Ind. Eng. Chem. Process Des. Dev. 1904, 23,67-72
Some data for the oxidation of acetic acid at 1%O2 and 0.1% CH3COOH are included in Figures 3 and 9. The oxidation of acetic acid is slower than that of ethanol and acetaldehyde. The oxidation of methanol has been carried out over the same catalysts used in the ethanol study. Detailed results have been published elsewhere (Yu-Yao, 1981). In general, the oxidation of methanol was faster than that of ethanol. Formaldehyde formation also went through a maximum. However, some difference in relative activity of the various catalysts for the two alcohols was found.
90
00 I
z
70
0
E
60
I
W
>
I p i / a - i 03(048%) 1% 02 SOLID LINES o 1 4 %cpn50n DASHED L I N E S 0 0 9 % CH.,CHO DASHED L I N E S 0 I X C H 3 C O O H
8 %
40
30
t
I I I
67
I
Acknowledgment
The author is indebted to Dr. J. T. Kummer for initiating this project and for many helpful discussions throughout the course of this work and to Mr. C. Peters for the XRD results. Registry No. ZrOz, 1314-23-4; Pt, 7440-06-4; Pd, 7440-05-3; Rh, 7440-16-6; Ag, 7440-22-4; CUO,1317-38-0; MnzO3, 1317-34-6; CuCrz04,12018-10-9;Co304, 1308-06-1; Crz03, 1308-38-9;Fe203, 1309-37-1;Vz06,1314-62-1;NiO, 1313-99-1;HzO, 7732-18-5;CeOz, 1306-38-3; ethanol, 64-17-5.
io0
200
300
400
TEMPERATURE, ('C)
Figure 9. Pt/a-Alz03 (0.48%); S.V.= 300 K h-l, 0% 02,0% H20: solid lines, 0.14% CzH,OH; dashed line, 0.09% CHJHO; dotted line, 0.1% CH,COOH.
indicates that CzH4oxidation competes unfavorably with that of ethanol over some of the catalysts. The oxidation of acetaldehyde for 1% O2 and 0.1% CH3CH0 was studied over Pt/a-A1203, Pd/a-A1203, CuO/y-Alz03,and Co304/.Zr02. C02was found to be the only product in all cases. Typical curves are shown in Figure 3 and 9. In general, the rates for the oxidation of ethanol and acetaldehyde are comparable. Quantitative results are more difficult to obtain for the oxidation of acetic acid than for the other compounds.
Literature Cited Chui, G. K.; Anderson, R. D.; Baker, R. E.; Pinto, F. B. P. "Proceedings of Thlrd Internatlonal Symposium on Alcohol Fuels Technology"; Asilomar, CA, 1979; Vol. 11. Dlxon, J. K.; Longfield, J. E. "Catalysis", Emmett, P. H., Ed.; Reinhold Publishing Corp.; Baltimore, MD, 1960; Vol. VII, p 366. Jacono, M. L.; Schiavelio, M.;Cimino, A. J. Phys. Chem. 1971, 75, 1044. Kurlna, L. N.; Morozov, V. P. Russ. J. Phys. Chem. 1976, 538. Pines, H.; Manassen, J. Adv. Catal. 1966, 16, 71. Yu-Yao, Y. F. J. Phys. Chem. 1965, 69, 3930. Yu-Yao, Y. F.; Kummer, J. T. J. Catal. 1977, 4 6 , 388. Yu-Yao, Y. F. U.S. Patent 4304761, 1981.
Received for review July 16, 1982 Accepted April 8, 1983 This paper was presented at the Second Chemical Congress of the North American Continent, San Francisco, CA, Aug 24-29, 1980.
.
Thermodynamics of Alcohol-Alcohol Mixtures. 1 A Continuous Linear Association Model for Alcohol-Alcohol Solutions Concepclon Pando,+Juan A. R. Renunclo,+ Rlchard W. Hanks, and James J. Christensen' Department of Chemical Englneering and Contribution 292 from the Thermochemlcal Institute, Brigham Young University, Provo. Utah 84602
An equation for the excess Gibbs energy of alcohol-alcohol solutions has been derived. The model used in the derivation is based on the hypothesis of a continuous linear association of both alcohol molecules. Expressions for the activity coefficients as well as for the heat of mixing are given. All these expressions contain three parameters which must be adjusted from experimental data; two of them have the physical significance of the equilibrium constants for the self-association process, while the third one is an interaction-energy parameter. The ability of the derived excess Gibbs energy equation to represent several sets of data is shown and the model is compared with other models widely used in the literature.
