Free Energies of Formation of Gaseous Hvdrocarbons and Related Substances J
C. M. THACKER, H. 0. FOLICINS, AND E. L. MILLER The Pure Oil Company, Chicago, Ill.
I
N 1937 Thomas, Egloff, and hforrell (SI)published tables giving the standard free energies of formation of a large number of gaseous hydrocarbons a t 298.1", 500", and 1000" K. Since that time more accurate data have been presented by Rossini, Pitzer, and others on heats of formation and entropies of a greater variety of hydrocarbons than were available to Thomas et al. This more recent work has been sufficiently extensive in scope to permit us to obtain, in the absence of direct determinations, reasonably accurate values of thermodynamic functions from the trends shown by the known values of compounds possessing one or more similar characteristics in structure. Using the more exact data now available, we have calculated the free energies of a number of gaseous paraffins and olefins. In addition, tables are included containing free energy values for a number of gaseous inorganic compounds that are of interest to petroleum chemists, either because of their own low cost which might permit their use as reactants or of the low cost of the raw material required to react with hydrocarbons to produce these substances as by-products of a inore desired primary reaction.
Standard free energies of formation have been calculated for seventy-seven hydrocarbons and eight inorganic compounds in the gaseous state at 100' intervals from 298.1' to 1200' IC. The tables include values for the normal paraffins (methane to n-decane), the 1-olefins (ethylene to 1decane), various branched-chained saturates and unsaturates of four to eight carbon atoms, and the inorganic compounds carbon monoxide, carbon dioxide, water, ammonia, carbon disulfide, hydrogen sulfide, sulfur dioxide, and sulfur trioxide. Distinction is made between the more accurate values for straight-chain hydrocarbons and those for their branched-chain isomers.
General Methods of Calcmlation The fundamental relations for obtaining an equation for the standard free energy of formation as a function of temperature were taken from Lewis and Randall (88). By the equation, AF = AH
- TAS
(1)
the free energy of any reaction can be obtained a t a given temperature if the heat of reaction and the entropies of all reactants and products are known a t that temperature. The relation between free energy and heat of formation a t any temperature is given by the equation:
GENERAL VIER- OF CHARGETANKS,FURNACES, TOWERS, AND INSTRUMENT P A N E L IN THE PILOT-PL.4NT CRACKING U N I T
584
From Equation 2 a free energy relation as a function of temperature can be obtained if the heat of reaction is known over a wide temperature range.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
May, 1941
585
The above discussion shows that the first data needed for deriving a general free energy equation are the free energy and heat of formation a t a given temperature, and that the free energy of formation can be obtained from a knowledge of the heat of formation and the entropies of all reactants and products. Tables I and I1 give this necessary data a t 298.1' K. for all substances considered in this discussion. Table I11 gives specific heats for the substances considered as a function of temperature and cites the literature from which the equations are taken or from which the data were obtained for deriving the specific heat equations. Specific heat equations are given only for the normal paraffins and the 1-olefins. This is due to the almost complete lack of reliable specifio heat data on the branched-chain hydrooarbons. For the branched-chain paraffin hydrocarbons we used the specific heat equation for the corresponding normal FURNACES AND TOWERS I N THE PILOT-PLANT CRACKING UNIT paraffin as given in Table I11 and for the branched-chain olefins, the specific heat equation for the corresponding 1-oleiin. Also, no specific heat equations are given for nitrogen, ammonia, sulfur, or sulfur-containing comThe heat of reaction as a function of temperature is given pounds, since we did not derive equations for these subby : stances but used the equations as given by Kelley (18,1.9). f d A H = f ACpdT (3) From the data in Tables I, 11, and 111, equations for free energies of formation us. temperature were derived and are given in Table IV. I n the equations for the free energies of Equation 3 indicates that a knowledge of the specific heats va. temperature of each reactant and product is required. ammonia and inorganic sulfur compounds taken from Kelley, The specific heat per mole of a substance is often expressed as the logarithmetic terms are to the base 10; all others are follows: natural logarithms. C, = a
+ bT + cTZ
(4)
The algebraic summation of the specific heat equations of r e a c t a n t s and products give a AC, relation identical in form to Equation 4. Substituting this value for AC, in Equation 3 and integrating give the following relation for heat of reaction as a function of temperature: AH = AH0 b'T'
+ + a'Tc+' T ~ ( 5 ) '/8
where a', b', etc. = summation of a's, b's etc. Substituting Equation 5 in Equation 2 and integrating give the following relation for the free energy of the reaction as a function of temperature: AF;: = AHo-a'TlnT b'Ta - '/a dT3
+ IT (6)
TABLEI. EXPERIMENTAL VALUESFOR ENTROPY, HEATOF FORMATION, AND STANDARD FRBIE ENERQY OF FORMATION OF GASEOUS SUBSTANCES AT 298.1 K. O
Substance Formula Smt References Elements Graphite C 1.365 (10,87,88) Hvdrogen Ha 31.23 (8.18. 87) paraffinsMethane 44.6 Ethane 54.8 64.7 Propane n-Butane 74.5 Isobutane 70.5 n-Pentane 83.1 Isipentiine 80.3 Tetramethylmethan 73.2 n-Hexane 94.1 102.5" n-Heptane 113.7 n-Octane n-Nonane 123.5 n-Decane 133.3 Unsaturates Ethylene C1H4 52.5 64.7 Propylene CsHs 1-Butene 74.5 C4Hs 2-2s-Butene 72.7 C4H8 2-trans-Butene C4Hs 72.1 C4Hs 70.5 Isobutene I-Pentene 84.3 C6HlO 1-Hex ene 94.1 CsHii I-Heptene CiHi4 103.9 I-Octene CoHie 113.7 I-Nonene CeHis 123.5 CioHm 133.3 I-Decene Inorganic compounds Carbon monoxide co ... ... Carbon dioxide COa Carbon disulfide cs2 Water Ha0 Hydrogen sulfide ... HzS Ammonia ... NHs Sulfur dioxide so2 Sulfur trioxide S0a a Calculated from Pitzer's value at the boiling point.
