1260
INDUSTRIAL AND ENGINEERING CHEMISTRY
up to the theoretical air ratio. From that point on, they remained substantially constant. Samples of a silica xerogel were heated for 4 hours a t different temperatures, and their catalytic activity was compared graphically. The highest conversion to acetic acid was obtained with the sample heated a t 718” C.
Acknowledgment The authors wish to express their appreciation to Sherlock Swann, Jr., for his helpful suggestions throughout this work, to K. K. Kearby who prepared a number of the catalysts studied, and to 8.T. Gross for making the x-ray study of the microcrystalline silica.
Bibliography (1) Burton, A. A.,Chem. Age (London), 31, 169 (1934). and Houghton, A. C., Am. Chem. J . , 32,43(1904). (2) Clover, A. M.,
VOL. 29, NO. 11
(3) Fajans, E., 2.physik. Chem., 28B,252 (1935). (4) Gayer, F.H., IND. ENC.CHEM., 25,1122 (1933).
(5) Hatcher, W.H., Steacie, E. W. R., and Howland, F., Can. J. Research, 5, 648 (1931); 7,149 (1932). (6) Kearby, K. K., Ph.D. Thesis, Univ. Ill., 1937; to be published. (7) Kjstler, S. S., J.Phys. Chem., 36,52 (1932). (8) a s t l e r , S. S., Swann, S., Jr., and Appel, E. G., IND. ENQ. C H ~ M26, . , 388 (1934); Swann, S., Jr., Appel, E . G., and Kistler, 5.S., Ibid., 26, 1014 (1934). (9) Marek, L. F.,and Hahn, D. A., “Catalytic Oxidation of Organic Compounds in the Vapor Phase,” A. C. S.Monograph 61,New York, Chemical Catalog Co., 1932. (10) Parkinson, A. E.,and Wagner, E. C., IND. ENQ.CHEM.,Anal. Ed., 6, 433 (1934). (11) Pease, R.N.,J. Am. Chem. Soc., 55,2753 (1933). (12) Vandaveer, F. E.,and Gregg, R. C., IND.ENG. CHEM.,Anal. Ed.,1 , 129 (1929).
RECFOIVED July 28, 1937.
Thermodynamics in Hydrocarbon
Research CHARLES L. THOMAS, GUSTAV EGLOFF, AND J. C. MORRELL Universal Oil Products Company, Chicago, Ill.
T
HE more efficient utilization of the natural hydrocarbon resources of the world is one of the major problems which faces the chemist today. The petroleum industry, in particular, is interested in better utilizing crude oil by converting more of it into useful products and in increasing the usefulness of products already being made. This can be done by converting the petroleum by reactions that will give the desired product and by carrying out the reactions under such conditions that the yield of the desired product is a maximum. Thermodynamics can be helpful by pointing out the operating conditions most favorable for the reaction involved. As is well known, thermodynamic calculations give no clue to the rate of a reaction. Since reaction rates are of prime importance in hydrocarbon chemistry, particular care must be used in interpreting thermodynamic calculations applied to hydrocarbon reactions. This has not always been done. For example, Schultze (34) used thermodynamics to calculate a number of equilibrium constants for reactions in the cracking of hydrocarbons and in coal carbonization. These constants have been used to interpret the yields of given products in spite of the fact that the respective reaction rates play an important role in determining the yields from such reactions. Unless reaction rates are considered simultaneously with the thermodynamic data, the novice is likely to infer that the thermodynamic data are the sole controlling factors. For example, Parks (24), in referring to thermodynamic data, concludes: “These facts throw considerable light upon the effect of variation in temperature in determining the character of the products in the oil-cracking process.’’ This conclusion was applied to the known tendency of increased temperatures to favor the formation of aromatic hydrocarbons in this process. In oil-cracking, even if the
standard free energy of each of the reactions is known, it must be remembered that the igcrease in temperature can cause an increase in the rate of the aromatic-forming reaction and thus explain the increased aromatic formation. If thermodynamic calculations are applied only to systems known to be in equilibrium, then such difficulties do not arise. Unfortunately, a t present, uncatalyzed hydrocarbon reactions which are in equilibrium are relatively few in number. Under these circumstances thermodynamics can be of greatest use to the research worker by indicating the most favorable temperature and pressure conditions for the reaction. If the reaction does not have a convenient velocity under these conditions, a catalyst must be sought to promote the reaction velocity. I n this way thermodynamics can be used to eliminate experiments designed to find a catalyst for a reaction which can occur to only a limited extent under a given set of conditions.
Accuracy of Thermodynamic Data on Hydrocarbons So far in this discussion it has been assumed that the data used in making the thermodynamic calculations are accurate. Some of the difficulties involving the accuracy of certain hydrocarbon data will be discussed briefly. [The nomenclature and symbols of Lewis and Randall (21) will be used throughout.] The entropy S , free energy P , heat content or enthalpy H, and heat capacity C, form the foundation for most of the calculations for hydrocarbons. All of these quantities may be evaluated by calorimetric measurements. For the simpler molecules these same quantities may also be calculated from infrared absorption and Raman spectra (IS). In many cases the values obtained by the two methods are
NOVEMBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
The differences between thermodynamic data from calorimetric measurements and that calculated from Raman and infrared spectra are discussed. The new equation, A F o r = - 10,550 - 5,890n 25.2nT 2.2T (n> 1) has been derived for straight-chain paraffin hydrocarbons. Similarly, the new equation A Far = 20,321 - 5,835n - 33.26T 24.52nT (n>2) has been derived for straight-chain olefins with the double bond in the terminal posit ion. A table of standard free-energy values for forty-two hydrocarbons at 298", 500", and in some cases at 1000" K. is given. These data may be used to decide whether a reaction is thermodynamically possible, and what temperature is advisable for finding a catalyst for the reaction.
