Thermodynamic Investigation of Complex Formation
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Thermodynamic Investigation of Complex Formation by Hydrogen Bonding in Binary Liquid Systems. Chloroform with Triethylamine, Dimethyl Sulfoxide, and Acetone Takeki MatsuimiaLoren G. Hepler,lb
* and David V. Fenbyic
Departments of Chemistry. University of Lethbridge, Lethbridge, Alberta. Canada, and University of Otago. Dunedin, New Zealand (Received May 27. 1973)
Calorimetric measurements have led to partial molar enthalpies of solution at infinite dilution and a t stoichiometric mole fraction 0.5 in binary mixtures of chloroform with triethylamine, dimethyl sulfoxide, and acetone. We have derived and used thermodynamic equations that relate these partial molar enthalpies of solution to equilibrium constants and enthalpies of formation of AB and AB2 complexes. Several procedures for obtaining molar enthalpies of complex formation are compared.
Introduction Complex formation equilibria in dilute nonelectrolyte solutions have been investigated by various spectroscopic methods and also by such classical thermodynamic methods as distribution between immiscible solvents and measurements of colligative properties. There are many equilibrium constants that have been determined by way of one or more of these methods. But very few such equilibrium constants, particularly for weak complexes, have been determined with sufficient accuracy to permit useful evaluation of the molar enthalpy of complex formation by means of AH” = R p ( In KlaT),. Partly because of the difficulty of obtaining accurate UT and AS’ values from equilibrium (constants a t different temperatures, there have been several calorimetric investigations of complex formation. Most of these investigations have been conB = AB in some more cerned with reactions of type A or less “inert” solvent. Similar investigations of this kind of reaction in binary mixtures of A and B over the entire range of composition from pure A to pure B are much less common. In this paper we describe some calorimetric methods for investigation of complex formation (AB and ABz) in such binary mixtures and apply these methods t o mixtures of chloroform with triethylamine, dimethyl sulfoxide, and acetone. Many years ago Dolezalekz and his followers tried to account for all deviations from ideal solution behavior in terms of chemical equilibria. This approach was soon shown to be chemically unrealistic and numerically inadequate for many systems. But many subsequent investigations of nonellxtrolyte liquid mixtures have provided compelling evidence for various complexes. For those systems in which complex formation takes place, it is often convenient to divide the deviation from ideal solution behavior into “physical” and “chemical” contributions, with the latter being due to the complex formation. The “physical” contribution can be considered to be negligible compared to the “chemical” contribution in certain systems so that it is appropria3te to attribute all deviations from ideality to the chemical reactions. The chemical species present (noncomplexed molecules and complexes) are thus assumed to mix ideally and we have what has been called the “ideal associated solution” model. In a previous paper3a we have shown how it is possible to analyze integral molar enthalpies of mixing (AH,) for
+
binary mixtures in terms of the equilibrium constant ( K 1 ) and the molar enthalpy of reaction (AH1”) for the complex formation represented by
A
+ B = AB
This method of analysis was applied t o triethylamine (A) plus chloroform (B). We have also applied3b the related McGlashan-Rastogi4 method of analysis (requires vapor pressures for evaluation of equilibrium constants and enthalpies of mixing for evaluation of molar enthalpies of complex formation) t o dimethyl sulfoxide (A) plus chloroform (B) in which there are AB and AB2 complexes so that values of K2 and AH2’ for the reaction represented by A 2B = AB, (2)
+
are obtained along with K1 and AH1”. Here we report on our use of differential or partial molar enthalpies of solution ( E ) in connection with investigation of reactions represented by eq 1 and 2 in mixtures of chloroform with triethylamine. dimethyl sulfoxide, and acetone. Our analysis is directly related to earlier attempts5,E to relate calorimetric results to enthalpies of hydrogen bond formation in these and similar systems.
