I
REMOLO CIOLA' Departamento de Fisica e Quimica, lnstituto Tecnol6gico de Aeronbutica, S6o Paulo, Brazil
Predicting Chemical Reactions by Thermodynamics A simpler method is needed for forecasting chemical behavior, especially in heterogeneous catalysis where reactions occur at high temperatures. This method requires only equilibrium constants far structural groups which are changed in the reaction
D u m m THE PAST 25 years, several attempts have been made to predict by thermodynamics, chemical reactions not yet described in the literature. Such predictions are exceedingly useful, principally in heterogeneous catalysis where reactions generally take place at high temperatures. Methods where free energy of formation for the compounds is estimated, using contributions of molecular structural groups, were reviewed by Janz (4). The principal methods are those of Pitzer (7), Franklin ( 3 ) , and Van Krevelen and Chermin ( 9 ) , who computed this free energy of formation by adding that for groups constituting the molecule, using its symmetry number and several corrective factors. Franklin (3) listed free energies of formation for several hydrocarbon and nonhydrocarbon structural groups a t several temperatures, but Van Krevelen and Chermin gave such values for groups by means of two linear equations -the first covers temperatures ranging from 300' to 600' K., and the second, from 600' to 1500' K . These equations, of the form AFjGAi = A B T X lo*, where A and B X are by approximation, equal to heats and entropies of formation for the groups. The methods of both Franklin and Van Krevelen are complicated ; the free energy of formation for each compound constituent of the reaction must be calculated. But in the method proposed here, only the equilibrium constants of formation for structural groups such as CH3 and CH2 which are altered by the reaction, are needed. Using methods of Franklin and Van Krevelen, free energy of formation for a generic compound, A,, considered an ideal gas in its standard state, may be calculated as follows:
known, the free energy change of a generic reaction,
can be calculated. In Equation 2 , ai and bi are moles of reagents A( and products B which react ; all compounds are considered ideal gases in their standard states. The free energy change (AF') for this reaction is given by 3
AFo =
AFO/A~=
gkAFo/uAi f +ai f RTln U
A ~
I
(1 1 Then, with AF", for each compound Present address, Chemistry Department, Northwestern University, Evanston, Ill.
bjAFo/Bi 1
-
$
aiAFo/Ai (3)
This is briefly the method used by Franklin and Vau Krevelen for calculating AF' a t selected temperatures. The calculation must be repeated for several temperatures in order to determine the temperature where AF' is negative. By substituting Equation 1 in Equation 3, and introducing by definition
b:zT+
2 i
k
bj
1
gk log KfuBj
-
1
Equation 5 is a general equation for calculating log X of the organic reactions, as a function of log ICf for structural groups. Equation 5, as function of his terms, shows that because a great number of Table
I.
+Hz
will have, with considerable accuracy, the same equilibrium constant because log X for both equals log K = log K / - C H O - log K/-CH~OH Because the correction factors of the first equation equal zero, those of the second are canceled, and the symmetry numbers of all compounds equal unity; therefore, its logarithm equals zero. Frequently, when logarithms for equilibrium constants of formation for some compounds participating in the reaction are known with great precision, they should be used in Equation 5 , instead of the respective groups-thus, some inaccuracies introduced by using log K f are eliminated.