.. . ... ...
...
...
..
AHzes
I
.... . ,
References
AF%a.i
References
...
... ...
... ...
... ...
... ...
...
-17,865 -20,191 -24.750 -29,715 -31,350 -34,739 -36.671 -39;410 -39,950 -45,290 50.630 -55,970 -61,310
... ...
... ... ...
...
... ... ... ... ... ...
-
.. .. ..
... ...
.. .. ..
12.556 4,956 383 1,388 -2.388 -3,205 -4,644 -10,160 16,500 -20,840 -26,190 -31,530
... ... ...
... ...
-
-
-26,394 -94,020 27.580 -57,798 -4,800 -11,040 -70,940 -92,835
... ...
I":
(86)
7 $0)
!Ti,%
... ... ... ...
..* ... ,..
...
... ... .. ... .. . ... ... .. . ... ,
INDUSTRIAL AND ENGINEERING CHEMISTRY
586
Substance
S298.1
2;4-Diniethylpentane) 3-Methylhexanel 2-Methylhexme 3-Ethylpentane 2,2.3-Trimethylbutane 2-Methylheptane 3-Methylheptane 4-Methylheptane 3-Ethylhexane 3-Methyl-3-ethylpentane 2 2-Dimethylhexane 3’3-Dimethylhexane 2lMethvl-3-ethvl~entane 2,3-Dimethylhcx&e 2 4-Dimethylhexane 2’5-Dimethylhexane 3’4-Dimethylhexane 2’3 4-Trimethylpentane 2’2’3-Trimethylpentane 2’3’3-Trimethylpentane} 2:2:4-Trimethylpentane 2,2,3,3-Tetramethylbutane
i
t
1Unsaturates
2-Methyl-2-butene 3-Methvl-1-butene 2-Methj.1-1-butene 2-trans-Pentene 2-cis-Pentene 2 3-Dimethyl-2-butene 3’3-Dimethyl-1-butene 4lMethyl-2-trans-pentene 2 3-Dimethyl-1-butene 2:Ethyl-1-butene
2-Methyl-1-pent ens} 4-Methyl-2-cis-pentene
2-Methyl-2-pentene 3-Methyl-2-cis-pentene 3-Methyl-2-trans-pentene 3-Methyl-1-pentene 4-Meth y1-1-pentene} 3-trans-Hexene 2-trans-Hexene} 3-cis-Hexene 2-cis-Hexenei 2 4 4-Trimet yl-1-pentene 2:4:4-Trimethyl-2-pentene
References
AHzaa.1
References (7,86) (7,261 (7,926) (7,926)
90.1 83.0 86.1 92.8
(7)
(7)
-41,700 -44,600 -43,500 -50,000
95 9
(7)
-48,900
(7,169
99 9
(7)
-47,100
(7,926)
88.8
(7)
-51,800
(7,86)
109 7
(7)
-52,400
( 7 , 86)
102.6
(7)
-55,300
( 7 , 36)
105.7
(7)
-54,200
(7,86)
101.7 98.6 100.9= 91 5
(7) (7) (84) (7)
-56,000 -57,100 -57,100 -60,000
(7,16)
78.5 80.3 80.3 81.9 82.5 85.9 83.0 87.7 86.1 90.1 88.3
(7)
(7)
-13,600 -13,500
(7.86) (7,26‘)
88.3
(7)
-15,200
(7,926)
90.1
(7)
-11,900
(7,26)
91.7
(7)
-12,700
(7,86)
92.3 95.6 96.8
(7) 7) /7)
-11,700 (7,26) -29 100 7 $6) -30:700 { 7 : 8 6 )
${
(7,869
.
(7,26) (7,926)
a Calculated from Pitzer’a value a t the boiling point.