+
+
not in agreement. A description of the situation as it concerns the evaluation of entropy will serve t o indicate the difficulties encountered. The entropy of a substance can be evaluated from lowtemperature heat capacity measurements, but there are two chief possible sources of error: ( a ) the inability t o obtain complete equilibrium a t low temperatures and ( b ) determining the heat capacity down to 90" K. and extrapolating to 0' K . Errors of the first type were realized and discussed by Giauque ( 7 ) , Pauling (98),and Simon, Mendelsohn, and Ruheman (56). These errors exist because a certain randomness of the bonds persists a t the low temperatures and, in the case of hydrogen, the mixture of 0- and p-hydrogen may not be in equilibrium. I n extrapolation from 90" to 0" K. there is always the possibility that unsuspected changes may be unaccounted for in the extrapolation. As more work becomes available on the heat capacity down to 2-20" K., it is surprising how accurate the extrapolations for organic compounds have been. The entropy of a substance may also be calculated using Raman and infrared spectra to evaluate the vibrational component of the entropy. Although this method is rigorous for diatomic or triatomic molecules, the complete interpretation of more complicated molecules is possible only by using certain simplifying assumptions. Even with these assumptions the entropies for methane, acetylene, and ethylene are in excellent agreement with those obtained by the low-temperature method. For the higher hydrocarbons the differences between the results from the two sources are appreciable (1, 13,96). Outside the hydrocarbon field there are differences in the cases of nitric oxide (.la), carbon monoxide (4), nitrous oxide (S), water (9, 2Q), and deuterium oxide (99). Although most of these differences have been explained, it is significant that the spectroscopic method has
1261
been instrumental in bringing t o light phenomona which were unsuspected from the low-temperature heat capacity measurements. I n some of the calculations of the entropy from spectroscopic data, free rotation around each carbon-carbon bond has been assumed (1, 13, 36, 38). I n this connection Smith and Vaughan (36) calculated the equilibrium constants for the dehydrogenation of ethane and found the constants to be uniformly one-half the corrected experimental values reported by Kistiakowsky et al. (18). Since the entropies calculated assuming unrestricted rotation of the carboncarbon system are invariably higher than the calorimetric values, it is clear that the assumption of a potential barrier restricting this free rotation is one method of bringing the values into agreement. Kemp and Pitzer (17) showed that the coprect results are obtained if a potential barrier of 3150 calories per mole is assumed for ethane. Howard (10) considered different spectroscopic data for ethane and indicated 2000 calories per mole as the minimum restricting potential. Pitzer (30) treated a whole series of hydrocarbons, assuming different restricting potentials to improve the agreement between the spectroscopic and calorimetric data. Storch and Kassel (37) presented new data for the equilibrium constant for the experimental dehydrogenation of ethane, which are more nearly in agreement with the data calculated by the spectroscopic method (assuming a zero potential barrier). As Storch and Kassel point out, the problem can hardly be solved by more calculations but can be solved by accurate determination of the equilibrium constants for reactions involving the appropriate hydrocarbons. Since these differences have not been reconciled, data calculated by both methods are included in the present work. The spectroscopic data were calculated by assuming a zero potential barrier for the carbon-carbon rotation.
Thermodynamic Data for Hydrocarbons I n order that the research worker in hydrocarbons may be able to make the most of thermodynamic calculations, the available literature data have been assembled to evaluate the standard free energy of formation and its change with temperature for as large a number of hydrocarbons as possible. In making these calculations the following data were used : HYDROGEN.1/2H2 (gas): = 15.815 E. U. (citation 8). For the heat capacity of hydrogen the data of Davis and Johnston (6) were used to derive the equation C, = 6.890
- 0.000,114T+ 0.000,000,444T2
CARBON. Graphite carbon (solid): per gram atom (11):
C, = 1.1
So298 =
1.38 E. U.
+ 0.0048T- 0.000,001,2T2(citation $0)
METHANE (GAS). The values AFoZgg = 12,300 * 80 and AH029818,070 (citation $3) were used to derive the equation AF'T = -15,378
+ 11.88Th T - 0.0091T2 + 0.000,000,75T8- 54.7T
This equation expresses the known calorimetric data on methane. For approximation purposes the equation AFOT = -19,050 22.8T may be used. The spectroscopic data give S O 2 9 8 = 44.602 (citation 15) and ASo298= -19.22, which with the AH'zMvalue above give AF'298 = -12,340, The data from the two sources are in excellent agreement. ETHANE (GAS). The values AFOZQS= -8260 * 300 and AHo298 = -2060 (citation 23) are in agreement with the
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
1262
entropy of ethane recently determined by Witt and Kemp (39). When used with C, = 4.26 0.0285T (citations 2 and 6)we obtain the equation
+
AF'T = -15,914
+ 18.612' In T - 0.0096T2 0.000,000,18T3 - 77.1T
+
from which the approximate equation AFOT = -22,630 48.3T was derived. Both of these equations apply t o the calorimetric data for ethane. The spectroscopic data' (assuming a Bero potential for the carbon-carbon rotation) are: S"293 = 56.569 (citation 16) and AS"298 = -39.84, which were combined with the calorimetric AH"29s to give AF"298 = -8730. The standard free energies obtained by the two methods differ by 470 caloriea per mole. Because of this difference, an equation was derived to represent the spectroscopic data: AFOT = -15,914
+ 18.61T In T - 0.0096T2 0.000,000,18Ta - 78.7T
The same AHo298and C, data were used in both equations. n-OCTANE (GAS). Rossini's (81) Value AH"zg8 -52,310 and Parks' (23) value AFo29g = 1520 were combined with Parks' value (16b)for C, to give: AF'T = -38,140
+ 56.41T In T - 0.0293T2 0.000,000,9Ta - 179.5T
+ 199.5T.