Introduction Although considerable heat-of-mixingand vapor-liquid equilibrium data for mixtures formed by two alcohols are 'Departamento de Quimica Fisica, Universidad Complutense, Madrid-3, Spain.
available in the literature, there apparently does not exist a specific semiempirical model able to describe the thermodynamic properties of these solutions. Kehiaian and Treszcza (1969) proposed to use the general theory of associations in which a macromolecule A,B, is formed from components A and B. Lee et al. (1973) applied a theory
0196-4305/84/1123-0067$01.50/00 1983 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 1, 1984
88
based on group contributions to these alcohol-alcohol systems. This theory failed to describe the mixtures formed by small-size alcohols, thus indicating the importance of the orientation factor. Other authors have considered the linear association of the molecules of one component (Renon and Prausnitz, 19671,the formation of dimers of both components (Francesconi and Trevissoi, 1971; Tamir and Wisniak, 1975), or the association of a molecule of one component to the polymer chain formed by molecules of the other component (Nitta and Katayama, 1973; Nagata, 1973, 1977). However, these models seem to be insufficient to explain the behavior of the alcohol-alcohol mixtures in which the formation of polymers of both components can be expected. A different approach to the study of these solutions is proposed in this paper. The model of Renon and Prausnitz (1967), which has been shown to provide good results for the alcohol-hydrocarbon mixtures, is extended to include associations of both components and applied to alcohol-alcohol mixtures. The Theory of Two Associated Alcohols In the derivation of a model for alcohol-alcohol interaction we have assumed that like molecules of both components may associate to form hydrogen-bonded polymers (A, and BJ. For simplicity, the formation of copolymers has not been taken into account in this formulation. If A and B stand for alcohol 1 and 2, respectively, the assumptions involved in the model are as follows. (1)The solution contains molecules in the form of monomers Al and B1, dimers A2, B2, ...,n-mers, A, and B,, formed by successive addition reactions of the type A1 + An = An+,
(la)
B1 + Bm = B m + 1
(1b)
(2) The association constants for the above reactions are independent of n or m. (3) The polymerization process does not contribute to the excess volume of the mixture. That is, the molar volume of an n-mer A,, is n times that of the monomer. (4) Intermolecular interactions are characterized by expressions of the van Laar type. (5) The temperature dependence of the association constants KA and KB is expressed in terms of the heat of formation of a hydrogen bond and the degree of association. (6) The entropy of the mixture is considered as the sum of the entropies of mixing of both kinds of polymers separately. These assumptions are essentially those used by Renon and Prausnitz (1967) for the derivation of the continuous linear association model (CLAM) but extended to a mixture containing two alcohols. The Gibbs Energy of Mixing As was suggested by Scatchard (1949), the Gibbs energy for mixing all species A,, ...,A,, B1, ..., B, is obtained by adding to the entropy of mixing, AS,, a van Laar-type expression, AG,, which represents the contribution to the Gibbs energy due to the physical interaction between molecules as shown in eq 2 AG = AG, - TAS, (2)
m
AG, = (PABUAUBNANB + PBBUB'NB' + PAAUA~NA~)/(UANA + UBNB)(4)
where only three kinds of interactions appear, two for like molecules and one for unlike molecules. AS, is the entropy of mixing one of the associated components into the other which is considered as the solvent. According to Flory's theory (Flory 1944), the entropy of mixing of the associated alcohol B into solvent A is given by
where 4Ais the volume fraction of component A, @B, is the volume fraction of m-mer molecules, B,, and z is the coordination number of the liquid lattice. The volume fractions of and 4Bmare given by
" m
~UBNB,
(7)
- uANA + v B N B
By substitution of eq 4 and 5 into eq 2 and further differentiation, we may obtain the partial molar Gibbs energy, AGB,, for each of the associated species of alcohol B. r
m
m
\
A similar derivation may be carried out assuming that alcohol B is the solvent and the associated alcohol A is the solute. Then an equation similar to eq 8 may be derived for the partial molar Gibbs energy of r-mer A,,
zA,
m
AGp may be given by AG, = m