The equations in Table IV were used for obtaining numerical values of standard free energies of formations as given in Tables V and VI. The values in section B of Table V are thought not to be so reliable as those in section A. The reasons will be more apparent from the discussion that follows. Discussion In recent years Rossini and co-workers (36-38) have determined very accurately the heats of formation at 298.1’ K. of many straight-chain hydrocarbons, carbon monoxide, carbon dioxide, and water. As a result of this work i t appears that the heats of formation of the heavier straight-chain gaseous hydrocarbons are a linear function of the number of carbon atoms. Rossini (26, B)also determined accurately the heats of formation a t 298.1’ K. of some of the branched-chain isomers. I n all our derivations the heats of formation determined by Rossini were used when available. I n cases where the heah of formation had not been determined directly, we used the extrapolations of Ewell (7). These extrapolated or approximation values were based on the known heats of formation of related hydrocarbons as determined by Rossini and co-workers. The entropies of hydrocarbons a t 298.1O K. were taken from Ewell ( 7 ) . Examination of the various entropy values that had been published as a result of their direct determina-
Vol. 33, No. 5
atoms in the molecuie. Various other deductions were made from known entropy data which led Ewell to publish the entropy values used in this discussion for straight-chain and branched hydrocarbons. I n spite of the fact that later direct determinations will probably prove, on the whole, that Ewell’s values are approximately correct, it was thought advisable to divide our table of numerical values of the free energies of formation into two sections. Section A of TabIe V contains free energy values based on direct determinations of heats of formation and entropies or on approximation values of these functions which are due to extrapolations that appear entirely reasonable, since the systems involved are relatively simple. Section B contains free energy values based almost entirely on approximation values of heats of formation and entropies, and the approximations involve more complex systems; consequently, these extrapolations are subject to more controversy. Another source of error in the values of section B, Table V, is that none of the specific heat equations used are the result of direct determination. The specific heat of branched-chain isomer was assumed to be the same as that of its corresponding straight-chain paraffin or 1-olefin. It is possible that some of the compounds in section A of Table V should be in section B, and that some values in section B may be of sufficient accuracy to warrant a place in section A . This question can be settled only when more accurate thermal data are available or when accurate equilibrium values are published in which these compounds appear as reactants or products. An important factor in arriving a t a satisfactory equation for free energy us. temperature is equations accurately representing the specific heat of reactants and products over the temperature range considered. With the exception of methane, practically no data are available on hydrocarbons of two or more carbon atoms above about 600” K. After studying the available data we decided to base our specific heat ,qua: tions for all hydrocarbons except methane on the data pub-
TABLE111. SPECIFIC HEATEQUATIONS FOR GASEOUS SUBSTANCES
+
General equation: C p = a 4- bT cT-a (or -k d T 9 Substance Formula a b X 103 c X 10-5 References Saturated hydrocarbons Methane CHd(g) 6.73 10.2 4.26 28.5 Ethane 4.16 42.8 Propane n-Butane CIHio(g) 4.64 55.8 n-Pentane CaHtz(g) 5.16 68.7 n-Hexane CsHu(g) 5.74 81.9 n-Heptane C?His(g) 6.38 94.6 6.89 107.6 CsHis g ) CaHzoig) 7.40 120.6 n-Decane CioHzz(g) 7.91 133.6 . (1)
2g$$
8
::: :: :
;:g:;e
I
{;]
,
Unsaturated hydrocarbons
E:$& : : ~ ~ 1-Hexene l-Heptene 1-Octene 1-Nonene l-Deaene
CzHd(g) CsHe(g) CaHs( ) ~ CgHiolg) ~ ~ e C6Hl? 8 ) C7Hu 9) CsHis[p) CaHia(g) CioHie(g)
~
~
3.82 4.00 4.61 4.95 5.57 6.24 6.75 7.27 7.78
22.0 37.2 51.3 65.9 79.5 92.5 105.5 118.5 131.4
.. .. .. .. .. .. .. ..
(I 6 81) (f: S i ) (1 51) (f:Sl) (1) (1)
..
(1)
,
N
:::
compounds and inorganic C(S)
Gra hite