and the approximate equation AF'T = -57,950
Straight-Chain Paraffin Hydrocarbons Using the method devised by Parks and Huffman (26b), the approximate equations for ethane (gas) and n-octane (gas) were combined as follows: n-CsH1, (gas): AF'T = -57,950 C2H6(gas): AF"T = -22,630 Subtracting -35,320
+
Dividing the difference by 6, we obtain -5887 25.2T as the effect on the standard free energy of the addition of one methylene group to a straight-chain paraffin. This difference gives the general equation,
+
AFOT = -10,550 - 5890n 25.2nT - 2.2T (n > 1) (n = no. of carbon atoms in the paraffin)
(1)
by considering the standard free energies of formation of ethane and n-octane both at 298" and 1000" K. Table I compares the values calculated from Equation 1 with those given by Parks (93) a t 298" K. and with those from the writers' own equations at 1000" K. When it is considered that approximate equations were used in deriving Equation 1, the agreement seems fortuitous indeed.
General equation 1 is useful in approximating free-energy values in the absence of other data. When it is possible to obtain the free-energy values in a more rigorous manner, the approximations should not be used. The following paragraphs give briefly the data sources and the equations derived from these data; data of both calorimetric and spectroscopic origin will be treated where possible: PROPANE (GAS). Calorimetric data: AFOZQS = -6220 * 300; AH"2gs = -25,390 (citation 2 3 ) ; and C, = 4.16 0.04282' (citation 2 ) . These data were used to derive the equation:
+
= -18,728
AF'T = -18,728
+ 26.70T In T - 0.0144T2 -
0.000,000,3T8 - 109.74T
?%-BUTANE(GAS).Calorimetric data: SO298 = 75.8 (citation26); AS"zs8 = -85.79; AF"298 = -5000; AH0298 = 30,570 (citation 23); and C, = 4.64 0.0558T (citation 2 ) . The equation for other temperatures is:
+
AF"T = -22,051
+ 34.212' In 2' - 0.0186T2 0.000,000,4T8 - 132.14T
Spectroscopic data: -80.96; and AF"298 derive the equation: AF'T
= -22,051
= 80.628 (citation 15); Afio2gs= -6445. These data were used to
So2g8
=
4- 34.21T In
T
- 0.0186T2
-
0.000,000,4T8
-
137.OT
ISOBUTANE (GAS). Calorimetric data: AH 0298 = -32,200 (citation 32) and SoZ~s = 70.0 (citation 26) so that Aso29g = -91.59 and AF"295 = -4900. The general equation was derived from these values by assuming, in the absence of better data, that the heat capacity of isobutane and n-butane are identical: AFOT = -23,681
+ 34.212' In T - 0.0186Te -
0.000,000,4T8
- 126.33T
Spectroscopic data: SoZ98 = 76.511 (citation 16); AS"293 = -85.08; and AFozes= -68846. On the basis of these values the general equation for isobutane is AF'T = -23,681
+ 34.21T In T - 0.0186TP 0.000,000,4T8 - 133.OT
TABLE I. COMPARISON BETWEEN APPROXIMATESTANDARD DATA FREEENERGIES FROM EQUATION 1 AND MORERIGOROUS AT 298" AND 1000° K. 7 -
Gas
Equation 1
AFOaos-
Parks (89) -8260 * 300 -6220 -5000 A 300 ($6') -2570 * 500 190 -t: 500 +1520 -t: 600
-AF'ioooEquation l
Thomas et a1.Q
-7966 Ethane -6346 Propane f -4726 n-Butane -3106 n-Pentane 134 n-Heptane +1754 n-Octane Values calculated from equations developed elsewhere in this paper.
+
+
n-Pm"ANE (GAS).Calorimetric data: For liquid npentane, AFo293= -2820 * 500 and AH"2gg = -2570 * 500; for gaseous n-pentane, AF"288 = -2570 (citation 23). Using AHo293 = 6350 for the heat of vaporization, we find AH02Q3 = -35,880 for n-pentane gas (at 1 atmosphere pres0.0687T (citation 2 ) . Based on these sure). C, = 5.16 values, the general equation for the standard free energy of formation of gaseous n-pentane a t 1 atmosphere is:
+
Other Paraffin Hydrocarbons
AF'T
= Spectroscopic data: S"ZQS = 68.559 (citation 16); -60.44; and AF"~298= -7380. From these data the equation is :
++ 199.5T 48.3T + 151.2T
VOL. 29, NO. 11
+ 26.70T In T - 0.000,000,3T8 0.0144T2 - 105.84T
AF'T = -25,503
+ 41.681 In T - 0.0227T2 0.000,000,6Ta - 154.7427
There is apparently no spectroscopic entropy for n-pentane on record. ISOPENTANE (GAS). Calorimetric data: AH "293 = -38,080 (citation 33) and SoZga = 59.5 (citation 27) for liquid isopentane, For vaporizing isopentane at 298" K., it was esti= 66 and AH"293 = 6350. These values mated that AFoZg8 give AFo298 = -4290, AH"298 = -44,430, and A s o m = -134.7 for isopentane liquid, and AFOm = -4225 and ASo2g8= -113.6 for isopentane gas (at 1 atmosphere). As-
NOVEMBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
1263