volumes, and N are the number of molecules of each kind. If we assume that the interaction energies are independent of the degree of association and that the polymerization process does not contribute to the excess volume of the mixture, eq 3 may be written as
\
m
where /3 represents the interaction energy between the two molecules indicated in the subscript, u are the molar
Equilibrium Constants The partial molar Gibbs energies of all species in the solution are at equilibrium - related, - - - GA,+, G A , + GA,,;GB,+i= G B , + GBm (10)
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 1, 1984 69
the gO are the standard Gibbs energies of formation for each species. These energies are considered independent of the degree of association, n or m, and are given by
where Ago is the Gibbs energy of formation of one hydrogen bond and subsequently is applicable to both alcohols. Making use of eq 8 and 9 it is possible to derive an expression for each of the partial molar Gibbs energies and thus to calculate Ago. The expressions for Ago are
-
--ago - I n
RT
--Ago RT
[ [
] [
-- -In( : -: 2 - 1 ) ~ J A , , ~ An~ + 1
- In -!.!&!-
-1
~ J B , ~ Bm~ + 1
-In
[2
]
(z - l ) ]
where the volume fractions of monomer in the solution, 4Aland @Bl, are given by
The volume fractions in the pure components, @A,* and 4B1*,may be obtained from $A and 4B1 by setting and ~p~equal to one, respectively. *he value of P in eq 21 and 22 is given by
P = DAB - PAA- PBB
(25)
(13)
which makes eq 21 and 22 functions of three unknown parameters 6 and two equilibrium constants, KA and KB.
(14)
T h e Excess Gibbs Energy The excess Gibbs energy may be expressed in terms of the activity coefficients as
Since the second terms on the right-hand side of eq 13 and 14 do not depend on the association process, we may define the association equilibrium constants, KA and KB, as
These expressions are in agreement with the one reported by Renon and Prausnitz (1967). KA and KB are only a function of temperature in these expressions. Activity Coefficients The activity coefficients may be derived from the partial molar Gibbs energies of species A and B
gE = RTCx, In yi
(i = A, B)
(26)
Substituting the expressions for Y~ and YB given by eq 21 and 22 into eq 26, we obtain the expression for the excess Gibbs energy corresponding to the model given in this paper. This expression contains several terms which depend on one of the three parameters KA1,KB, and P. The term depending on is due to the physical interaction defined by eq 4 while the other terms are due to the association process (chemical interaction). The excess Gibbs energy may be written thus gE = gEp + gEc
(27)
where gEpis the physical contribution and gEc is the chemical contribution to the excess Gibbs energy. The physical contribution term gEpmay be written as gEp= P ~ A ~ B ( x A u A+ x B u d
(28)
the chemical contribution is given by [~A,/~A~X+ A xIB In [4B1/4B1*XBI + X A K A (4~~ ~ A- 4 ~ , * + ) X B K B ( ~ -B#B,*) ~ B ~ (29)
gEc/RT = XA
If we consider the standard states for A and B as the pure associate alcohols, the expressions of S A and m B are given by (19) =A = =A1 + =A1* where S A l * and mB1* are the partial molar Gibbs enof monomers ergies - in the pure alcohols. Expressions for AGA1, AGB1, AGA,* and z B 1 * can be derived from eq 8 and 9. The expressions for the activity coefficients, YA .and yB, may be obtained after substituting eq 19 and 20 into eq 17 and 18 In YA =
The Excess Enthalpy The excess enthalpy may be derived from the excess Gibbs energy by making use of the Gibbs-Helmholtz relation (30)
The excess enthalpy may also be written as the sum of a physical and a chemical contribution, hEpand hEc,respectively hEp= P'+A r
+
~ B ~ A U A XBUB)
(31)
70
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 1, 1984
KA=KB=10
where
and Aho = P d(R In K)/dT
(34) where K may be either KA or KB, since both are association equilibrium constants. The different volume fractions defined by eq 23 and 24 have been taken into account in the derivation of eq 32 in order to get a more simplified expression. Discussion of the Model For any alcohol-alcohol system at constant temperature the model used here requires three parameters, 0, KA, KB when fitting Gibbs energies and p', KA, KB when the fitted magnitude is the excess enthalpy. The equilibrium constants should depend only on their respective alcohols and should be independent of the other component. However, it can be seen in Table 111that KA for methanol varies from 0.383 to 0.627 as the second component is changed. Also, KA does not exhibit the temperature dependence of an equilibrium constant as seen from systems IIIa, IIIb, and IIIc in Table 