H. Landeck, H. Meier, W. Albrecht, U. Tschirwitz, and E. Zimmerhackl, Ber. Bunsenges. Phys. Chem., 77, 843 (1973). H. Meier, E. Zimmerhackl, W. Albrecht, and U. Tschlrwitz in “Katalyse an Phthalocyaninen”, H. Kropf and F. Steinbach, Ed., G. Thieme Verlag, Stuttgart, 1973. H. Meier, U. Tschlrwitz, E. Zimmerhackl, and W. Albrecht, BMVg-FBWr 75-6, 1975. L. Y. Johansson, J. Mrha, and R. Larsson, Electrochim. Acta, 18, 255 119731. .- . - I . \
Grluft, K. Mund, G. Richter, R. Schulte, and F. v. Sturm, Siemens Forsch. Entwicklungsber., 3, 177 (1974). G. Booth in ‘‘Chemistry of Synthetic Dyes”, Vol. 5,K. Venkataraman, Ed., Academic Press, New York, N.Y., 1971, p 271. D. Wohrle, Adv. Polym. Sci., 10, 35 (1972). A. A. Berlin and A. I. Sherle, Inorg. Macromol. Rev., 1, 235 (1971). H. Binder, A. Kohling, and G. Sandstede, Chem. Ing. Techn., 40, 543 (1968). A. Hudson and H. J. Whitfield, Inorg. Chem., 6, 1120 (1967). D. C. aenoble and H. G. Drickamer, J. Chem. phys., 55, 1626 (1971). E. Fluck in ref 21, p 37. J. Blomquist and L. C. Moberg, Phys. Scr., 9, 350 (1974). J. R. Sams and T. B. Tsin, Chem. Phys. Lett., 25, 599 (1974). T. S.Srivastava, J. L. Przyblinski, and A. Nath, Inorg. Chem., 13, 1562 (1974).
H. Wolff,
and R. Gotz
R. Larsson, J. Mrha, and J. Blomquist, Acta Chem. Scand., 26, 3386 (1972). J. W. Klein and H. Faatz, GI-T 2. Lab. H. 617, 645, 741 (1969). T. I. Zalkind, V. A. Shepelin, and V. I. Veselovskii, Sov. EleMrOchem., 2. 1066 (1966). K: Schwabe, d. Kopsei, K. Wiesener, and E. Winkier, Electrochim. Acta, 9, 413 (1964); 12, 873 (1969). K. Schwabe, Z. Phys. Chem., 226, 391 (1964). J. F. Henry and E. Gevenols, cited in ref 9. A. B. P. Lever in “Advances in Inorganic Chemistry and Radiochemistry”, Vol. 7, H. J. EmelGus and A. 0.Sharpe, Ed., Academic Press, New York, N.Y., 1965, p 89. G. Lang and W. Marshall, Proc. Phys. Soc. (London), 87, 3 (1966). J. E. Falk and J. N. Phillips in ‘Chelating Agents and Chelate Compounds”, Mellor and Dwyer, Ed., Academic Press, New York, N.Y., 1964. U. Eisner and M. J. C. Harding, J. Chem. Soc., 4089 (1964). I. Madi, Ber. Bunsenges. Phys. Chem., 68,601 (1964); Inorg. Nucl. Chem. Lett., 9, 767 (1973). I. Madi and A. Boly6s, Radiochem. Radioanal. Lett., 20, 215 (1975). H. Meier, “Organic semiconductor: Dark- and photoconductivity in organic solas’ , Verhg Chemie, Weinheim, Bergstrasse, 1974, p 455. H. Meier, U. Tschirwitz, E. Zimmerhackl, and W. Albrecht, Ger. Offenlegungsschrift, submitted for publication.
Two-Constant Model to Describe Amine and Alcohol Association from Vapor Pressure Measurements Heiner Landeck, Hans Wolff,” and Ralner Gotz Physikalisch-chemisches Institut, Universitat h‘eidelberg, 69 Heidelberg, Federal Republic of Germany (Received July 1, 1976: Revised Manuscript Received January 18, 1977) Publication costs assisted by Fonds der Chemie, Frankfurt
Equations are developed to describe the association of the most simple aliphatic amines and alcohols in saturated hydrocarbons from vapor pressure measurements by means of a two-constant model. The equations permit the calculation of the dimerization constant K2 and of the constant K3 for formation of higher polymers direct from the constants of the equations for the representation of the activity coefficients. The expression for Kz agrees with that for the dimerization constant of the model allowing for differences between the constants for the higher equilibria, while the expression for K3 differs from the trimerization constant of this model. The numerical values of constants K2 and K3 and of the corresponding association energies prove the alcohols to be more strongly associated than the amines. The dimerization energy and the energy for the formation of higher polymers are nearly the same, 2-3 kcal/mol for the amines and 5 kcal/mol for the alcohols. This result and the observation of only one NH stretching vibration for the hydrogen-bonded species suggest the presence of only one kind of hydrogen bonds, probably of linear bonds, in the amines. The observation of two OH stretching vibrations, on the other hand, suggests the presence of two kinds of hydrogen bonds in the alcohols. The determination of the same energy value for dimer and polymer formation does not exclude the description of these bonds as the bonds of cyclic dimers and linear higher polymers, as suggested by previous authors. However, due to the complications of the alcohol association as well as to the inherent simplifications of the model the calculated energies may not be related to the bonds in a simple manner. From K2 and K3 the activity coefficients and the excess free energy can be recalculated. The comparison of the obtained values with the conventionally calculated values proves that the amines and the short chain alcohols fit the two-constant model within a wide range of concentrations, while this is not the case with long chain alcohols.