FREEENERGIES OF FORMATION' OF HYDROCARBON GASESAND VAPORS TABLE11. STANDARD Referenoe AFOsao AF'iaoo -8,060 (-8,050) 48 100 (47 160) 18'520 (18'830) 1:960 (150) 22510 (20930 ?:a40 (5:640] (40,000 26;QfO (25,5001 29 440 (27 000) 27'440 26'290) 27:390 {25:640) 14 670 (11 440) 13:500 (11:070) 57 000 !9 Teit 36'000 sb:OOO Estimated 19:8bO 85,300 87,33 2 1 040 86 670 83 901950 (84.020) 21:lSO (17.760) ~, I (1) 38.700 69,600 32'100 42'000 99,100 34'600 103,500 21:500 28.000 103,000 28,440 41,200 74,200 20 720 48,720 118,400 -1:300 35 700 d6d -930 36:360 25d -130 37,050 d6d -130 38 300 85d -430 37:lOO 85d 2'4-dimethyl pentane 370 38,500 86d -730 3'3-Dimethylpentane 37 300 86d 870 2:2 3-Trimethylbutane 40'000 86d 122.500 351000 190 wf2ePtane 89 CaHio 29 660 m-Xylene 47'300 92,800 CsHis 21:530 56'090 Diisobutene (low b, p.) 146,700 CeHis 22,260 58'450 Diisobutene (high b. p.) 150,200 2,2,4-Trimet hylpentane CsHia 1570 46'000 n-Ootane CBHIB 1:520 40:OOO i 4 i ,'eo0 CioHs 50,400 Naphthalene 62,000 93,500 Cl4HlO 72,400 Anthracene 89,200 135,000 0 The references cited, in many cases, give only the. AF"198 values. The values !or higher temperatures were estimated by the methods described in the text. Where the original reference gives data only for the liquid, they were used to estlmate values for the vapors b Values in parentheses were obtained from spectroscopic data, assuming free rotation for the C-C bonds.' Subst,ance Methane Acetylene Ethylene Ethane Propene Propane 1 3-Butadiene IAobutene 1-Butene 2-Butene c i a ) 2-Butene itrans) Isobutane lo-Butane 1CPentadiene lkentene bopentane n-Pentane Neopentane Benzene Cyclohexene 1-Hexene Cyclohexane Methylcyclopentane n-Hexane Toluene 1-Heptene Z-Methylherane 3-Meth~lhexane 3-Ethyfpentme 2 2-Dimethylpentane 2'3-Dimethylpentane
Formula
AFOm
I
+ 41.68T In T - 0.0227T2 0.000,000,6T3 - 152.91T
TETRAMETHY LMETHANE (GAS). Calorimetric data : A.Ho2g8 = -40,660 (citation 32) and SO298 = 72.94 (citation I). From these, calculation gives A F " z s ~= -4500. If we assume that tetiramethylmethane has the same heat capacity as n-pentane, wle derive: AFOT = -30,497
+ 41.86T In T - 0.0227T2 0.000,000,6T3 - 144.462'
Spectroscopic data: SO298 = 80.12 (citation I), ASo2g8 = -114.06. This last value, when used in conjunction with the above data, permits the derivation of the equation: AFOT = -30,497
?
.... .... .... .... .... .... .... ,...
s u i n g that the heat capacity for isopentane is the same as that of n-pentane, the general equation for isopentane gas is: AFOT = -27,7013
.
.... ....
+ 41.86T In T - 0.0227T2 -
0.000,000,6T8 - 151.5T
ISOMERIC HEF~TANES AND OCTANES.Standard free energies of formation for a number of these liquid parafins at 298" K. are given by Parks and Huffman (255~).Assuming that the standard free energies of vaporization and heat capacities of the isomers are alike, the standard free energies of formation for the vapors were estimated at 298" and 500" K. (Table 11).
Olefin Hydrocarbons ETHYLENE (GAS). Calorimetric data: AHozs8 = 11,975; AFoz0s = 15,820 (citation 23); C, = 3.82 0.022T (citations 2, 6). From these data the general equation for the relation between the standard free energy of formation of ethylene and temperature was derived: AF'T = 15,026 -k 12.16T In T - 0.006,31T2 -
+
0.000,000,26T3
- 64.8T
Spectroscopic data: SO298 = 53.263 (citation 16), ASo2gs = -11.92. From this we calculate AF"29a = 15,530. The calorimetric and spectroscopic values are in excellent agreement. PROPENE (GAS). Calorimetric data: AHozss = 4475; AFo298 = 14,820 (citation $3); and C, = 4.00 0.0372T (citation 2 ) . These data permit the derivation of the equation :
+
AF"T = 9373
+ 19.96Tln T - 0.0116Ta 0.000,000,4TS - 91.9T
From the latter equation the approximate straight-line equa40.3T, was derived. tion, AF", = 2816 Spectroscopic data: SO298 = 66.071 (citation I S ) , AS"298 = -31.70. Employing AH"298 and C, from the calorimetric data, we obtain the equation
+
AFOr = 9373
+ 19.96T In T
-
- 0.0116T2 0.000,000,4T3
- 94.971
~-HEPTENE (GAS). Calorimetric data for liquid 1-heptene: AFo2s3 = 19,050 and AH0298 = -25,520 (citation 27). For the vaporization process it was estimated that AH"2gs = 8920 and AFozg8= 1670 (from the corresponding data for nheptane) whence we obtain AH"298 = -16,600 and AFOZOB = 8920 for gaseous 1-heptene. From Beeck's data (2) C, was 0.09T. These data permit the estimated to be 6.27 derivation of the general equation for gaseous 1-heptene:
+
AFOT = -4688
+ 48.66T In T - 0.0286T2 0.000,000,9T* - 183.7T
For approximation purposes, AFoT = -20,523 may be used.