+
log K =
+
b--C -CH H O3
AFO~GA =~ -RTln K / u A ~ (4) where IC,,,, is the equilibrium constant for formation of groups considered ideal gases, obtained from compound Ai by the hypothetical reaction, C H2 -+ -CHswhere all reagents are in their standard state, we can deduce the following equation
+
k
organic molecules are asymmetric, their symmetry number is equal to 1; therefore, log u equals 0. Also, because correction factors, 6, equal zero, or associate with both reagents and products, they are canceled. Frequently, several groups such as CHJ, CH2, and OH belong to both reagents and products; consequently, for these, AFofUAior log K / Q A ~ are also canceled. Thus, similar organic reactions-Le., those involving reactivity of the same structural groups-have the same change of free energy and the same equilibrium constant apart from correction factors, and the symmetry number. For example, according to Equation 5, the reactions, CHaCHzOH -C CHaCHO Hz and c1 c1
Calculating Equilibrium Constants ( l o g K,Q) for Group Formation
Log K,, was calculated by two equations. T h r first is log K ~ G = -AF"/G/RT. 2.305
Log Kfu for Paraffinic Groups
CH3 Temp., OK. 300 400 500 600 700 800 900 1000
I I - 4.962
-C-H
-GHa 2.986 I. 093 -0.105 -0.937 1.551 2.024 -2.400 -2.705
-
--CHr-
-
1.496 -2.421 -3.008 -3.417 -3.718 -3.948 -4.130 -4.277
-5.299 -5.498 -5.628 -5.716 -5.777 -5.822 -5.852
I -cI -8.373 -8.205 - 8.069 -7.951 -7.847 -7.743 -7.652 -7.570
VOL. 49, NO. 10
I
CH3
I (3Hr-C-CHs I +0.571 -4.926 -8.384 10.762 12.500 - 13.815 14.852 15.685
-
-C-
I
CH3 -2.401 -6.019 -8.279 -9.823 - 10.949 -11.791 -12.452 -12.979
OCTOBER I957
1789
Table 11.
\
I
Temp., K. 300 400 500 600 700 800 900 1000
\
/
HzC=C-
-13.872 -11.259 - 9.701 - 8.689 - 8.159 - 7.446 - 7.040 - 6.714
\
I
-
~ j a A i
log
UAi
t (6)
uses log K f A ( (logarithm of the equilibrium constant of formation for organic compound Ai at temperature T ) given by Rossini and others (8). Hydrocarbon Groups. The structural groups, CH8 and CH2, were considered fundamental for calculating log K , of all groups. CHI was calculated from log K , of ethane and CH2 from the increments of log K, for paraffins (8). From log K/ca,, using as fundamental log ICf of neopentane and other hydrocarbons (a), and with the aid of Equation 6, the groups included in Table I were calculated. Table I1 lists values of several olefinic groups calculated from log K, ( 8 ) and Equation 6. Table I11 lists values of log K , for acetylenic groups, H-Cd2and -C=C-, calculated as in Tables I, 11. T o avoid correlations from conjugation effects which are not constant, values of Van Krevelen for AF0oai were used
111.
Table Temp., K. 300 400 500 600 700 800 900 1000
1790
Log K f Q for Acetylenic Groups
H-CEC- 36.600 -26.684 -20.725 - 16.761 - 13.929 - 11.809 - 10.170 - 8.913
--CZC-37.770 - 27.459 -21.400 -17.360 - 14.472 -12.303 -10.619 - 9.272
H%C=C-
I
- 15.863 - 12.927 -11.194 - 10.045 - 9.232 - 8.625 - 8.153 - 7.778
- 14.340 -13.030 - 12,044 -11.271 -10.650
- 9.196
HC-C=CH
I
1-’
Table
I
7
-c
olefin
I(
and
H-C,
were
P
k!
toluene (8),and group C from its IC.
‘L Table VI.
Temp., K. 300 400 500 600 700 800 900 1000
Log K,c for Groups
Aromatic
P
k!
-C
?\ -3.576 -3.008 -2.678 -2.470 -2.328 -2.226 -2.148 -2,088
7 k!
d
C-tC
\\
\\
-6.175 -5.088 -4.477 -4.069
-5.937 -4.734 -4.012 -3.530 -3.228 -2.983 -2.794 -2.642
-3.775 -3.547 -3.376 -3.233
free energy of formation ( 9 ) . Nonhydrocarbon Groups. Log K, for oxygen-containing groups, -OH and (-CH20H), was calculated from log ICj for ethyl alcohol ( 7 ) , -CHO “Om the free energy Of formation of acetaldehyde ( 6 ) , and -C02H from the thermodynamic data of acetic acid
Log KIG for Oxygen-Containing Groups
-CH$OH 26.089 17.656 12.552 9.128 6.669 4.820 3.380 2.226
-c-0II
Temp., O K. 300 400 500 600 700 800 900 1000
-9.956 - 8 * 290 - 7,289 -6.623 -6.096 -5.690 -5.377 - 5,125
7
I(
?\ ?\ calculated from 1% K/ of benzene and
Table VII.