Experimental Section Enthalpies of solution have been measured by the ampoule method with an LKB precision reaction calorimetry system. Ampoules containing about 10-3 mol of a pure liquid were broken in calorimetric vessels containing 100 ml of another pure liquid or 100 ml of a solution with stoichiometric mole fraction x = 0.500 f 0.002. Thus the observed enthalpies of solution (with corrections for vapor space in the ampoules) are very close t o the desired differential or partial molar enthalpies of solution ( L ) . All results refer to 298.15 f 0.05”K. Chloroform (Spectroanalyzed, Fisher Scientific Co.) was washed several times with distilled water. dried over fused CaC12, and then fractionally distilled. The middle fraction was dried over PzO5 and then fractionally distilled in an atmosphere of dried Nz. The resulting middle fraction was stored in an atmosphere of Sz in the dark. Even with these precautions, it was found that calorimetric measurements made with chloroform that had been stored more than 2 days sometimes yielded erratic results. The Journai of Physical Chemistry. Voi. 77. No. 20. 1973
T. Matsui, L. G . Hepler, and D. V. Fenby
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Triethylamine (BDH Laboratory Reagent) was refluxed over KOH pellets, distilled from KOH, and then dried over CaH2. The middle fraction was again fractionally distilled at about 100 mm pressure in an atmosphere of
Nz. Dimethyl sulfoxide (Baker Analyzed Reagent) was dried with Type 4A molecular sieve for at least 1 week and then distilled at reduced pressure ( t < 50") in an atmosphere of Nz. The middle fraction was again treated with the molecular sieve and then distilled as above before being stored in a desiccator in the dark. Acetone (Analar grade) was dried by prolonged contact with molecular sieve and then twice fractionally distilled. Results Our experimental results are summarized in Table I. All reported partial molar enthalpies of solution ( E ) are based on at least four separate calorimetric measurements. In the next section of this paper we are concerned with interpretation of these results in terms of the reactions represented by eq 1 and 2. In this section we compare our experimental results with those we calculate from A H , values reported by other investigators. Molar enthalpies of mixing (AH,) may be calculated from partial molar enthalpies of solution ( E ) by means of
AH,
= X.kz~
+
(3)
X B ~ B
in which x.4 and X B represent stoichiometric mole fractions in the final solution formed from the pure components. Using this equation with our values for triethylamine plus chloroform a t x = 0.5, we calculate AH, = -4.08 kJ mol-l, in excellent agreement with AH, = -4.07 kJ mol-1 reported previously2b on the basis of integral molar enthalpies of mixing measured with an entirely different calorimeter. A similar calculation with our present results for acetone plus chloroform at x = 0.5 gives AH, = -1.845 kJ mol-1, in satisfactory agreement with AHm = -1.85 kJ mol-1 and AH, = -1.92 kJ mol-1 interpolated from the integral molar enthalpies of mixing reported by Campbell and Kartzmark? and by Morcom and Travers.8 Calculation of partial molar enthalpies of solution a t infinite dilution (Eo)from integral molar enthalpies of mixing necessarily involves some sort of differentiation and/or extrapolation. Even using the "best" methodg.lo of data treatment, partial molar enthalpies of solution at infinite
e
TABLE I:
Partial Molar Enthalpies of Solution at 298°K
dilution derived from AH, results that typically cover the composition range x N 0.1 to x N 0.9 have considerably larger uncertainties than do the presently reported E o values that are based on measurements on solutions with x 2 10-3. Following Van Kess and Mrazek,9JO we have constructed graphs of A H m / X A X B us. XA and X B to obtain values from the extrapolated intercepts. These graphs were based on AH, values from our previous investigationZb of triethylamine plus chloroform, on A H , values from Fenby, Billing, and Smythell for dimethyl sulfoxide plus chloroform, and on A H , values from Campbell and Kartzmark? for acetone plus chloroform. (The A H , results for acetone plus chloroform from Morcom and Travers8 do not extend close enough to x = 0 to permit evaluation of Eo.)The results of these graphical evaluations of Eo,given in parentheses in Table I, are in satisfactory agreement with the considerably more accurate Lo values based on our enthalpies of solution in very dilute solution.
e'
Evaluation of the Molar Enthalpy of Complex Formation (AB Complexes) Several earlier workers (see, for example, ref 5 and 6) have implicitly assumed or explicitly stated that partial molar enthalpies of solution at infinite dilution (E') can be related directly to formation of 1 mol of hydrogen bonds. We now consider this matter in relation to our analysis of Eo values in terms of chemical reactions such as those represented by eq 1and 2. At first we restrict our attention to systems in which only AB complexes are formed, as represented by eq 1. The (mole fraction) equilibrium constant for this reaction may be written (all activity coefficients are unity in the "ideal associated solution" model)
KI
-
- 12.68 -5.06
(-5.0)'
( C H 3 ) & 0 in HCC13 HCC13 in D M S O D M S O in HCC13
-8.24
(-8.7)a
-5.68
(-5.g)a (-14)'
-11.55
-13.1
(-1 2 . 7 ) a ( - 1 1. l ) a
Lo.s.kJ mol-' HCC13 in HCC13-Et3N ( x = 0.5) Et3N in HCClS-EtsN ( x = 0.5) (CH3)zCO in HCC13-(CHs)zCO ( x = 0.5) HCC13 in HCC13-(CH3)2C0 ( x = 0.5)
-3.950 -4.217 -1.18
-2.51
a All values In parentheses have been derived graphically from previously reported AH, values and have considerably greater uncertainties than do the values based on measurements with very dilute solutions.