+ 138.48
VOL. 29, NO. 11
INDUSTRIAL AND ENGINEERING CHEMISTRY
1264
Straight-Chain Olefins with Double Bond i n Terminal Position I n arriving a t a general equation for this type of olefin, the method of Parks and Huffman (26e) was followed. They used ethylene and 1-hexene for deriving their equation; the writers used propene and 1-heptene. Since ethylene is the first member of a homologous series and shows differencesfrom z0,oao
I
'STA~DARD F R E ~E ~ E R G YOF FORMATION
PERI
+
+ +
AF"T = 2816 - 5835(n - 3 ) 40.3T 24.52(n - 3 ) T (n > 2 ) or A F o T = 20,321 - 5835n - 33.26T 24.52nT (n > 2 ) ( 2 ) where n = no. of carbon atoms in molecule
Available data permit the testing of Equation 2 only in the case of 1-butene, in addition to the propene and 1-heptene used to derive the equation. A comparison of the standard free energies a t 298" K. is as follows:
1 a
Calcd. by Substance Equation 2 From Parks (83) Propene ( g ) 14,824 14,820 * 300 1-Butene (g) 16,297 16,780 =t600 1-Heptene ( 9 ) 20,713 2O,72Oa See the paragraph on "I-Hepcene" for this value.
These data do not provide a conclusive test for Equation 2, although the agreement seems satisfactory as far as the test goes. Dividing Equation 2 by n , we obtain: A.poT= 2o 321 L5835 -
n
n
26T + 24.52T - 33 n
This equation shows that, when 33.26T = 20,633, A ( F o T / n ) will equal 24.52T - 5835. This means that, for all olefins whose standard free energies of formation are represented by Equation 2, the standard free energy of formation per carbon atom will be equal to 24.52T - 5835 and will be independent of the number of carbon atoms in the molecule a t one temperature. This temperature is 611' K. and A (F061l/n) = 9147 calories per carbon atom. This means that all such olefins are interconvertible a t 611' K. with a zero standard free-energy change in the presence of a suitable catalyst. I n Figure 1, A ( F T " / ~ is ) plotted against T for a number of olefin hydrocarbons. The curves for propene and 1heptene are taken from Equation 2. The other curves are taken from data which will be treated in the following paragraphs, At this time it should be indicated that this point a t 611" K. and 9147 calories for A (F0611/n)is useful in estimating the standard free energy of an olefin a t higher temperatures when AFozss is known. A straight line is drawn through the value for A(F "zos/n) and a t 611" K. and 9147 calories, extrapolating or interpolating to the desired temperature. The method is approximate but is useful in the absence of other data. For example, this method applied to the diisobutenes gives 138,800 compared with the more rigorously derived values of 146,700 (low-boiling) and 150,200 (highboiling) for the standard free energy of formation a t 1000" K.
i
Other Olefinic Hydrocarbons the rest of the series, it is not a truly representative member. Also, there is some doubt about the AF"m value for 1-hexene used by Parks and Huffman (%e) because the entropy was merely estimated. Further, Parks ( O 3 ) showed that A F O m for dehydrogenating a straight-chain paraffin to the corresponding 1-olefin is about 21,000 calories per mole. The value used by Parks and Huffman for 1-hexene does not fit this generalization, whereas the data for propene, 1-butene, and 1-heptene do. For these reasons propene and 1-heptene seem preferable. Following the procedure used above for the general equation for paraffins : 1-Heptene (gas): AP'T Propene (gas): A F o T Subtracting
Dividing by 4 1
t
= -20,523 = 2,816
-23,339 -5,835
+ 138.42' + 40.3T + 97.9T + 24.52T
The last line gives the change in standard free energy due to the addition of one methylene group to the olefin. Adding this to the equation for propene:
BUTENE (GAS). Calorimetric data: A F O m = 16,780 = 600; = -480 (citation 93); and C, = 4.61 0.0513T (citation 9). These data permit the derivation of the general equation:
+
aFoT =
6200
+ 27.35T
In T
- 0.0163T2 -
0.000,000,5T3 - 115.2T
= Spectroscopic data: S O 2 9 5 = 78.307 (citation Is), AS'Z~R -53.05. Using the above values for AHoz98 and C,, the following equation was derived: AFOT = 6200
+ 27.35T In T
-
0.0163T2 0.000,000,5T3
-
120.13T
c ~ s - ~ - B u T E N E (GAS).Calorimetric data: AF"m = 14,860, AHoZBB = -2250 (citation $3). Assuming that this butene has the same heat capacity as 1-butene, the following equation was derived:
aFoT = 4427
+ 27.35T In T
-
0.0163T2 0.000,000,5T3 - 115.8T
NOVEMBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
Spectroscopic data: S O 2 9 8 = 75.274 (citation IS), AS0,$, = -55.09. Using AH"z98 and C, from the calorimetric data, we obtain : A F O= ~ 4427 27.35T In T - 0.0163T2 -
+
0.000,000,5T3 - 118.OT
hm5-2-BUTENE (GAS). Calorimetric data: AF02Qg = 14,450, AHo2,s = 3200 (citation 23). The heat capacity is assumed to be the same as 1-butene:
+ 27.35T In T
AFOT = 3477
-
0.0163T2 0.000,000,5~3- 1 1 4 . 0 ~
Spectroscopic data: SoZ9g = 74.663 (citation 16), AS"298 = - 55.70:
+ 27.35T In T
AFOT = 3477
-
0.0163T2 0.000,000,5~3- 1 1 7 . 4 ~
ISOBUTENE
(GAS), Calorimetric data: AF '298 = 14,290, AHoZ98= -4060 (citation 23). The assumption that this
compound will have the same heat capacity as 1-butene cannot be fully justified; however, in the absence of any other data, the assumption was made: M
O
T
= 2716
+ 27.3517 In T - 0.0163T2 0.000,000,5T3 - 112.1T
Spectroscopic data: S'zgg = 74.048 (citation 16), A8'298 - 57.31 : AFOT= 2716