Hy&ogen Oxygen Carbon monoxide Carbon dioxide waterD
a Value for d
x
107
2.673
::!% 8%?) 6.60 COzh 10.34
2.617
Ha(g)
-
HzO(g)
2.084.
7.187
-1.169 -1:877
1.20 2.74 2.373
-1:b55
.
,
EirT) (17)
(6.9, l r )
($0)
FOR STANDARD FREEENERQIES OF FORMATION OF TABLEIV. EQUATIONS GASEOUSSUBSTANCES AS A FUNCTION OF TEMPERATURE
General equation:
AF; = AHQ
Substance
Formula
Saturates Methane Ethane Propane n-Butane Isobutane n-Pentane Isopentane Tetramethylmethane n-Hexane n-Heptane n-Octane n-Nonane n-Decane
CHa CzHs CaHs CiHio C4HlO CsHiz CiHin CsHii CeHi4 CrHis CsHis C9Hzo CioHzn
Unsaturates Etbylene Propylene 1-Butene 2-&-Butene 2-trans-Butene Isobutene I-Pentene I-Hexene I-Heptene 1-Octene I-Nonene I-Decene
CaH4 CsHs C4Hs CbHa C4Ha C4Ha CsHio CaHia C7Hi4 CsHis CpHe CioHw
Saturates 2-Methylpentane
3-Meth ylpentane}
2 2-Dimethylbutane 2'3-Dimethylbutane 2:Z-Dimethylpentane 3 3-Dimethylpentane 2:3-Dimethylpentane 2 4-Dimethylpentane 3-Methylhexane] 2:Methylhexane
b X IO*
c X 10-6
I
-- 15 376 14:088 --18,309 15,938
9.183 20.95 30.34 39.15 39.15 47.93 47.93 47.93 56.64 65.29 74.07 82.89 91.64
-2.98 -10.42 -15.86 -20.64 -20.64 -25.38 -25.38 -25.38 -30.27 -34.90 -39.69 -44.45 -49.25
-0.0255 -1.169 -1.754 -2.338 -2.338 -2.923 -2.923 -2.923 -3.507 -4.092 -4.676 -5.260 -5.845
-40.55 -93.84 -131.5 -165.5 -161.5 -198.2 -195.4 -1188.3 -232.7 -264.3 -299.6 -333.7 -367.3
19,944 -20,745
-22,677 -25,416 -23 403 -26:183 -28,939 -31,681 -34,447
17,069 12 056 9'988 8'217 7:267 6 400 7:530 4 538 1:732 1.023 -3,787 -6,639 Section
14.77 23.88 32.56 32.56 32.56 32.56 41.52 50.19 68.81 67.59 76.37 85.15 B
-7.575 -13.46 -18.80 -18.80 -18.80 -18.80 -24.35 -29.45 -34.25 -39.05 -43.80 -48.55
-1.169 -1.754 -2.338 -2.338 -2.33s -2.338 -2.923 3.507 -4.092 -4.676 -5.260 -5.845
-83.04 -120.9 -153.7 -151.9 -151.3 -149.7 -188.3 -221.2 -253.9 -287.8 -321.6 -355.5
-
-3.507 3.607 -3.507 -4.092
-228.7 -221.6 -224.7 -264.6
-
CeHu Cdh4 CoHir CrHis
-25,153 -28,053 -26,953 -30,893
56.64 56.64 66.64 65.29
-30.27 -30.27 -30.27 -34.90
CrHis
-29,793
65.29
-34.90
-4.092
-257.7 -261.7
-
C7Hia
-27,993
66.29
-34.90
-4.092
CrHis
-32,693
65.29
-34.90
-4.092
-250.6
CsHis
-30,709
74.07
-39.69
-4.676
-295.6
CsHia
-33,609
74.07
-39.69
-4.676
-288.5
CaHia
- 32.509
74.07
-39.69
-4.676
-291.6
2'3'3-Trimeth ylpentane} CsHls 2:2:4-Trimethylpentane CsHis
CsHia
-34,309 -35.409 -35,409
74.07 74.07 74.07
-39.69 -39.69 -39 69
-4.676 -4.676 -4.676
-287.6 -284.5 -286.8
CiHii
-38,309
74.07
-39.09
-4.676
-277.4
3-Ethylpentane 2 2 3-Trimethylbutane 2:Methylheptane
pentine 2 2-Dimethylhexane 3'3-Dimethylhexane 6Methyl-3-ethylpentane 2 3-Dimethylhesane 2'4-Dimethylhexane 2'6-Dimethylhexane 3'4-Dimethylhexane 2'3 4-Trimethylpentane 2'2'3-Trimethylpentane
t
2,2,3.3-Tetrarnethylbutane
Unsaturates 2-Methyl-2-butene 3-Methyl-I-butene 2-Methvl-I-butene 2-trans-Pentene 24s-Pentene 2 3-Dimethyl-2-butene 3'3-Dimethyl-I-butene 4:Methyl-2-Canspentene 2 3-Dimethyl-I-butene 2:Ethyl-I-butene
2-Methyl-I-pent em} 4-Methyl-2-cis-pentene
CsHio CsHio CsHio CbHio CsHio CsHit CsHir
2.179 5,596 3,750 4 822 5:769 -2,402 198
41.52 41.52 41.52 41.52 41.52 50.19 60.19
-24.35 -24.35 -24.35 -24.36 -24.35 -29.45 -29.45
-2.923 -2.923 -2.923 -2.923 -2.923 -3.507 -3.507
-182.5 -184.3 -184.3 -185.9 -186.5 -213.0 -210.1
CaHia CiHin CsHir
198 -1.002 1,098 1,198
50.19 50.19 50. I9 50.19
-29.45 -29.45 -29.45 -29.45
-3.507 -3.507 3.507 -3.507
-
-214.8 -213.2 -217.2 -215.4
-502
50.19
-29.45
-3.507
-215.4
2,798
50.19
-29.45
-3.507
-217.2
1,998
50.19
-29.45
-3.507
-218.8
2,998
50.19
-29.45
-3.507
-219.4
67.69
-39.05
-4.676
-272.7
10,883 67.59 Section C
-39.05
-4.676
-270.9
2-Methyl-2-pentene 3-Methyl-2-cis-pentene 3-Methyl-2-trans-
'
+ oTlnT + bT9 + cT-1 (or +dT9 + I T
AHo a Section A
3-E.YZl-pentene 4-Meth 1 1 pentene} 3-trans-Kiene 2-trans-Hexenej pentene 2.4.4-Trimethvl-2. pentene .
-9,283
-
Inorganic substancee Carbon monoxide Carbon dioxide Carbon disulfide
COS CSn
Watera Hydrogen sulfide
H2O Has
CO
-
-25,656 93,478 26,320
-56,485 -3,725
0.208 0.603 -9.03b
0.773 -1.054 0.0675 -0.6455 7.30 1.106
-24.49 5.398 -17.04
3,568 7.02b
0.7172 -0.4693 1.865
-13.39 -31.82 (28) -15.39
...
Ammonia
" I
-0,660
13.96,
Sulfur dioxide
so1
-70,635
1.04,
2.542
0.084
Sulfur trioxide
SO8
-92,235
3.34b
2.542
0.084
0
Value for d X 108
-
-3.474.
b
-2.19
0.199
The a term should read U T log T.
