 1 to 6. The only olefin in Table IV which has four substituents on the double bond is 2,3-dimethyl-2-butene (tetramethylethylene). A test of the estimated entropies in Table IV can be made using the data of Parks and eo-workers (10, 20) and the methods described in connection with the similar test in Table 111. Table VI11 shows the results of this test. The agreement is not so good as could be desired but is fairly satisfactory nevertheless. The experimental result that 2,4,4-trimethyl-l-pentene has a lower entropy than 2,4,4trimethyl-2-pentene is not consistent with statistical theorye. g., the work of Pitzer (21). TABLE VIII.
COMPARISON OF EXPERIYESTAL A N D CALCULATED ESTROPIES OF OLEFISS
Olefin 1-Heptene 2.2-Dimethyl-1-bmene 2,3-Dimethyl-Z-butene 2.4,4-Trimethyl-l-pentene 2,4,4-Trimethyl-2-pentene
--
Su:d'
80.0 62.4 66.5 74.6 76.0
---Qdga
-
AS& 3rd law Calcd. E. C. p e r mole23.4 103.4 103.9 20.8 83.2 83.0 22.5 89.0 85.9 23.9 98.5 98.6 24.0 100.0 96.8
Probable Errors A possible source of error in using the rules in Table VI lies in their neglect of attractive and repulsive forces between adjacent groups within the molecule. This might be significant in molecules which have branching on adjacent carbon atoms such as 2,3-dimethyl and 2,3,4-trimethyl substituted compounds. The rules in Table VI and the estimated data in Tables I and I1 are admittedly rough generalizations and may be subject to fairly large errors. Severtheless they must represent the general nature of the change in thermodynamic properties with change in structure, and they should be
INDUSTRIAL AND ENGINEERING CHEMISTRY
782
VOL. 32, NO. 6
useful in estimating equilibria until more experimental data are available. No attempt to estimate probable errors will be made. Since such estimations would have to be largely intuitive in any case, the writer will leave that for each reader to judge.
Below'To the side of the equation having the greater heat of formation will be the more stable, and above To the side of the equation having the greater entropy will be the more stable. In the exceptional case, where AH and AS do not have the same sign, TOas defined above is meaningless.
Calculation of Equilibrium
Equilibrium among the Hexenes
For the prediction of the equilibrium state of any chemical reaction the following relations are important:
The equilibrium proportions among all seventeen of the isomeric hexenes can be calculated a t any temperature, using the data in Table IV and the method of approximation described in the last section. The proportions so calculated are given for four temperatures in Table IX. The hexenes were selected as an example because the work of Whitmore and co-workers (14, SO) on the three doublebranched hexenes provides the only clear-cut isomerization equilibrium study in the paraffin and olefin series, except the n-butane-isobutane study already mentioned (16). Whitmore and Meunier (SO) found that the dehydration of methyl tertbutylcarbinol (pinacolyl alcohol) over a phosphoric acid catalyst a t 300 O C. gave 2,3-dimethyl-l-butene, 3,3-dimethyl-1butene. and 2.3-dimethvl-2-butene in the ratio of 31:3:61. Furthe; ( 1 4 , 'equilibrium was studied by passing each of these three olefins over the same catalyst a t 300" C., and the same mixture of the three hexenes was found in each case. The relative proportions of these three hexenes calculated in Table IX correspond to the ratio dT) (3) 25.4:2.2:72.4. The agreement of these figures with Whitmore's experiments is considered satisfactory.