+ 27.35T In
T
-
=
0.0163T2 0.000,000,5T3 - 116.162'
BUTADIENE (GAS). From AHoa55 = 57,070 (citation 19) for the heat of hydrogenation of butadiene and the heat of formation of n-butane, the heat of formation (AHo2gg) of butadiene was estimated to be 25,770. For the entropy of butadiene the translational plus rotational entropy, 8, + = 66.824 (citation 16) was used a t 298" K. The vibrational component was assumed to be the same as the vibrational component of the entropy of 1-butene-i. e., 5.833 E. U. (citation i6)-giving a total entropy X o Z 9 8 = 72.657 and As02Qg= -27.47. From AH'2Q8 and Aso2Q8 we obtain AF029g= 35,250. For calculation of the free energy a t higher temperatures, we need the heat capacity of butadiene as a function of temperature. Although no data are available, this was estimated according to the following scheme: ~
C,
= 6/2
R (translation)
+ R (internal R (external rotation) + rotation) + (vibration)
I n order to approximate the vibrational contribution to the heat capacity, it was assumed that the vibrational contribution to the heat content ( H ) of butadiene would be approximately equal to the vibrational contribution to the heat content of 1-butene. From tables of the vibrational H / T (citation 16) for 1-butene, (SH/ST), = C, was approximated for the vibrational component. This, in turn, used in the above 0.0448T. Using equation for C, gives: C, = 11.6 AFoz9s, AH'299, and C,, the following equation was derived:
+
M O T
=
34,465
+ 34.14T In T - 0.0176T2 -
0.000,000,4T3 - 192.OT
This equation is to be regarded as applying to spectroscopic data since both S and C, are of spectroscopic origin. The equation is only approximate since the vibrational component in both S and C, is actually that of 1-butene. DIISOBUTENE (GAS). Calorimetric data: There are two isomeric diisobutenes; these will be designated as 1. b. (lowboiling) and h. b. (high-boiling). AH'ZQ~= -36,360 (1. b.), = 19,530 (1. b.), 20,260 (h. b.) (cita-35,250 (h. b.); AF'ZQ~ tion 27) for the liquid diisobutenes. The values AH'298 = 9350 and AF'293 = 2000 were estimated for the conversion of the liquid to the vapor a t 298' K. These values give AH '295 =
1265
-28,010 (1. b.), -25,900 (h. b.), and AF'298 = 21,530 (1. b.), 22,260 (h. b.) for the gaseous hydrocarbons. As the 0.0838T was used for heat capacity, the value C, = 19.1 both hydrocarbons. This equation is just a guess based on the heat capacity of other hydrocarbons; as such, any calculations made with it will be uncertain. In the absence of other data, i t was used to calculate the following general equations for the gaseous diisobutenes:
+
1. b.: AF'T
=
-15,757
h. b.: AF"T
=
-14,647
+ 44.82T In T 0.0231T2 - 0.000,001T3 - 123.1T + 44.82T In T -
0.0231Ta - 0.000,001T3 - 120.6T
Standard Free Energy of Formation After having calculated the standard free energy of formation for a number of hydrocarbons, a few examples showing how these calculations may be used in hydrocarbon research will be given. Such use usually involves the well-known relation: AFOT = -RT In K
where K
=
equilibrium constant for the reaction in question
When we have AFOT for every component of a reaction a t a given temperature, by simple algebraic differences we can calculate the AF'T for the reaction and immediately the equilibrium constant. This will be exact (a)if exact thermodynamic data are used and ( b ) if the substances taking part in the reaction are in equilibrium one with the other. Condition b is important because such equilibria are seldom encountered in uncatalyzed hydrocarbon reactions. However, by the use of the appropriate catalyst, one can hope to approach the equilibrium constants calculated by the thermodynamic method. It will be remembered that when the AF'T equals 0, K equals 1; when AF'T is negative, K is greater than 1; and when AF'T is positive, K is less than 1. It is well to point out here that the loosely used phrase "thermodynamically impossible" when applied to a chemical reaction has no meaning. This is evident from the expression AF'T = -RT In K , from which all reactions are thermodynamically possible although they may occur only to an infinitesimal extent. Since there is no sharp division in the extent to which reactions can occur thermodynamically, we will say in a purely arbitrary way that, when AF'T is less than or equal to 0, the reaction can occur to a "conveniently usable extent." Similarly when AF"T is greater than 0, we will say that the reaction cannot occur to a "conveniently usable extent." Admittedly the classification is a loose one. I n case the reaction does not occur to a ('conveniently usable extent" it is always possible that the reaction can be made to go by changing the operating conditions. These may include changing the pressure, removing the reaction products, and recycling, adding a cheap reagent that will combine with one of the reaction products and displace the equilibrium. With these possibilities in mind and the knowledge that no chemical reaction is thermodynamically impossible, there remains the selection of the proper catalyst when needed. Table I1 includes AF'293, AF'600, and in some cases AF'IOOO from which the standard free-energy change and its variation with temperature may be estimated for any reaction involving the hydrocarbons listed. Three examples will be given to illustrate the use of the table: EXAMPLE 1. What is the standard free energy change a t 450' C. (723" K.) for the reaction: 2CpH4 (9)