587
-
(18)
-
';8& (18)
lished by Beeck (1). He gives specific heat values up to 573' K. for normal saturated hydrocarbons up to heptane and for three unsaturates-ethylene, propene, and butenes. The specific heat equations for normal saturates above heptane are based on the trends shown by the specific heat values of the other saturates. Table VI1 shows the changes in specific heat caused by the addition of each methylene group in going from propane to n-heptane. From the observed differences the following equation was derived for ACp per methylene group added to hydrocarbons above propane: ACp (per CHz added) = 0.51
+ 0.13 T
Adding the above to the specific heat equation for n-heptane gave the specific heat equation for n-octane; the above equation added to that for n-octane gave the specific heat for n-nonane. %Decane was obtained in the same manner from n-nonane. A somewhat different procedure was followed in arriving a t specific heat equations for olefins higher than butene, Table VI11 gives the ratios at various temperatures of the specifio heats of the three lower saturates (ethane, propane, and butane) to the corresponding olefin. The table shows that there is no great change in ratio of specific heats with rising temperature with the hydrocarbons of four carbon atoms but a somewhat greater change in ratio with the hydrocarbons of three carbon atoms, These values would suggest that, with increasing temperature, there would be little or no change in ratio between specific heats of saturates and unsaturates containing five or more carbon atoms, It is only reasonable to expect the specific heat of the saturate to be somewbt greater than that of the corresponding unsaturate, and the data are in agreement with this theory. At 273" K. the difference in ratio of the specific heats of saturates to unsaturates in going from three to four carbon atoms is about half the difference in going from two to three carbon atoms. At other temperatures these differences are somewhat more erratic. From the above consideration we arbitrarily decided to use the observed trends in ratios at 273' K. in arriving a t the ratios of specific heats of saturates to unsaturates for hydrocarbons Containing five or more carbon atoms. Calculated ratios are given in Table VIII. To arrive a t the specific heat equations given in Table 111 for 1-olefins containing five or more carbon atoms, we divided the specific heat equation of the corresponding normal paraffin by the values given in Table VIII.
INDUSTRIAL AND ENGINEERING CHEMISTRY
588
TABLE v.
STANDARD
FREEENERGIES O F FORMATION O F HYDROCARRONS I N THE SECTION -4.
Temp.,
K.
298.1 400 500 600 700 800 900 1000 1100 1200
Methane CHI 12,134 -10,070 -7,860 6,530 -3,110 620 1,940 4,530 7,150 9,800
Ethane C2Hs
Propane CsHs
-
-
n-Butane C~HIO -3,748 5,430 14,960 24,840 34,930 45,150 55,450 65,760 76,220 86,270
Temp.,
a
-
Saturated Hydrocarbons TetraIsomethyln-Pentane pentane methane CaHii CSHIZ CSHIP -1,617 -2,714 -3,337 10,050 9,240 9,340 22,160 21,630 22,440 34,680 34,420 35,950 47,460 47,490 49,720 60,400 60,710 63,650 73,430 74,020 77,670 86,470 87,340 91,700 99,480 100,630 105,700 112,420 113,850 119,630
2,2 3,3-Tetramethylbutane CsHii
2,3Dimethylbutane C6Hl4 -1,557 13,190 28,430 44.140 60,160 76.370 92.670 1OS.980 125.250 141,430
2- 3- and 4-MAhylheptane 3-eth l h e d n e &HIS 1,941 21,050 40,790 61,160 81.930 102,930 124,050 145,190 166,270 187,220
3-Methyl-3ethylpentane 2.2; and 3 3-' dimethyfhexane CsHis 1,157 20.990 41,440 62,520 84,000 105.710 127,540 149,890 171,180 192,840
2,2- and 3,3Dimethylpentane C71116 -337 17,130 35,140 53.700 72,610 91,730 110,960 130,210 149,400 168,480
Temp., 298.1 400 500 600 700 800 900 1000 1100 1200
K.
Carbon Monoxide -32,787 -34,990 -37,170 -39,350 -41,520 -43,870 -45,820 -47,940 50,050 -52,150
-
-
STANDARD
Carbon Dioxide -94,239 -94.320 -94,400 -94,470 -94.540 -94,600 -94,650 -91,700 -94,740 -94,770
FREEENERGIES OF
- 161
16,996 34,690 02,940 71,540 90,350 109,270 128,210 147,090 165,860
2 3 4-Trik k t h ylpentane CsHis 725 20,650 41.190 62,360 83,930 105,730 127,650 149,590 171,470 193,220
6,429 28.920 53 170 78:200 103,720 129,530 155,480 181,450 207,340 233,070
2,2,3-Trimethylbutane
2 2 4-Trik k t h ylpentane C6HlS
-
lRli
I9,EO
40.490 61,740 83,390 105,270 127,270 149,290 171,250 193,080
INORGAKIC SUBSTANCES IN T H E
Water
Hydrogen Sulfide
15,600 11.550 7,660 3,860 140 -3,470 6,990 -10.400 13,700 16,890
-54,638 -63,620 62,370 -51,170 -49,930 -48,650 -47,350 -46.030 -44;690 -43,330
-7,870 -8,850 -9,700 10 440 -11:100 -11,680 -12,190 12,620 12,990 13,290
-
3,975 25,070 46,870 69,370 92,310 115,520 138,870 162,230 186.520 208,670
c1h16
- 0 l.44
16.930 35.340 54,300 73.610 93.130 112,760 132,410 182.000 171,480
ii
2 3 33-Triand
h k t h ylpentane CsHia 550 20.790 41.640 63 120 8.5:OOO 107,110 129,340 151,590 173,780 195,840
chain isomer. This presupposes that the specific heat equation for the straight-chain hydrocarbons is correct. Table IX gives some values of free energies of formations on the assumption that the specific heat equations for carbon and hydrogen are correct but that the specific heat equations used for the hydrocarbon in preparing Tables I, 11, and I11 were 10 per cent too high. Table IX shows that the maximum errors in free energy values occur a t the higher temperature and amount t o only 3 per cent a t 1200" C. At a lower temperature, such as 400" K., the error amounts t o a maximum of 0.6 per cent.