A. Introduction The association of simple aliphatic amines and alcohols in n-hexane and other saturated hydrocarbons has been described in vapor pressure by the chemical theory of solution nonideality, i.e., by the theory of ideal associated solution^.^-^ The assumption that the successive equilibria Ai-l + AI F? Ai (i = 2, 3, etc.) exist in the solutions and that all constants of these equilibria are different,”’ is the most general form of this approach. However, considering the solutions in a wider range of concentrations, it is difficult to determine the constants of the equilibria with i > 3 with sufficient accuracy. The Journal of Physical Chemlstry, Vol. 8 1 , No. 6, 1977
Therefore, it is of interest to examine whether a description may be possible where only the dimerization constant is assumed to be different, the other constants being equal. Such a model has already been used by Van Ness et ala4 to describe the association of ethanol in n-heptane. They determined K2 and K 3 by varying the initial values until accordance was reached with experimental values of the excess free energy and the heat of mixing.
B. Determination of the Association Constants 1. Dimerization Constant. In the following derivation the calculation of the association constants starts from the
Two-Constant Model for Amine-Alcohol Association
719
assumption that the analytical mole fraction xA of the amine or alcohol, the activity coefficient yB of the hydrocarbon, and the true mole fractions x1 of the amine or alcohol monomers, x 2 of the dimers, etc., are related by
+ 2x2 + 3x3 + 4x4 + . . . = XAYB
(1) (cf. eq 8 in ref 2a; cf. also ref l a and 3). If x 2 , x3, etc., are replaced by means of the relations for the equilibrium constants, i.e., by Kl,z= x Z / x l 2 ,K2,3 = x 3 / x 2 x 1 ,etc., eq 1 can be formulated as XI
xi
2K1,2Xi2+ 3Ki,zKz,3Xi3 i4Ki,zKz,3K3,4Xi4t
a
. = XAYB
(2)
Assuming the two-constant model, where Kz is the dimerization constant and K3the constant for the formation of higher polymers, the following equation results
x1 + 2K2x12+ 3KzK3xI3 f 4K2K3'Xi4 f . . .=XA')'B
(AABand ABA = constants) results in2a
Kz = 2 - AAB - AABABA~ 2AAB
2. Constant for the Formation of Higher Polymers. The association constant K3cannot be determined in the same way as constant K2,3. It is derived from the concept that in addition to eq 1 and 2 the relation XI
+ x2 ix3 + x4 + . . = zxi
= XAYBPI (4) (pl denotes the fraction of the associating component present as monomers), K z results in accordance with the expression for K1,21a'2a XI
(5) Furthermore, the same expressions result if YA and YB are replaced by the equations used for their representation, simultaneously applying the r e l a t i ~ n ~ " , ~ ~ ~ ~
(11)
a
is valid. After replacement of xz,x3, etc., by the equilibrium constants and by equating all higher constants, the following relation results:
x1 + K2x12+ KzK3x13+ K2K3'x14+
. . . = Xxi (12)
Considering K3x1< 1, summation of the terms KZK3xl3, etc., yields
(3)
Using the model which allows differences between the higher constants, the dimerization constant Kl,z is obtained, if for a sufficiently high dilution the terms containing x13,x14, . . ., are neglected. The trimerization constant follows by omission of the terms containing x14, x15,. . ., etc.'" This procedure may also be applied for the determination of K z from eq 3. The terms in which eq 2 and 3 differ are omitted. Therefore, after considering'"
(10)
(13)
Cxi = 1for the undiluted amine or alcohol. Denoting the true mole fractions of the monomers in the undiluted state as xl,o and regarding the association constants as independent from the concentration, the expression (14) follows. Solving for K 3 yields
To calculate K 3 from this expression, xl,o has to be determined. The solution can be considered as a nonideal binary system of the macroscopic components as well as an ideal multicomponent system of the solvent and of the various forms of the associating c~mponent.~ Viewing the mixture as a nonideal binary system, the chemical potentials of the components can be expressed by
where
x g = nB 'A
'
nB
indicate the moles of the amine or alcohol and of the solvent. Regarding the mixture as an ideal multicomponent system, the expressions are pi =pie
+ RT1nxi
PB(l)= PB(l)e
+ RT In
( i = 1,2 , . . .) 'B(1)
(18a) (18b)
where
The Journal of Physical Chemistry, Vol. 81, No. 8 , 1977
720
H.
bandeck, H. Wolff, and
R. Gotz
denote the true mole fractions of the various forms of the associating component and of the solvent, re~pectively.'~'~ and, after considering the definitions (17b) and (19b), as From the eq 16a and 16b the free energy of 1mol of the mixture and the free energy of the components before Y B = (1 - x x j ) / ( l .- x A ) (33) mixing can be expressed as Inserting this expression in (31) and considering addi1 = xA(pAo + In [TAXA] XB(P< + tionally eq 14, there results' RT In [YE$B]) (20) X 1 3 ( K s 2 - K 2 K 3 )- x12(2[K3- K21 t xA[K3' K J )
+ Xi( 1 + ~ K ~ X-AXA) = 0
and G2 = xAPAO
+X~P