* 1-CdHs ( g )
(3)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1266
From Table I1 : 2CzH4 ( g ) : AF'i.8 = 2(15,820); AF'IOOG = 2(27,670) 1-CaH8 ( g ) : AF 298 16,780; AF'looo = 62,960
For reaction 3: AF'zss = 16,780 - 2(15,820) = -14,860 AFOlooo = 62,960 - 2(27,670) = 7620
Using these values to calculate A and B in the approximate equation: AFOT = A BT
+
+
we obtain A = -24,400, B = 32.0, or A F O T = -24,400 32.02'. Solving this equation for T = 723" gives AFOm = - 1260. Thus reaction A may occur to a conveniently usable extent a t this temperature. EXAMPLE 2. What temperature range is advisable in seeking a catalyst for the reaction:
+
7~-CaHro C2H4 e CaH6
From Table 11: n-CaHio: AFoozes = -6450;
+-CzHa + H L
(4)
AF"IOOO = 58,300 CzHa: AB' 298 = 15,820; AFOiooo = 26,700 C4He: AF'zgs 33,960; AF"10oo = 60,000 AF0m -8260; AF'looo 24,190 E
For reaction 4: AF"2w = 16,330 AB'"10oo = -810
+
From these values the equatioll AFOT = A BT becomes AFOT = 23,600 - 24.4T. Since the reaction is capable of occurring to a measurable extent between 900" and 1000" K. ( 6 2 7 O and 727" C.), this temperature range would be suitable to use in seeking a catalyst for the reaction. EXAMPLE 3. Can benzene be conveniently converted into acetylene according to the equation CeH6 (g) ---f 3CzHz ( g )
(5)
in the presence of a suitable catalyst? From Table 11: CeHe ( g ) : AF'zss = 30,640; AF"iooo 59600 = 3(41,300) 3CzHz: AB'Ozss = 3(50,740); AF"IODO
For reaction 5 : A F":gs = 3(50,740) A F"looo =i 3(41,300)
- 30,640 121,580 - 59,600 = 64,300
Again using these two values for determining A and B in the BT, we obtain AF"T = 146,000 equation AFOT = A 81.7T. From the last equation AFOT > 0 up to 1790" K. (1517" C.). Since the present data are questionable a t such temperatures, the quantitative effect of temperature cannot be given. If a catalyst for this reaction is to be sought, then the catalyst activity tests should be carried out a t temperatures of 1000° C. or higher. Both calorimetric and spectroscopic data are included in Table 11. In most cases the same result will be obtained from either alone. I n cases where the two types of data differ, they should not be mixed. The method of expressing AFOF as a straight-line function of T is approximate and is recommended for use when an approximate result will suffice. For this reason a solution of BT equation which has been derived using the AF"T = A 298" and 1000" K. to establish the values of A and B, will usually give a slightly different result a t 500° from that obtained if the values given in Table I1for 500" are used directly. If the more rigorous equations given in this article are used, such differences naturally disappear. Such equations are
+
+
VOL. 29, NO. 11
rather cumbersome to handle so that some of the accuracy may in many cases be sacrificed for the sake of the convenient straight-line approximation. It cannot be emphasized too strongly that the accuracy of the data in numerous cases can be improved. I n view of this situation conclusions reached by means of the data are preferably used as indications of trends. The data in the vicinity of 298' K. are much more accurate than those a t higher temperatures. Beyond this it is not possible to make any generalizations as to the relative accuracy. Even so the data should prove to be of value to the research worker in hydrocarbon chemistry.
Summary and Conclusions 1. In seeking to utilize a given reaction to its fullest extent, thermodynamic calculations are most useful to the research worker in hydrocarbons in helping him to decide whether or not the reaction may occur to a usable extent and what temperature range is favorable for the reaction. After this is answered affirmatively, it usually remains for the investigator to find a suitable catalyst to accelerate the rate of the desired reaction to the practical exclusion of undesirable reactions. Where the reaction cannot occur to a usable extent, obviously time need not be wasted in any catalyst search. 2. The differences between thermodynamic data calculated from low-temperature heat capacities and those from infrared and Raman spectra are discussed and AFOT values based on data from both sources are included when possible. 3. Using recently available data the new equation
+
AFOT = -10,550 - 589On 25.2nT - 2.2T (n > 1) (n = No. of carbon atoms in the molecule)
has been derived for straight-chain paraffin hydrocarbons, Similarly the equation A F"T = 20,321
- 5835n - 33.2611 + 24.52nT (n > 2)
has been derived for straight-chain olefins with the double bond in the terminal position (1-olefins). This last equation leads to the conclusion that all olefins whose free energytemperature relations are expressed by the equation, have a constant standard free energy of formation per carbon atom of 9147 calories a t 611" K. Such olefins should be interconvertible a t this temperature with a zero standard freeenergy change in the presence of a suitable catalyst. 4. Using the above equations and other data from the and in literature, Table I1 gives values for AFOm, AF"~OO, some cases AF olooo for forty-two hydrocarbons. Examples show how these data can be used to decide whether a reaction is likely to occur and if so what temperature range is available for use in seeking a satisfactory catalyst for the reaction.