Carbon Disulfide
--
nn Nonsne Decane COHIO CloHw
T
2- and 3Methylhexane, 3ethylpentane C7Hia 447 17,190 34,490 52,340 70.540 88,950 107,470 126.010 144,490 162,860
2,3- and 2 4Dirnethdpentane C7Hla
2-Methyl-3ethylpentane, 2 3- 2 42,5);, Ln6 3,4dimethylhexane CaHis 1.333 20,850 40,990 61,760 82,930 104,330 125,850 147.390 168,870 190,220
If the specific heat equations derived from Beeck's data are accurate over the temperature range covered by the data, as well as a t the higher temperatures being considered, probably no great errors are introduced in the final free energy values by our method of obtaining specific heat equations for the higher straight-chain saturates and unsaturates. It is unlikely that the branched-chain compounds will have exactly the same specific heat values as the straightchain hydrocarbons. However, our assuming that they do have the same specific heat will probably not introduce an error of over 10 per cent in the specific heat of the branched-
TABLE VI.
nn-Hexane Heptane n-Octane CaHir CiH16 CsHis 392 1,482 2,518 17,960 21,220 13,540 27,980 35,000 40,560 42,490 02,590 60,530 70,530 58,110 80,900 88,680 101,500 73,520 89,020 106,940 122,220 104,530 125,220 142 960 120,000 143,440 163:640 134,380 161.550 184,190
DATAXOT So RELIABLE As SECTION A
2,2Dimethylbutane C6Hl4 1.733 13,330 28380 44,900 61 230 77:750 94.360 110.980 127 660 144:050
-
G.4SEOU8 S T A T E
RELIABLE DATA
Saturated Hydrocarbons
2- and 3Methylpentane CaHir 950 13.390 28,230 43,540 59,180 74.970 90,870 108.780 122.650 138,430
IC.
-4,190 5,400 15,330 25.600 36,090 46,720 57,410 68,120 78,810 89,430
SECTION B.
Temp., K 298.1 400 500 600 700 800 900 1000 1100 1200
Isobutane C4HlO
Vol. 33, No. 5
-
-
--
GASEOUS STATE
Ammonia
-- 3,980 1,480 970 3,730 6,430 9,170 11,960 14,760 16,610 20.380
Sulfur Dioxide
Sulfur Trioxide
-71,750 -71,990 72.1 80 -72,270 -72 320 -72:310 -72,250 -72,130 -71,950 -71,720
-87,850 -85,820 -83,930 - 81,970 -79,930 -77,820 -75 610 -73:&0 -71.070 -68,690
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1941
TABLE V.
STANDARD FREE ENERGIES OF FORMATION OB HYDROCARBONS IN ~ s i GASEOUS i STATB (Cmtinued)
-
SECTIONA.
Eth lene Prop lene CS& c2%4 14,820 16 339 18,330 17:750 22,090 19,320 26.030 21,010 30,090 22,790 34,210 24,030 38,350 26,490 42,480 28,370 46,580 30,230 50,620 32.080
298.1 400 500 600 700 800 900 1000 1100 1200
1-Butene C4Hs 17,041 22.950 29,140 35,580 42,170 48,830 55.510 62,170 68 780 75:310
24sButene C4Hs 15,806 21,900 28,270 34,890 41,660 48,490 55,360 62,200 68,990 75,690
SECTIONB.