The Journal of Physical Chemistry, Vol. 77, N o . 20. 1973
(4)
+ nAd
=
-
KJ(1
+ KJ
(5)
+
Taking A B to be an "ideal associated solution" in which all enthalpy changes are due t o the reaction represented by eq 1, we have L B O = KlAHl"(1 + K I ) and hence
AH:
HCC13 in Et3N Et3N in HCC13 HCC13 in (CH3)zCO
ndZn,)/nm
-
nkB/(nH
L, kJ mol-'
"Solute" in "solvent"
=
in which n4, ng, and TZAB represent the numbers of moles of each species a t equilibrium and ( Z n , ) represents the total number of moles of all species in the solution at equilibrium. In the limit of infinitely dilute solution of B 0 and (Zn,) nA so that K1 nAB/nB. in A, ne/nA The fraction of B that is complexed is therefore
= LB"(1
+ KI)/K,
(6)
in which L B O represents the partial molar enthalpy of SOlution of B (at infinite dilution) in A. Because the system A B is symmetrical when AB is the only complex, we also have
+
AH:
=
z,ko(l4-K , ) / K ,
(7)
in which EA" represents the partial molar enthalpy of solution of A (at infinite dilution) in B. Our eq 6 and 7 show that it is proper to take Lo s AHl" only when K1 >> 1. Since reported K1 values (cited below) for the three systems under consideration in this paper range from 0.97 to 4.7 at 298"K, the factor (1 K1)/KI ranges from 2.0 to 1.2 and cannot properly be approximated by unity. To make use of our L A o and E B " values (Table I) in eq 6 and 7 we must have an independently determined value of K1. The nmr measurements of Huggins, Pimentel, and Shooleryl2 on triethylamine plus chloroform led them to
+
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Thermodynamic investigation of Complex Formation report K1 = 3.0 f 1.0. Subsequent nmr measurements on triethylamine plus chloroform in cyclohexane as solvent led Creswell and Allredl3 to report K1 = 4.20. The nmr investigation of the same system by Howard, Jumper, and Emerson14 led to a reported K1 = 4.70 & 0.12. They14 also quote K1 = 4 f 1 from Martin's nmr investigation of triethylamine plus chloroform. On the basis of these results (all for 298'10, we take 3 < K1 < 4.7. Thus we calculate (using an average of LAoand L B O ) a range of AHi0 from -16.2 to -14.7 kJ mol-1. We adopt AH1" = -15.4 kJ mol-1 as the best value to be obtained by this method. It is also possible to use our partial molar enthalpies of solution in solutions with stoichiometric mole fraction x = 0.5 ( L o . 5 ) t o obtain AH1" as follows. In our earlier investigation3a of complexing in triethylamine plus chloroform we derived and used the equation
xAxB/AH~:= -[(Ki
+ l)/Kl(AH1')~]AHm~+ (K1
W e also hav'e
AHm = AH/(Na
+ l)/KiAHio
+ NB)
(8) (9)
TABLE II: Comparison of Plus Chloroform
=
NANB/(NA+ NE?