V.
-C++
I
\
-7.658 -6.309 - 5.499 -4.960 -4.557 -4.283 -4.073 -3,903
-4.446 -3.852 - 3.456 -3.223 -3.047 -2.911 -2.801
H-C
I n Table V: log K, of aromatic
Temp., O K. 300 400 500 600 700 800 900 1000
HzC-
- 5.436
7
-32.203 - 26.383 - 22.527 - 19.773 - 17.708 - 16.110 - 14,823
in calculations for conjugate (Table IV).
groups,
-C
Temp., OK. 300 400 500 600 700 800 900 1000
- 42.897
-25.412 - 21.668 - 19.004 - 17.022 - 15.467 - 14.231
1 8Ai
- 15.809 - 13.616 - 12.149 -11.097 - 10.310 - 9.691
- 40.328 - 30.999
-37.575 - 28.706 - 23.419 - 19.916 - 17.427 -15.569 - 14.129 - 12.980
k
gr-log
1
- 19.508
HzC=C=C-
H
where A F 0 / Q is the free energy for group formation as given by Franklin (3) or calculated from Van Krevelen’s data ( 9 ) for the necessary temperatures. The second equation, ~ j A = i
I
-c=c1 1 - 23.344 - 18.847 - 16.152
Conjugate
7
I(
H-C=C-
trans - 16.695 - 13.543 -11.656 - 10.405 - 9.517 - 8.872 - 8.348 -. 7.896
-11.857 - 10.548 - 9.658 - 8.984 - 8.459 - 8.039
HzC=C=CTemp., O K. 300 400 500 600 700 800 900 1000
/
H
H cis H - 17.144 - 13.800
Log K,Q of Olefin Groups
IV.
H
/“=t
/
c=c
H
log
Table
Log K,o for Olefinic Groups
0
61.770 44.901 34.778 28.033 23.212 19.592
-OH
-c-/I
-CHO
27.585 20.077 15.550 12.545 10,387 8.768 7.510 6.503
20.130 14.726 11.457 9.268 7.699 6.516 5.591 4.846
-09.648 6.768 5.043 4.203
-011.637 8.287 6.280 4.942 4.142 3.515 3.027 2.637
-COzH +51.819 +34.473 +24.018 $17.111 12.206 4- 8.529 3- 5.690 3.432
0
18.467 13.353 10.285 8.239 6.778 5.681 4.830 4.148
+ +
-c=c=o I
-c=c=o I
H
5.430 3.638 2.631 1.931 1.333 0.967 0.682
8.363 6.021 4.616 3.679 3.010 2.507 2.117
/”
Log K i G for Nitrogen-Containing Groups &/
Temp., OK. 300 400 500 600 700 800 900 1000
INDUSTRIAL AND ENGINEERING CHEMISTRY
-N-
-CzN -20.821 -15.227 -11.867 - 9.627 - 8.026 - 6.691 - 5.894 - 5.116
-hTsC -31.799 -23.363 -18.301 -14.927 -12.506
-NHz -7.977 -7.463 -7.155 -6.950 -6.581 -6.844 -7.052 -7.216
-22.525 -18.981 -16.854 -15.804 -14.424 -13.663 -13.074 -12.601
-h?\ -16.673 8.611 7.374 6.549 5.926 5.446 5.075 - 4.777
-
-N-H
I
-16.326 -13.971 - 12.558 -11.616 - 10.942 - 10.436 - 10.046 - 9.731
--KO2
- 1.846 -3.293 -4.164 -4.793 -5.179 -5.496 -5.740 -5.935
PREDICTING BY THERMODYNAMICS monomer (70). Other data in Table VI were calculated from ( 9 ) . For nitrogen-containing groups in Table VII, log XI was calculated from the corresponding values of AF',Q ( 9 ) and log iT,-f-~o*from nitromethane (5). Data for sulfur-containing groups (Table VIII) were calculated from AFOIff ( 9 ) . Data in Table I X for halogen-containing groups were calculated from AF"m (9). Table X gives data calculated (8, 9 ) for some compounds which cannot be calculated from group contributions Correction Factors
its practical application. This as a limiting factor can be circumvented, however, by using selective catalysts. Equation 5 is needed to determine the most probable temperature range within which a certain reaction is thermodynamically feasible. For example, in hydrogenating alcohols, the eqiation, CHSCHZOH -+ CHsCHO Hz,
(6)
Corrective terms appearing in Equation 8 come principally from cyclization and introduction of lateral chains in rings. Table XI gives the most important corrections, necessitated by ring formation, calculated for rings with three and four carbon atoms from Franklin'sdata ( 3 ) ; other data are from log XI of cycloalkanes (8). Table X I 1 gives correction factors necessitated by introduction of lateral chains in cyclopentane, cyclohexane, and benzene rings calculated from log
4
Table VIII. Temp., o
K.