111. Thus, ICs should be treated as empirical binary parameters from equilibrium constants for selfassociation processes. Figure l a shows calculated chemical contributions to the excess Gibbs energy, gE, for molar volumes of A and B of 100 cm3/mol at different values Of KA = KB Values of 100 were chosen for uA and U B as representing intermediate values for the range of volume found for alcohols in this study. Figure l b shows the results of the same calculation as in Figure l a except that allowing UA = l ! t ~ =~ 50 cm3/mol. It may be observed that the position of the maximum in gE,/RT depends on the relative values of UA and uB. Similar plots may be made for the excess enthalpy. From eq 27,28, and 29 one may calculate the slope of the excess Gibbs energy or excess enthalpy in the region close to xA= 0 or to XA = 1. It may be observed that these slopes depend mostly on the equilibrium constant of the component in which the mixture is rich in these regions. In Figure 1, KA essentially determines the slope of the right side of the curves and KB the left. That is, although the analytical expressions for the respective limiting slopes involve all three parameters, the slope at XA = 1 depends primarily on KA while that at X A = 0 depends primarly on KB The addition of the physical term to the values given in Figure 1 determines the total amount of the excess Gibbs energy predicted by the model. Comparison with Other Models In order to compare the capability of this model to represent the gEdata calculated from experimental data, a few sets of isothermal vapor pressure data from the literature have been considered. Table I gives the purecomponent properties as well as the source references for these systems. Some systems have small molar volumes (system I), some have large molar volumes (systems IV and V), some have similar volume of both components (systems I, IV, and V), different molar volumes (systems I1 and 111), large values of g E (systems I1 and 111),small gE (systems I, V) and negative g E (system IV). The excess Gibbs en-
3
0
0.2
0.6
0.4
0.8
1.0
XA
XA
Figure 1. (a) Chemical contribution to gE vs. composition when uA = UB = 100 cm3/mol and KA = KB. (b) Chemical contribution to gE vs. composition when CIA = 50 cm3/mol, UB = 100 cm3/mol, and KA = KB.
40-
30-
101;-
' 0
EXPERlME;L, NRTL-UNIQUAC - THIS WORK 0.2
0.6
0.4
)
0.8
0
xA
Figure 2. Excess Gibbs energy for the methanol + ethanol system.
ergies have been calculated from total vapor pressure and the liquid composition data by Barker's method (1953). The calculated excess Gibbs energies were fitted to the Redlich-Kister equation ,=n
gE/RT = x A x B C C,(xA - xB)' ,=O
(35)
Table I1 gives the coefficients and standard deviations of the calculated total pressure values from the experimental total pressure. The excess Gibbs energy values at experimental liquid-composition values have been fitted to eq 27, 28, and 29. Table I11 gives the values obtained for the parameters KA, KB, and 0 as well as the standard deviation of the calculated gEvalues from those obtained with eq 35. The same values of gE have been also fitted to the UNIQUAC equation (Abrams and Prausnitz, 1975) and to the NRTL equation (Renon and Prausnitz, 1968). The required values of the pure-component molecular structure constants r and q used in UNIQUAC model have been taken from Prausnitz et al. (1980). Table I11 also gives the values of the parameters Anzl and Anl2, for the UNIQUAC equation and those of the parameters AgI2, AgZl,and a for the NRTL equation. All parameters have been obtained from the same sets of gE values with the same regression method (Pennington, 1970). The parameter CY of the NRTL equation has been allowed to vary in the 0.3-0.4 interval. Our three-parameter model gives, in general,
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 1, 1984 71 Table I. Molar Volumes and References for Isothermal Data system TIK VAa I. methanol t ethanol I I a methanol + 1-propanol, 2-methyl IIb. methanol + 1-propanol. - %methyl IIIa. methanol + 1-butanol, 3-methyl IIIb. methanol + 1-butanol, 3-methyl IIIc. methanol + 1-butanol, 3-methyl IV. 2-propanol, 2-methyl + 2-butanol V. 1-butanol 2-butanol a
I n cm3 mol-':
reference
VBa
333.15 323.15
42.412 41.885
61.091 95.335
Schmidt (1926) Lestera and Khrapkova (1972)
333.15
42.412
96.364
Udovenko and Frid (1948)
323.15 333.15 343.15 313.15 313.15
41.885 42.412 42.952 96.511 93.555
111.66 112.62 113.60 94.124 94.124
Udovenko and Frid (1948) Udovenko and Frid (1948) Udovenko and Frid (1948) Geiseler et al. (1973) Geiseler et al. (1973)
from Timmermans (1950, 1965).
