Journal of Solution Chemistry, Vol. 25, No. 7, 1996
Thermodynamics of Complex Formation in Chloroform-Oxygenated Solvent Mixtures Vladimir D o h n a l 1 and Miguel Costas 2'* Received January 4, 1996; revised April 16, 1996 Complex formation equilibria in binary mixtures of chloroform with dipropyl ether (PE), diisopropyl ether (IPE), methyl tert-butyl ether (MBE), tetrahydrofuran (THF), 1,4-dioxane (DOX), acetone (AC), and methyl acetate (MA) have been analyzed in detail using several association models. Vapor-liquid equilibria, excess enthalpy and excess heat capacity data for these mixtures have been correlated using a multiproperty global fitting procedure. The thermodynamic properties for chloroform + PE, + IPE, + MBE, + AC, and + MA are best correlated using the ideal association model while for chloroform + THF and + DOX the best model is an athermal solvation model where the Flory-Huggins expression for the species activity coefficients is considered. The model parameters, i.e., the equilibrium constant, enthalpies and heat capacities of complexation, were found to be reliable, well representing the chloroform-oxygenated solvent H-bonded complexes. A detailed discussion is given on the test proposed by McGlashan and Rastogi to decide whether the solution contains only 1:1 complexes or 2:1 complexes as well The complex formation equilibria in chloroform mixtures is compared to those previously examined for halothane (2-bromo-2chloro-l,l,l-trifluoroethane) mixed with the same oxygenated solvents. It was found that the H-bonds formed by halothane are stronger than those formed by chloroform.
KEY WORDS: Chloroform; oxygenated solvents; hydrogen bonding; complex
formation equilibria; association models.
Department of Physical Chemistry, Institute of Chemical Technology, 166 28 Prague 6, Czech Republic (e-mail:
[email protected]). 2Laboratorio de Termofisica, Departamento de Fisica y Quimica Teorica, Facultad de Quimica, Universidad Nacional Autonoma de Mexico, Cd Universitaria, Mexico D.E 04510, Mexico (e-mail: miguel@ mizton.pquim.unam.mx). 635 0095-9782/96/0700-0635509.50/09 1996PlenumPublishingCorporation
636
Dohnal and Costas
1. INTRODUCTION The acidic hydrogen atom in chloroform can readily form complexes,
via H-bonding, with the oxygen atoms of the solvent molecules. Hence, these mixtures are an interesting set of systems where complex formation equilibria can be studied. Several studies 0-9~ have been devoted to characterize and understand chloroform + oxygenated solvents mixtures. As a result, considerable experience has been gained regarding the behavior of the thermodynamic properties in these systems and the application of chemical equilibria models to these data. However, it has been a common practice in the literature to fit the association models parameters (equilibrium constants, enthalpies of complexation etc.) to one or two experimentally determined thermodynamic quantities, vapor-liquid equilibria (VLE), and excess enthalpies HE being the most common set of properties used. In going from one system to another, the application of association models differs not only in the fitting procedure employed but also in the size of the property set available. As a consequence, for a given oxygenated solvent or a series of them, it is often difficult to compare both the performance of different models and the values of their parameters with the concomitant difficulty in interpreting on physical terms the behavior of the solution. In an effort to introduce a more articulate and systematic methodology to analyze complex formation equilibria via H-bonding in binary non-electrolyte mixtures, we have recently presented ~176~ a detailed study of eight 2-bromo2-chloro- 1,1,1-trifluoroethane or halothane + oxygenated solvent mixtures, i.e., using another halogenoalkane which, as chloroform, has a single acidic hydrogen atom. In this work, we present an analogous thermodynamic study for chloroform + oxygenated solvent mixtures using thermodynamic data measured at our laboratories and reported elsewhere, ~ as well as data from the literature. The seven mixtures studied here are: chloroform + dipropyl ether (PE), + diisopropyl ether (IPE), + tert-butyl methyl ether (methyl tert-butyl ether or MBE), oxolane (tetrahydrofuran or THF), + 1,4-dioxane (DOX), + 2-propanone (acetone or AC), and + methyl ethanoate (methyl acetate or MA). The main differences between the analysis we present here and those in the literature can be summarized as follows: (i) the use of data, for all oxygenated solvents, for large set of properties viz. VLE, HE and excess heat capacities C~ and (ii) the employment of a multiproperty, well defined and statistically sound, global fitting procedure. Since the size of the property set available and the fitting procedure are identical for all chloroform mixtures studied here and for those studied by Dohnal, Costas and coworkers, ~176t) it is possible to compare the seven chloroform + oxygenated solvent mixtures amongst themselves and against the corresponding halothane mixtures, and hence discuss their thermodynamic behaviour on entirely the same basis.