[(K,
+ l)A11*/Kl(AHi0)*I[ ( K , + l)AH(N.4 + NB)/KIAH;I +
NANB = 0
(11)
Solving this quadratic equation for AH and then differentiating as indicated by ( ~ A H / ~ N A ) Ngives ~ , T a, ~complicated general expression for E A , which concerns us only in two special cases, In the limit of small N A that corresponds to infinitely dilute A in B, we obtain eq 7 as previously derived in a simpler way. At X A = 0.5 = X B we obtain
AHl' = 2z,.j/[l
in which Z0.5 lution of a pure component into solution with stoichiometric mole fraction x = 0.5. Because of the symmetry of the system under consideration, eq 12 applies to 10.5 values for both A and B. On the basis of an average of our Eo.5 values for triethylamine plus chloroform and 3 < K1 < 4.7 as above, we find from eq :12 AH1" between -16.3 and -14.2 kJ mol-1. We chose AH;" = -15.2 kJ mol-l as the best value to be obtained by this method. We may also solve (analytically or graphically) the simultaneous equations 6 or 7 and 12 for both K1 and AH1" in terms of E o and L 0 . 5 . Using our partial molar enthalpies for the triethylamine plus chloroform system in this way, we calculate K1 = 3.3 and AH1" = -15.8 kJ mol-;. All of our results for triethylamine plus chloroform as described abo've are summarized in Table 11, along with results of some earlier investigations of this system. I t may be that the overall "best" AH1" value will be obtained by cornbination of calorimetric results with a K1 derived spectroscopically. But it should be noted that our treatment of E" and L0.5 values in the combination of eq 6, 7, and 12 leads to AH1" and K1 values that are within the ranges of values obtained in other ways.
-15.8 (and K1 = 3.3) - 14.2 (and K 1 = 4.7) -17ab
- 1 7ac
a Based on A H , " , = RT2 (d In K , / d T ) , . K 1 values at only two temperatures. Based on triethylamine plus chloroform in cyclohexane as solvent. Reference 3a.
Evaluation of Molar Enthalpies of Complex Formation (AB and AB2 Complexes) Consider partial molar enthalpies of solution at infinite dilution for binary systems in which both AB and AB2 complexes may form as represented by eq 1 and 2. In this case we have
KJKi
=
~ A B ~ @ ~ J / ~ . A B(13) ~B
-
In the limit of infinitely dilute B in A, (hi)nA so that eq 13 becomes
nAB2/nAB = KznBIK1n.t
nB/nA
-
0 and
0
(14) Because eq 14 shows that only A, B, and AB need be considered in the limit of infinitely dilute B in A, we have eq 6 applicable to solutions of the type now under consideration as well as to the solutions considered in the preceding section. It is not correct to interpret the infinite dilution partial molar enthalpy of solution of A in B in terms of complete conversion of A to AB2. Rather, it is necessary to consider fractional conversion of A to both AB and AB2 as in
Lo= fABAH1'
=
fAB2AHZ0
(15)
+ n.4B2)
(16)
in which
- (1 + KJ1"]
(12) represents the partial molar enthalpy of so-
- 15.4 - 15.2
Present work, eq 6, 7 Present work, eq 1 2 Present work, eq 6, 7 , 12 Previous calorimetryd ( A H m ) Reference 1 2 Reference 13
(10)
in which AH:, represents the molar enthalpy of mixing, AH represents the enthalpy of mixing of N A moles of A with N B moles of B, and X A and X B are stoichiometric mole fractions. Combination of eq 8-10 gives
AHl". kJ mol-'
Source
and XAXB
AH," Values for Triethylamine
fAB
= nAB/(nA
f nAB
fAB2
= nAB*/(nA
and
-
+ n4B + n.AB1)
In the limit of infinitely dilute A in B, ( Z n i ) n B . We therefore have fAB
nA/nB
-
(17) 0 and
K I / ( ~+ KI Kz)
(18)
+ K1 + K,)
(19)
and JAB2 =
K2/(1
Substitution of eq 18 and 19 in 15 gives
AH2' =
[ZA'(l
+ K l + KL)/K1]- [KIAH,"/KJ
(20)
Further substitution of eq 6 in 20 gives
AH;
=
+
[zAo(l K 1
+ KJIK,]
- [EBo(K,+ 1)/K2]
(21) For the system dimethyl sulfoxide (A) plus chloroform (B) we take K1 = 1.2 and Kz = 4.5 from our analysissb of the vapor pressures reported by Philippe, Jose, and Clechet.15 Use of this K1 with our L B O = -5.68 kJ mol-; from Table I in eq 6 gives AHl' = -10.4 kJ mol-1 as compared to AH1" = -11 kJ mol-1 found previously3b by way of a McGlashan-Rastogi4 analysis. Use of the above The Journal of Physical Chemistry, Vol. 77, No. 20. 1973
2400