Literature Cited Aston and Messerly, S.Chem. Phys., 4, 391 (1936). Beeck, Ibid., 4, 680 (1936). Blue and Giauque, S.Am. Chem. SOC.,57, 991 (1935). Clayton and Giauque, Ibid., 54,2610 (1932). Davis and Johnston, Ibid., 56, 1045 (1934). Euoken and Parts, Z . p h y s i k . Chem., 20B, 184 (1933). (7) Giauque, S. Am. Chem. SOC.,52, 4808 (1930). (8) Ibid., 52, 4825 (1930). (9) Giauque and Stout, Ibid., 58, 1144 (1936). (10) Howard, Phys. Rev., 51, 53 (1937); J. Chem. Phys., 5, 442, 451 (1937). (11) Jacobs and Parks, S.Am. Chem. SOC.,56, 1513 (1934). (12) Johnston and Giauque, Ibid., 51, 3194 (1929). (13) Kassel, Chem. Rev., 18, 276 (1936). (14) Kassel, S.Am. Chem. Boc., 55, 1351 (1933). (15) Kassel,S. Chem. Phys., 4, 276 (1936). (16) Ibid., 4, 435 (1936). (1) (2) (3) (4) (5) (6)
NOVEMBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
(17) Kemp and Pitzer, Ibid., 4, 749 (1936); J . Am. Chem. SOC.,59, 276 (1937). (18) Kistiakowsky, Romeyn, Ruhoff, Smith, and Vaughan, Ibid., 57, 65 (1935). (19) Kistiakowsky, Ruhoff, Smith, and Vaughan, Ibid., 58, 146 (1936). (20) Lewis and Randall, Ibid., 37, 458 (1915). (21) Lewis and Randall, “Thermodynamics,” p. 4, New York, McGraw-Hill Book Go., 1923. (22) Long and Kemp, S. Am. Chem. SOC.,58, 1829 (1936). (23) Parks, Chem. Rev., 18, 325 (1936). (24) Parks, IND.ENG.CHEM.,25, 891 (1933). (25) Parks and Huffman, “Free Energies of Some Organic Compounds,””New York, Chemical Catalog Co., ( a ) p. 64, (b) P. 68, (c) P. 69, (d) P. 71, (e) P. 83, (I)P. 84, (Q) PP. 90-3. (26) Parks, Shomate, Kennedy, and Crawford, J. Chem. Phys., 5, 359 (1937). (27) Parks, Todd, and Shomate, J. Am. Chem. Soc., 58, 2505 (1936).
(28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39)
1267
Pauling, Ibid., 57, 2680 (1935). Pauling, Phys. Rev., 36, 430 (1936). Pitser, S. Chem. Phys. 5, 469, 473 (1937). Rossini, Bur. Standards S. Research, 13,21 (1934). Rossini, S. Chem. Phys., 3 , 4 3 8 (1935). Roth and Pohlke, Angew. Chem., 49, 618 (1936). Schultse, Oel Kohle Erdoel Teer, 12, 267 (1936); Angew. Chem., 49, 268,284 (1936). Simon, Mendelsohn, and Ruheman, Naturwissenschaften, 18, 34 (1930). Smith and Vaughan, S. Cham. Phys., 3, 341 (1935). Storch and Kassel, S.Am. Chem. SOC.,59, 1240 (1937). White and Morgan, S. Chem. Phys., 5, 655 (1937). Witt and Kemp, b. Am. Chem. Soc., 99, 273 (1937).
R ~ C J O I YJuly ~ D 20, 1937. Presented before the Division of Physical and Inorganic Chemistry a t the 93rd Meeting of The American Chemical Society, Chapel Hill, N. C., April 12 to 15, 1937.
Oxygen-Induced Gelation of Unsaturated Polyesters Polyglycol Maleates as Drying Oils HOWARD L. VINCENT George Vincent, Inc., New York, N . Y.
T
H E complexity of the composition and behavior of the natural drying oils has been reflected in the innumerable and often vague theories which have been proposed in the past by organic and colloid chemists in explanation of the drying mechanism. The experimental difficulties in this field of research have been enormous, particularly where analytic and synthetic technics have been applied, and experimental work has not always kept pace with theoretical speculation. It therefore seems advisable to report without delay certain experimental observations on oxygen-induced gelation which give promise of being developed into a more flexible method of attacking the problem of air-drying than has heretofore been available. Ethylene fumarate and ethylene maleate were first prepared by Vorlander (16),who observed that these esters became insoluble and infusible when heated. Carothers and Arvin (4) described them as linear polyesters and confirmed their heat convertibility, but Carothers (3) did not provide for this exceptional behavior in his theoretical consideration of polymerization, as pointed out by Bradley (I). With this in mind, Bradley proposed a revision of the classification scheme of Kienle and Ferguson (7‘) so that it would include in one class both addition and condensation polymers. Bradley also stressed the parallelism in heat convertibility between the natural drying oils and polyethylene maleate, thus allowing the application to drying oils and resins of his revised principles of functionality and convertibility, originally proposed by Carothers (3) and by Kienle (6). Subsequently, in experiments with drying-oil fatty acid esters, Bradley (2)
Linear polyesters derived from glycols and unsaturated aliphatic dibasic acids und e r g o a n oxygen-induced gelation resembling the drying of natural oils. Oxidizing agents and cobalt salts promote drying. The theory that gelation is the result of three-dimensional polym er iza t i o n i s considerably strengthened. The necessity of conjugate double bonds for the polymerization of the natural drying oils is questioned because of the absence of such bonds in these convertible linear polyesters.
showed that heat conversion and oxygen conversion went hand in hand with the probable functionality of the components of the esters studied. The present work confirms this parallelism and provides additional evidence that gelation occurs through so-called three-dimensional polymerization. It has been found in this laboratory that a number of linear polyesters prepared from glycols and unsaturated aliphatic dibasic acids are not only heat convertible but oxygen convertible as well. The gelation is strikingly like that of the natural drying oils. Linear polytriethylene glycol maleate, typical of the group, is a viscous oil or balsam drhich, when suitably promoted by a cobalt salt, commences to air-dry in about 5 hours to an infusible and insoluble film. The oxygen conversion is accompanied by the formation of a wrinkled