Chloroform-Oxygenated Solvent Mixtures
637
2. ASSOCIATION MODELS AND FITTING PROCEDURE Four simple association models have been used in this work: (1) an ideal association model where it is considered that only a 1:1 complex is present in solution (AB model), (2) an athermal solvation model considering only 1:1 complexes and the Flory-Huggins (FH) expression for the activity coefficients of the species involved (ABP model), (3) an ideal association model where 1:1 and 2:1 complexes are taken into account (A2B model) and (4) an athermal solvation model with 1:1 and 2:1 complexes and the FH activity coefficients equation (A2BP model). For the athermal models the size (volume) parameters for the monomeric species were taken equal to unity. The expressions for the thermodynamic quantities corresponding to these four models have been given in an Appendix by Dohnal et al. d~ It should be emphasized that the passage from an ideal to an athermal model (AB to ABP or A2B to A2BP) does not imply the introduction of any new adjustable parameters. The simultaneous fitting of VLE, HE and Cp~ data was performed using the maximum likelihood procedure with the objective function
S = ~ {[~xi/s(x)]22r- [~yi]s(y)]2+ [~Pi/s(p)]2+ [~Ti/s(T)]2} i=l
1
+ ~ {[~H[/s(I-~i)] 2 + [~x~/s(xH)] 2 }
(1)
i=l
+
+ [axF/s(xC)] i=l
where ~X is the difference between experimental and calculated values of the quantity X. Equation (1) holds for those cases where VLE data is available as a complete PTxy set; for those cases where instead an incomplete PTx VLE data set is available the vapor-phase composition term is, of course, omitted. Weighting factors for the optimization were based on experimental uncertainties which were either reported together with the data in the original literature or estimated by us. The estimates of experimental uncertainties are listed in Table I along with the literature references and additional characteristics of the thermodynamic data treated in this study. For some of the mixtures, it is possible to find in the literature more than one reference for a given property. In these cases, we selected the data to be processed in this work giving preference to accurate and numerous measurements at temperatures near the ambient. The quality of the fitting was judged by the standard deviation of fit or, cr = [S/(kn + 1 + m - p)]l/2
(2)
where k = 1 or 2 for P T x or PTxy data respectively, and p is the number of
638
Table I.
CHC13+
Dohnal and Costas
Source and Characteristics of the Experimental VLE, H E and C~ Data Used in this Work PE
IPE
MBE
THF
DOX
AC
MA
Ref. Data Type T/K na s(x) s(y) s(P)/Pa s(T)/K
21 PTx 298.15 13 0.0005 -25 0.02
2 PTxy 308.15b 18 0,001 0.001 50 0.05
VLE 22 23 1 24 4 PTxy PTx PTxy PTx PTxy 313.15 303.15 323.15 313.15/323.15 313.15 30 21 11 30c 16 0 . 0 0 0 5 0.0005 0.0005 0.0005 0.001 0.0005 -0.001 -0.001 10 50 25 40 13 0.01 0.001 0.02 0.02 0.05
Ref. T/K la s(xH) S(14E)/1-1z
25 298.15 39 0.0005 0.005
HE 25 12 26 27 298.15 298.15 303.15 303.15 39 20 33 27 0 . 0 0 0 5 0 . 0 0 1 0 . 0 0 0 5 0.0005 0.005 0.02 0.005 0.005
Ref. T/K rna s(xc) s(C~)IC~
12 298.15 9 0.001 0.02
12 12 12 12 298.15 298.15 298.15 298.15 9 9 9 9 0.001 0.001 0.001 0.001 0.02 0.02 0.02 0.02
28 298.15 38 0.0005 0.007
4 308.15 17 0.001 0.005
12 298.15 9 0.001 0.02
12 298.15 9 0.001 0.02
c~
aNumber of experimental points. bAverage temperature for isobaric data at 32.80 kPa. c15 points at 313.15 K and 15 points at 323.15 K. adjustable parameters involved in the fitting. By definition, ~r is a d i m e n sionless quantity which approaches unity if the data are fitted within the stated experimental inaccuracies. To optimize the objective function S an algorithm analogous to the procedure of Rod and Hancil (13~ was employed. Lagrange multipliers were used to account for the model constraints and the N e w t o n - R a p h s o n technique was applied to search iteratively, in separate loops, for optimal values of the model parameters and the u n k n o w n true values of the variables in the individual data points. Details c o n c e r n i n g the vapor-liquid equilibrium calculations have been described previously. (~4~The vapor-phase nonideality was accounted for by the virial equation of state, the second virial coefficients being calculated by the H a y d e n - O ' C o n n e l l method. (15~ Since the solvation parameters "q~j were not available to calculate the second cross virial coefficients for chloroform + PE, + IPE, and + MBE, we estimated them considering the results ~16~ for chloroform + DOX, and + T H F for which we found ~ 2 = 2B~2 - B91 - B22 ----- - 1 2 5 0 cm3-mol - l
Chloroform-Oxygenated Solvent Mixtures
639
at 25~ Thus, keeping the same 812 value, the values of Xhj for the other ether systems were estimated as follows: chloroform + PE 0.85, + IPE 0.80, and + MBE 0.85.
3. RESULTS AND DISCUSSION 3.1. Application of the Association Models For the seven chloroform + oxygenated solvent mixtures studied here, the four association models have been tested using the data whose sources are given in Table I. We followed two main criteria to decide which model describes better the experimental data, namely the magnitudes of the standard deviation of fit ~ in Eq. (1) and the standard deviations of the model parameters. An additional and very important requirement is that the thermodynamic parameters obtained from these models are physically meaningful. Our previous experience with halothane + oxygenated solvents~~ indicates that for single-oxygen atom ethers the solution contains only 1:1 complexes while for ethers that have two oxygen atoms and also for AC and MA, 2:1 complexes are also present. In fact, we foundC1~ that there is a clear correspondence between the polar areas of the oxygenated solvents and the stoichiometry of the complexes present in solution; this can be understood at the molecular level as a consequence of the solvent's polar surface area which interacts strongly with the acidic hydrogen atom of halothane or, in the present case, chloroform. Hence, although all four models were tested for each chloroform + oxygenated solvent mixture, in Fig. 1 we only display the standard deviations of fit cr that comply with this stoichiometry; the results for the models not shown in Fig. 1 will be commented in the text.
8
~0.