300 400 500 600 700 800 900 1000
O
X.
300 400 500 600 700 800 900
COClZ
CHsOH
HCOzH
300 400 500 600 700 800 900 1000
35.835 26.362 20.678 16.890 14.183 12.150 10.575 9.312
28.411 19.407 14,004 9.310 7.732 5.727 4.171 2.924
58.534 42.568 32.989 26.604 21.811 18.272 15.528 13.328
Cyclohexane
-
log
KfCHO
f log
KlCH,
log K ~ C H ~ f O H&oh
+ RTlog
- log
-k HA, (7)
BHA,
-S-
//B
-S-
0
14.584 9.086 5.787 3.588 2.168 0.838 -0.078 -0.811
47.964 32.924 23.900 17.885 13.696 10.545 8.098 6.139
-S-
0
C--tSC-+
-SH
-0.408 -0.584 -0.691 -0.761 -0.758 -0.783 -0.804 -0.820
5.442 3.497 2,330 1.552 0.996 0.579 0.254 -0.044
-0.685 -1.289 - 1.652 - 1.894 -2.110 - 2.240 -2.341 -2.421
Log KIQ of Halogen-Containing Groups
- CI
-F 33.292 25.078 20.149 16.864
-Br
-1 -5.680 -4.260 - 3.409 -2.841 -2.435 -- 2.130 - 1.894 - 1.705
1.748 1.453 1.276 1.158 1.073 1.010 0.959 0.922
6.100 4.508 3.606 3.005 2.576 2.252 2.003 1.802
1000
OK.
KfCHi
=
Log K l for ~ Sulfur-Containing Groups
o It
Table IX.
Table X.
log Ka
+
Temp.,
Temp.,
represents dehydrogenation of ethyl alcohol to acetaldehyde and hydrogen. Its equilibrium constant, using Equation 5 , is
Log K,, for Some Organic Compounds HzC=C=O 9.929 7.286 5.700 4.642 3.887 3.320 2.880
...
Kl of corresponding hydrocarbons in Rossini's tables (8).
H&=O 19.785 14.482 11.300 9.179 7.602 6.690 5.498 4.760
Table XI.