2-kanaButene C4Hs 15,035 21,190 27,620 34,300 41,130 48,020 54,950 61,850 68,700 75,460
RH~LIABLE DATA(Continued) Unsaturated Hydrocarbons Isobutene 1-Pentene 1-Hexene C4Hs CKHIQ CsHn 14,645 18,811 20,088 20,960 27,090 30,750 27,560 35.720 41,830 44,660 34.390 53,270 53,770 64.930 41.380 48,440 62,980 76.090 55.520 72,210 88.490 62 580 81,400 100,240 69:590 90,520 111,900 76,520 99,520 123,420
Unsaturated Hydrocarbons
2-MethyI2-butene C~HIO 15.188 24,060 33.270 42.790 52.480 62,270 72.070 81.850 91,540 101,130
2-Ethyl-1-butene, 2-mcthyl-1T:mb, pentene CIHIZ 17,841 298.1 28,910 400 500 40,390 52,230 600 700 64 290 800 76:450 9 0 88.650 1000 100,800 1100 112,860 1200 124,780
3-Methyl1-butene C~HIQ 18,069 26,760 35,790 45 130 54:640 64 240 73:870 83,470 92,980 102,380
2-MethylI-butene CKHIO 16,223 24,910 33,940 43,280 52.790 62,400 72 030 81:620 91,140 100,540 2-Methyl-2oentene. 3ðyl-Zr?&pentene, 3-methylP-t.ra&a-gntene
4-Methyl-2cis- entene &Hiz 18,477 29.730 41,390 53.410 65,650 77.990 90,370 102,700 114,940 127,040
6
I2
16,777 28,030 39,690 51,710 63,950 76.290 88,670 101,000 113,240 125,340
%transPentene CIHIQ 16.818 25 340 34:210 43,390 52 740 62:190 71,660 611.090 90,450 99.690
3- and 4Methyl-1peatene
CsHu 19,541 30 1310 42:090 53 930 66:9RO 78.1 h0 90.550 102,500 114.A60 126,480
Conclusions Owing to lack of more reliable data for their entropies, heats of formation, and specific heats, the values for most branched-chain hydrocarbons are only approximations. It is therefore doubtful if these values for branched-chain isomers are sufficiently accurate to estimate closely equilibrium conversions in reactions, such as isomerizations, where the free energy changes involved are small. It is thought, however,
TABLEVII. DIFFERENCE IN SPECIFIC HEATIN GOINGFROM ONE NORMAL SATURATE TO THE NEXTHIGHER SATURATE" 273' K. 4.03 4.04 4.00 Cr to CB 4.10 c s to c7 4.05 Av. per CHn group added 0 From Beeck's specific heat data ( 1 ) . c 8 to c 4 c 4 to CS
TABLE VIII. Compounds
373' K. 5.33 5.34 5.33 5.30 5.33
473' K. 6.69 6.76 6.70 6.64 6.70
573a K. 7.93 7.93 7.94 7.95 7.94
RATIOSOF SPECIFIC HEATSOF PARAFFINS TO THE CORRESPONDING OLEFINS
From Beeck's Data. ( I ) 273' K. 373' K. 473O K.
.
573O K.
GHe: CZH4 1.224 1.243 1.261 1.273 CaHs:CaHc 1.122 1.127 1.132 1.134 C ~ H ~ D : C ~ H1.069 P 1.074 1,077 1.078 Differences in Ratio Caused by Addition of One CHn Qroup Cz-Ca 0.102 0.116 0.129 0.139 cs-c4 0.053 0.053 0.055 0.056
1-Octene CsHls 22,969 38,430 54,400 70,880 87.670 104.610 121 610 138:560 158,390 172,060
1-Nonene CpHn 24.445 42.280 60 720 79:730 99,100 118.650 138,260 157.840 177.290 196,550
1-Decene CIQHZO 25.899 46,100 66,990 88,530 110,470 132,620 154,840 177,030 199,080 220.930
DATANOT So RmLIAsLB As SmonoN A (Continued)
,-Temp., O K. 298.1 400 500 600 700 800 900 1000 1100 1200
1-He tene C~fitr 21,545 34,610 48,140 62,110 76.330 90,680 105 070 llb:420 133,660 147,750
2-cisPentene CiHio 17,586 16,050 34.860 43.980 53.270 62.660 72.060 81,440 90,730 99,920
2- and 3-transHexene CsHu 18,264 29,170 40.490 52,170 64.070 76,070 88.110 100.100 112,000 123,760
3 3-Dimethyl1-butene CsHir 19,057 30,850 43 040 55:590 68.300 81.230 94,140 107,000 119,770 132,400
2- and 3 4 s -
Hexene CsHii 19,085 29 930 41:190 52,810 64.650 76,590 88.570 100,500 112,340 124,040
2,3-Dimethyl1-butene CsHin 16,933 28,410 40,290 52,530 64.990 77,h50 90.1 50 102,700 115 160 1273480
4-Methyl-2trans-pentene CEHIZ 17.656 28,970 40 690 52:770 65,070 77.470 89.910 102.aoo 114,600 126,760
2,4,4-Trimethyl1-pentene CBHM 19,240 36,210 53.090 71.680 89,980 108.430 126,940 145,400 163,740 181.920
-
2 4 4-Tri&e(thyl-2pentene CsHis 18,176 35,330 52.990 71,160 89.640 108.270 126.960 145.600 164,120 182,480
that these approximations will be of value in reactions where the free energy changes are large. The data presented in this paper on sulfur compounds probably should be classified also as approximations because of our limited knowledge of the thermodynamic properties of sulfur and its compounds. The authors believe that the data presented here will give results, with few exceptions, that will accurately predict equilibrium trends with changes in temperature; in the majority of cases, the actual percentage of reactants and products present in an equilibrium mixture can be closely estimated from these values. For some time to come, tables of free energy values will be subject to frequent revision owing to the more exact values for heats of formation and entropies that are constantly being published. Unfortunately specific heats are not included in the above statement. This is due only to the fact that from
TABL Ix. ~ ERRORS IN FREE ENERGY VALUES IF SPECIFIC HEAT VALUES USEDIN TABLE 111 WERE10 PERCENTToo HIGH
-Estd. ValuesCompounds Ratio
Substance
CKHIY: CaHtl 1.043 CsHi~:CsHir 1.030 CYHI~:CIHII1.023
n-Decane
~~~~~
2,3-Dimethy12-butene CaHn 15.593 27,090 38.990 51,250 83 770 7633'10 88.930 101,500 113,980 426,320
I
n-Pentane
l.pentene
CioHzz: CIQHZO 1.017 1-Decene
Temp., 400 1200 400 1200 400 1200 400 1200
K.