Table 11. Coefficients of Eq 3 5 and Total Pressure Standard Deviations system C" x l o 2 c, x 102 c2x l o 2 I IIa IIb IIIa IIIb IIIc IV V
5.5372 34.673 35.346 37.403 40.094 39.975 -23.780 9.2980
-4.5113 9.4902 8.8766 10.892 9.5340 10.368 7.3741 -1.8958
3.8302 2.5777 2.5303 5.5107 3.6754 -0.6014 0.1361 -0.8501
c, x l o 2
c, x 102
2.9410 2.9591 3.1001 3.4077 2.6387 3.9969
15.265 15.176 19.332 29.669 27.385
6.3882
18.000
Table III. Values of the Parameters and Standard Deviations for Three Different Models this work UNIQUAC system
I IIa IIb IIIa IIIb IIIc IV V a
KB
ob
fJa
Au21a
0.358 0.811 0.829 1.452 2.398 1.366 0.950 0.428
-5.31 18.1 18.3 21.1 20.1 22.2 -14.6 -4.17
0.42 3.44 3.51 6.10 9.33 6.05 28.8 3.07
1756 948.9 1054 1474 1682 1668 403.3 653.3
KA 0.333 0.362 0.384 0.492 0.627 0.515 0.381 0.433
In J mol-'.
Au
-1177 11.61 -43.95 -181.8 -275.5 -245.1 -551.8 -505.6
a/ kPa
0.25 0.13 0.13 0.15 0.28 0.31 0.02 0.01
NRTL
aa
3.76 7.83 8.32 12.1 17.6 12.6 13.1 6.62
2531 -1447 -1345 -1398 -1300 -1471 -3385 1034
-1824 3019 2919 3131 3043 3323 4843 -682.5
01
Ua
0.31 0.30 0.31 0.32 0.30 0.30 0.32 0.34
3.23 8.78 9.16 13.1 18.2 13.2 4.53 6.65
In J ~ m - ~ . 300
I,-:: 1
0
0.2
0.6
0.4
0.8
,
1.0
0
0.2
EXPERIMENTAL, NRTL-UNIPUAC THIS WORK 0.4
0.6
0.8
,
1 1.0
XA
XA
Figure 3. Excess Gibbs energy for the methanol propanol system.
+ 2-methyl-l-
better results than the two-parameter UNIQUAC and three-parameter NRTL models. Figures 2 to 6 show the values of gE calculated by Barker's method (points) and the values predicted with our model (full line) and with the UNIQUAC and NRTL equations (dashed lines). It may be observed that the model derived here is able to bend the gE curve to the shape of the experimental points for low and high positive values of the excess Gibbs energy better than the UNIQUAC and NRTL models which are almost coincident in these examples. Figure 5 is one example of negative and
Figure 4. Excess Gibbs energy for the methanol + 3-methyl-l-b~tanol system.