CHI
-
CZH4
-
CzHz
CfiH12'
- 11.878
8.818 5.490 3.427 2 * 000 0.953 0.150 0.488 1.008
- 5.693 -11.286 - 14.893 - 17.432
9.657 8.412 7.619 7.080 6.690 6.400 6.174
-19,310 -20.750 - 21.885 -22.794
-36.406 -26.541 -20.629 - 16.695 13.893 -11.798 - 10.170 8.874
-
-
Correction Factors for Cyclization
Using Log K, of Groups for Predicting Organic Reactions
The process consists of plotting logarithms of equilibrium constants as a function of temperature. For temperatures either below or above those where log K is greater than zero, reaction is probable because AFo is less than zero. When log X is less than zero (AFO > 0), reaction is either improbable, or probable only under drastic conditions ( 2 ) . O n the other hand, because log XI, for several groups is inaccurate, especially when applied to complex compounds, it is necessary to attribute an arbitrary error of about 100' K., either above or below (depending on whether the curve decreases or increases with log IC) to the temperature at which log X equals zero. This method refers to thermodynamic feasibility of the'reaction, but it specifies nothing about rate which regulates
Temp., O K. 300 400 500 600 700 800 900 1000
-9.231 -6.889 -5.484 -4.547 -4.012 -3.376 - 2.986 -2.673
3.694 2.634 1.998 1.574 1.451 1.335 1.206 1.120
7.078 5.420 4.425 3.762 3.203 2.859 2.591 2.378
3.187 2.521 2.121 1.855 1.714 1.561 1.443 1.347
.No. of C Atoms in Ring 300 400 500 600 700 800 900 1000
3
4
5,
6
- IO. 528 - 6.190 - 3.549 - 1.843 - 0.671
-8.714 -4.371 1.748 -0.00 f 1.236 +2. 168 4-2.889 +2.797
1.580 2.640 3.210 3.558 3.784 3.944 4.121 4.147
4,507 4.377 4.248 4.143 4,063 4.004 3.961 3.929
+ 0.248
f 0.945 4- 1.490
-
VOL. 49, NO. 10
OCTOBER 1957
1791
Table XII.
Temp.,
Correction Factors Necessitated b y Introducing Lateral Chains Cyclohexane cis-Cyclopentane 1.2, 13, 1.3, 1.4,
K. 300 400 500 600 700 800 900 1000
1.2
1.3
1.1
CiS
trans
trans
cis
1.281 0.990 0.828 0.714 0.629 0.557 0.559 0.459
0.544 0.425 0.372 0.331 0.293 0.246 0.287 0.212
-0.989 -0.798 -0.637 -0,592 -0.551 -0.518 -0.501 -0.475
- 1,979
-0.798 -0.615 -0.513 -0.428 - 0.358 -0.333 -0.295 -0.273
- 1.120
- 1.407
O
Double 300 400 500 600 700 800 900 1000
-1.470 - 1.173 -0.997 -0.825 -0.715 -0,639 -0.570
Branching in Aromatics
-0.791
-1.112
- 0.600
- 0.897
-0.497 -0.413 -0.345 -0.286 -0.262
-0.774 -0.691 -0.604 -0.583 -0.563
1.3
1.2.3
1.2.4
1.3.5
-0.353 -0.375 -0.302 -0.242 -0.200 -0.172 -0.140 -0.122
0.182 0.103 0.111 0.124 0.130 0.130 0.137 0.137
-0.904 -0.849 -0.669 -0.550 - 0.468 -0.418 -0.363 - 0.333
-0.178 -0.310 -0,241 -0.194 - 0.162 -0.150 -0.125 -0.118
0.582 0.350 0.348 0.346 0.332 0.331 0.336 0.317
Here, correction factors, 6, and log u for all compounds entering the reaction equal zero and log X j - CH,’S are canceled ; thus, Equation 7 is reduced to log Ka = log K ~ C HO log KKH~OH (8) which is a general equation for log X in dehydrogenating primary alcohols, provided all symmetry numbers equal zero or the ratio equals 1 and the corrective factors equal zero or belong both to reagents and products. Table XI11 lists the balues of log Ka computed from 300’ to 1000’ K. Log K is greater than zero above 580’ K. ; thus, the reaction proceeds smoothly over this temperature range if a good selective catalyst is used or if kinetics is favorable.
log K = 2 log K m o d
-
+
For the reverse reaction, CH,CHO Hz CH,CH*OH, the opposite is true as shown by log Kb. Therefore, it is concluded that below 580’ K., hydrogenations of aldehydes proceed easily, and above this temperature dehydrogenations of alcohols proceed easily. A second example is hydrogenation and dehydrogenation of olefins. Consider the reactions,
Table XIII. Log K for Dehydrogenation of Alcohols and Hydrogenation of Aldehydes Temp., Log Ka -5.959 -2.927 - 1.095 $0.140 1.030 1.696 2.116 2.620
OK.