Table I 9 570 llO:9SO 28,920 233070 27;090 99,520 46,100 220,930
AF Values Calculated Difference
9,630 114,210 28.990 239,100 27 150 l02:620 46.200 226,890
60 3230 70 6030 60 3100 100 5960
%
Error
0.6 2.9 0.2 2.6 0.2 3.1 0.2 2.7
590
the data being published, investigators are not so active along this line as in the other two. It is hoped that more specific heat data on hydrocarbons will soon be obtained and published because this information is badly needed, particularly a t higher temperatures.
(15) (16) (17) (18) (19) (20) (21)
Literature Cited
(22)
(1) (2) (3) (4)
(5) (6) (7) (8) (9) (10) (11) (12)
(13) (14)
Vol. 33, No. 5
INDUSTRIAL AND ENGINEERING CHEMISTRY
Beeck, J . Chem. Phys., 4, 680 (1936). Clayton and Giauque, J. Am. C h m . Soo., 54, 2610 (1932). Ibid., 55, 5071 (1933). Egan and Kemp, Ibid., 59, 1264 (1937). Eucken, 2.Physik, 37, 714 (1926). Eucken and Parts, Z . physik. Chem., 20B, 184 (1933). Ewell, IND.ENQ.CHEM.,32, 778 (1940). Giauque, J . Am. Chem. SOC., 52, 4816 (1930). Gordon and Barnes, J . Phys. Chem., 36, 1143 (1932). Jacobs and Parks, J. Am. Chem. SOC.,56, 1513 (1934) Johnston and Davis, Ibid., 56, 271 (1934). Johnston and Long, J . Chem. Phys., 2, 389 (1934). Johnston and Walker, J . Am. Chem. Soc., 55, 172 (1933). Kassel, Ibid., 56, 1838 (1934).
(29) (30) (31)
Kassel, J . Chem. Phys., 1, 576 (1933). Kelley, U. S. Bur. Mines, Bull. 350 (1932) Zbid., 371 (1934). Ibid., 406 (1937). Ibid., 407 (1937). Kemp and Egan, J . Am. Chem. SOC.,60, 1521 (1938). Landolt-Bornstein, Physikalisch-Chemische Tabellen, 1st supplement, pp. 702, 817-28, Berlin, Julius Springer, 1927. Lewis and Randall, "Thermodynamics", McGraw-Hill Book Co., New York (1923). Messerly and Kennedy, J. Am. Chem. SOC.,62, 2989 (1940). Pitzer, Ibid., 62, 1224 (1940). Rossini, Div. Petroleum Chem., A. C. S., Cincinnati, 1940. Rossini, J. Research Natl. Bur. Standards, 13, 21 (1934). Zbid., 22, 407 (1939). Rossini and Jessup, Zbid., 21, 491 (1938). Rossini and Knowlton, Ibid., 19, 339 (1937). Spencer and Justice, J. Am. Chem. SOC.,56, 2311 (1934). Thomas, Egloff, and Morrell, IKD.ENG. CHEM., 29, 1260
(1937). (32) Witt and Kemp, J . Am. Chem. SOC.,59, 273 (1937). PRESENTED before the Division of Petroleum Chemistry a t the IOlst Meeting of the American Chemical Society, St. Louis, 110.
Liquid-Vapor Equilibrium Relations in Binarv Svstems J
J
n-Butane-n-Heptane System W. B. KAY Standard Oil Company (Indiana), Whiting, Ind.
T
HIS investigation is the third of a series designed t o discover the effects of variables on the phase-equilibrium composition relations in the critical region of hydrocarbon mixtures. I n previous papers (1, 2 ) the P-V-T-x relations a t the liquid-vapor phase boundaries were presented for the ethane-n-heptane and ethane-n-butane systems. These data made possible a comparison of the phase-equilibrium constants for ethane dissolved in butane and in heptane, and thus yielded valuable information on the effect of the physical properties of a mixture on the phase-equilibrium constants of one of the constituents. Additional information on this point has now been obtained through a study of the butane-heptane system. I n the present paper a summary is given of the P-V-T-x relations at the liquid-vapor phase boundaries for this system, and a comparison is made of the phase-equilibrium constants for n-butane dissolved in ethane and in n-heptane and for n-heptane dissolved in ethane and in n-butane. The apparatus, experimental procedure, and method of preparation of the mixtures were the same as those employed in similar work on the ethane-heptane (1) and ethane-butane systems (2). The n-butane and n-heptane were samples of the same materials that were purified and used in the earlier studies. FIGURE 1. PRESS~E-TEMPERATURE RELATIONS FOR MIXTURES OF *BUTANEAND +HEPTANE
TO OBTAIN the P-V-2'-z relations of the n-butanela-heptane system a t the liquid-vapor phase boundaries, the complete