large values of gE. This fact, together with the fact that the two components are isomers, makes this system difficult to fit by any of the three models considered here. The NRTL model seems to give the best agreement. Conclusions The ability of eq 27,28, and 29 to represent the excess Gibbs energy data of alcohol-alcohol systems has been tested with several different systems. The systems used were formed by molecules of different sizes and exhibited widely varying shapes of the excess energy curve. The model proposed in this paper was able to fit the data from
72
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 1, 1984
go = standard Gibbs energy gE = excess Gibbs energy hE = excess enthalpy
K
I
Figure 5. Excess Gibbs energy for the 2-methyl-2-propanol+ 2butanol system. loo
7 7 t i i
I
r
1
= equilibrium constant N = number of molecules P = pressure R = constant of gases T = temperature v = molar volume x = molar fraction z = coordination number cy = parameter of NRTL model fl = physical interaction parameter p’ = physical interaction parameter in the hE expression activity coefficient = partial molar Gibbs energy of mixing AG = Gibbs energy of mixing A,@ = Gibba energy of formation of one mole of hydrogen bond Agbz, Agz, = adjustable parameters in NRTL model Ah = enthalpy of formation of one mole of hydrogen bond A S = entropy of mixing A U ~ ZAuzl , = adjustable parameters in UNIQUAC model C#I = volume fraction C#I* = volume fraction in the pure component u = standard deviation
5
Subscripts 1 = monomer A = first component of the mixture B = second component of the mixture n, m,r, s = polymer of n, m,r , s monomers
p = physical contribution c = chemical contribution Literature Cited
1
2017 o
0
0
0.2
EXPERIMENTAL NRTL-UNIOUAC THIS WORK 0.4 X
0.6
0.8
1
‘t 1.0
A
Figure 6. Excess Gibbs energy for the 1-butanol + 2-butanol sys-
tem.
the various systems better than other equations widely used in the literature. Acknowledgment This work was partially funded by U.S. Department of Energy Contract No. DE-AC02-82 ER 13024. C. Pando wishes to acknowledge the Board of Foreign Scholarships and the Ministry of Education of Spain for their support through a Fulbright/MUI award. Nomenclature A, B = components of mixture C = coefficients of eq 35 G = partial molar Gibbs energy
Abrams, D. S.; Prausnitz, J. M. AIChE J . 1975, 2 1 , 116. Barker, J. A. Aust. J . Chem. 1953, 6 , 207. Flory, P. J. J . Chem. Phys. 1944, 12, 425. Francesconi, R.; Trevissoi, C. Chem. Eng. Sci. 1971, 2 6 , 1331. Geiseler, G.; Suhnell, K.; Quitzsch, K. 2.Phys. Chem. (Leipzig)1973, 254, 261. Kehiaian. H.; Treszcza, A. Bull. SOC.Chim. f r . 1969, 1561. Lee, T. W.; Greenkom. R. A.; Chao, K. C. Chem. Eng. Sci. 1973, 28, 1005. Lestera, T. M.; Khrapkova, 2. I. Zh.Flz. Khlm. 1972, 4 6 , 612. Nagata. I. Z . Phys. Chem. (Le/&) 1973. 252, 305. Nagata, I. FluM Phase Equlllb. 1977, 1 , 93. Nitta, T.; Katayama, T. Chem. Eng. Jpn. 1973, 6 , 1. Pennlngton, R. H. “Introductory Computer Methods and Numerical Analysis”, 2nd ed.; Macmlllan: London, 1970. Prausnltz, J. M.; Anderson, T.; Grens. E.; Eckert, C.; Hsleh, R.; O’Connell. T. Computer Calculatlons for Multicomponent Vapor-Liquid and Liquid-Liquid Equllbrla”; Prentlce: New York. 1980; pp 145-159. Renon, H.; Prausnltz, J. M. Chem. Eng. Scl. 1967, 2 2 , 299. Renon, H.; Prausnitz. J. M. AICM J . 1968, 14, 135. Scatchard, G. Chem. Rev. 1949, 4 4 , 7. Schmidt, G. C. Z . Phys. Chem. 1926, 121, 221. Tamir, A.; Wisniak, J. Chem. Eng. Sci. 1975, 30, 335. Timmermans, T. “Physico-Chemlcal Constants of Pure Orgenic Compounds”; Elsevier: New York, 1450; VoI. 1. Timmermans, T. “Physico-Chemlcal Constants of Pure Organic Compounds”; Elsevier: New York, 1965; Vol. 11. Udovenko, V. V.; FrM, T. S. 6. Th. Flz Khim. 1948, 2 2 , 1135.
Received far review September 7 , 1982 Revised manuscript received March I , 1983 Accepted March 25, 1983