300 400 500 600 700 800 900 1000
O K .
300 400 500 600 700 800 900 1000
1792
Log K Calculated b y Group Contribution Compared with That Calculated from (8) Calcd.“ Calcd.d Calcd.“ Ca1cd.f Groups (8) Groups (8) Groups (8) Groups (8)
15.363 15.453 15.062 15.002 15.062 15.262 15.062 9.931 9.290 9.631 9.517 9.631 9.830 9.631 6.588 6.142 6.288 6.220 6.288 6.484 6.288 4.015 4.335 4.035 3.991 4.035 4.226 4.035 2.890 2.483 2.590 2.394 2.590 2.332 2.590 1.474 1.329 1.374 1.191 1,329 1.372 1.329 0.510 0.424 0.210 0.254 0.424 0.406 0.424 -0.268 -0.302 -0.564 - 0.493 -0.302 -0.365 -0.302
INDUSTRIAL AND ENGINEERING CHEMISTRY
2 log K/neae ( 9 )
Logarithms of equilibrium constants for hydrocarbon group formation are fairly accurate but are less so for nonhydrocarbon groups because thermodynamics of the corresponding compounds is less known. particularly a t high temperatures. Therefore, values of log given in the tables are not significant beyond the first decimal. However, three decimals are given for consistency with data furnished bv Rossini and by the Kational Bureau of Standards. Nomenclature AFO f A t , AFO f B l = free energy offormation
for compounds, A , and B,, considered ideal gases in their standard state AFoIGA,,AFolcs, = free energy of structuralgroupswhich built compounds A , B, in their standard state uAr,uB, = symmetry number for molecules of A , and B, Pic = number of groups, GA, or GB,, which built A , and B, molecules = moles of A , and B, considered a,, b, in the equation r e p r e sentative of the reaction +bB,, 6A1., aB, = empiric corrective factors Literature Cited ( I ) Brickwedde, F. G., Moscow, ht., Aston, J. G., J . Research Natl. Bur. Standards 37, 263 (1946). (2) Dodge, B. F., Trans. Am. Inst. Chem.
Log I‘& 5.959 2.927 1.095 - 0.140 -1.030 - 1.696 -2.116 -2.620
Table XIV.
Reaction,
-
Accuracy i n Calculating Equilibrium Constants
Triple
1.2
Corrective factors equal zero for all compounds; the symmetry number equals 1 for all olefins and ethylbenzene, but equals 2 for other hydrocarbons. Table XIV gives values of log X at several temperatures for reactions c, d, e, and f accompanied by the values of log X calculated with the aid of Rossini’s tables (5)using the equation
15.197 9.665 6.176 3.789 2.074 0.750 -0.305 - 1.162
Engrs. 34, 540 (1938). ( 3 ) Franklin, J. L., IND. ENG. CHEM. 41,1070 (1949). (4) Janz, G. J., Quart. Reus. IX, 229 (1955). (5) McCullough, J. P., J . Am. Chem. Soc. 76, 4791 (1954). ( 6 ) Pitzer, K. S., Zbid., 71, 2842 (1949). ( 7 ) Pitzer, K. S., J . Chem. Phys. 8, 711 (1940). (8) Rossini, F. D., Pitzer, K. S., others, “Selected Values of Physical and Thermodynamic Properties of Hy-
drocarbons and Related Compounds,” Carnegie Press, Pittsburgh, Pa., 1953. ( 9 ) Van Krevelen, D. W., Chcrmin,
H.A. G., Chem. Eng. Sci. 1, 66
(1951); 1, 238 (1952). (IO) Weltner, W., J. Am. Chem. 3949 (1955).
S;)G.
77,
RECEIVED for review July 7, 1956 ACCEPTEDFebruary 28, 1957