AF; = A H ; - ThS; where KeQ.= equilibrium constant AF = free energy change of reaction AH = heat content change of reaction 4s = entropy change of reaction
Subscript T refers to any temperature, T oK. Superscript zeros refer to changes in the free energy, heat content, or entropy when all reactants and products are in the standard state of unit activity (appfoximately 1 atmosphere pressure for a gas). If the entropy and heat of reaction data are known only a t 25" C., the free energy change a t any temperature T can be calculated if the heat capacities are known, as follows: AF; = ( A H &
+
lsT AC; d T )
- T (AS&
+
lsT
Unfortunately, the heat capacity data on hydrocarbons are still quite meager, so that this type of exact calculation is seldom possible. However, a fair approximation is given in many cases by the following relation: AFB = A H &
- TAS,",~
(4)
AH' and ASo both change with temperature as shown in Equation 3; but they both change in the same direction, and their respective changes, being of opposite sign, largely offset each other. The approximation of Equation 4 obviously assumes that
LgT lgT Ac;
dT
-T
T Ac; dT
=
I
I
I
I
I
I
I
I
I
I
I
I
I
lu I
PENTANES
0
1
which is strictly true only if AC,O = 0. If AC; is assumed t o be a constant, ACE[T - TlnT]$s = 0 The quantity in brackets differs from zero as follows: T 298 400 500 600
[T-TlnTlXs 0 - 16
-
57
--119 196
700
AC," would be very small, of the order of 1 calorie per moledegree, for isomerization and cyclization reactions, and somewhat larger, of the order of 4 calories per moledegree, for cracking, polymerization, alkylation, and hydrogenation reactions, where there is a change (usually of 1) in the number of molecules. This method of approximation (Equation 4) will be used in some examples to be discussed in the remainder of this paper. A useful characteristic temperature to compute for many reactions is the temperature of neutral equilibrium, TO where A F o = 0, given approximately by T~ = AH,"ea/~SzDes
I
a
I
I
Y EXANES
taoA 60
-/OO
0
/OO 200 300 400 T E M P E R A TURE, 'C.
500
600
FIGURE 3. EQUILIBRIUM PROPORTIONS OF BUTANES, PENTANES, AND HEXANES
JUNE, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
Equilibrium among Some Paraffin Hydrocarbons The equilibrium proportions among any group of isomers can be calculated a t any temperature in the same manner as was done for the hexenks in the last section. The results for the butanes, pentanes, and hexanes from - 100" to 600 " C. are shown in Figure 3. TABLE IX EQIXLIBRICTM PROPORTIONS OF HEXENES IN VAPORPHASE 100' C.
Hexene Straight-chain 1-Hexene 2-cis-Hexene 2-trans-Hexene 3-cis-Hexene 3-trans-Hexene
700O C.
300' C.
TEE
400' C.
2.3 3.6 6.5 3.6 6.5
3.9 5.1 7.9 5.1 7.9
5.1 0.8 0.8 11.2 11.2 11.2 2.0 4.0 5.1
6.4 1.5 1.5 10.6 10.6 10.6 2.4 4.3 6.4
6.9 1.9 1.9 9.7 9.7 9.7 2.6 4.1 6.9
7.1 0.5 2.5 6
5.9 0.5 16.8
4.8 0.4 11.5
0.2 0.7 2.1 0.7 2 1
1.0 2.8
Single-branched 2-Methyl-1-pentene 3-Methyl-1-pentene 4-Methyl-1-pentene 2-Methyl-2-pentene 3-Methyl-2-cis-pentene 3-Methyl-2-trans-pentene 4-Methyl-2-cis-pentene 4-M ethyl-2-trans-pentene 2-Ethyl-1-butene
3.2 0.3 0.3 11.3 11.3 11.3 1.1 3.2 3.2
Double-branched 2,3-Dimethyl-l-butene 3,3-Dimethyl-l-butene 2,3-Dimethyl-Z-butene
8.5 0.4 40.1
4.4
2.8 4.4
These curves show clearly that the branched-chain hydrocarbons are more stable a t low temperatures and the straightchain hydrocarbons a t higher temperatures, the dividing line being approximately 150" to 1'75" C. Each of the three sets ,of curves crossw in approximately the same temperature range, which means that in the range 150° to 175" C. all the isomers of any paraffin have approximately the same free energy. The effect of progressive degree of branching is apparent in the curves for the hexanes. At low temperatures and up to 100" C. the equilibrium proportions are: 2,2-dimethylbutane > 2,3-dimethylbutane > 3-methylpentane = 2-methylpentane > n-hexane; at 200" C. and higher the order is exactly rei-erw I
Examples of Polymerization and Alkylation Equilibria 2 Isobutene
2,4,4-trirnethyl-l-pentene 29.1 SP,, 2 X 70.5 98.6 A H L = -22.7 kcal. ASBa = -42.4 E. U. TO = 535" I