K1, Kz, and L B O with LAo= -13.1 kJ mol-1 from Table I in eq 21 leads to AHz" = -16.7 kJ mol-1 as compared to the previously found3b AHz" = - 16 kJ mol-l. For the system acetone plus chloroform we take K1 = 0.967 and K Z = 1.117 from analysis of vapor pressures by Kearns.16 Use of these values with our EAoand L g 0 values for this system from Table I in eq 6 and 21 leads to AHi" = -10.3 kJ mol-1 and AHz" = -13.0 kJ mol-1. Morcom and Trave& have reported AHl' = -10.3 kJ mol-1 and AHz" = -13.0 kJ mol-1 on the basis of their McGlashanRastogi4 analysis. Discussion In the "ideal associated solution" approach used in this paper it is assumed that the chemical species (A, B, AB, A B 2 ) mix ideally; i.e., deviations from ideal solution behavior are attributed entirely to the chemical reactions represented by eq 1 and 2 . The activity coefficients of all chemical species are therefore taken to be unity, and all enthalpies of solution and mixing are attributed to chemical reactions represented by eq 1 and 2. This approximation is expected to be reasonable only for those systems in which the "physical" interaction is negligible compared with the "chemical" interaction. This requirement suggests that - A H , should be greater than about 1.5 kJ mol-1 at x = 0.5 and that -Eo should be greater than about 3 kJ mol-l. It is to be emphasized that this "ideal associated solution" assumption is not peculiar to calorimetric methods. In application of other methods (spectroscopy, vapor pressures, etc.) it has been necessary (and reasonable) to attribute all of some observed property to specific chemical species (AB, ABz, etc.) in solution and to take all activity coefficients to be unity. When this kind of treatment with activity coefficients taken equal to unity is carried out at more than one temperature, it follows that all enthalpies of mixing and solution are attributed to the chemical reactions represented by eq 1 and 2 . Because the methods we have described in this paper and also the other methods mentioned that lead to equilibrium constants at different temperatures are based on the same "ideal associated solution" model, we cannot say that any one method is fundamentally better than any of the others. We can, however, offer some generalizations about advantages, disadvantages, and limitations of the various approaches. For systems in which there are only AB complexes, we have shown here and earliersa that calorimetric measurements can lead to reasonable values of both K1 and AH1". Other methods, such as spectroscopy, can lead to Ki
The Journal of Physical Chemistry, Vol. 77, No. 20, 1973
T. Matsui, L. G. Hepler,
and D. V. Fenby
values at several temperatures and thence to AH1" from
R P ( a In KlIaT),. It is reasonable to expect, however, that the best approach is one in which K1 from some noncalorimetric method is combined with calorimetric results to yield AH1". For systems in which there are AB and AB2 complexes, noncalorimetric methods can lead to values of K1 and Kz a t several temperatures and thence to values of AH1" and AHz0. But the difficulties associated with simultaneous evaluation of both K1 and Kz are such that it is reasonable to expect that there will be substantial uncertainties associated with the derived AH1" and AHz" values. Although it is possible in principle to evaluate all four reaction parameters (K1, Kz, AH1', and AHzo) from AH, values that cover a substantial range of composition or from values a t a suitable number of mole fractions. it is unreasonably optimistic to expect one set of enthalpy values to lead to accurate and unequivocal determination of all of these parameters. It is again reasonable to expect the best approach to be one in which K1 and Kz from some noncalorimetric measurements are combined with calorimetric results for evaluation of AH1" and AHz".
Acknowledgments. Acknowledgment is made t o the donors of The Petroleum Research Fund, administered by the American Chemical Society, and to the National Research Council of Canada for support of part of this research. References and Notes (a) University of Lethbridge. (b) Melior Visiting Professor, University of Otago, on leave from the University of Lethbridge. (c) University of Otago. F. Dolezalek, Z.Phys. Chem.. 64, 727 (1908). (a) L. G. Hepier and D. V. Fenby, J. Chem. Thermodyn., in press; (b) D. V. Fenby and L. G , Hepler, to be submitted for publication. M . L. McGlashan and R . P. Rastogi, Trans. Faraday Soc., 54, 496 (1958). S. Murakami, M. Koyama, and R. Fujishiro, Bull. Chem. SOC.Jap., 41, 1540 (1968). T. J. V. Findlay, J. S. Keniry, A. D. Kidman, and V. A, Pickles, Trans. Faraday SOC.,63,846 (1967) A. N. Campbell and E. M. Kartzmark, Can. J , Chem.. 38, 652 (1960), K. W. Morcom and D. N. Travers, Trans. Faraday SOC., 61, 230 (1965). H. C. Van Ness, "Classical Thermodynamics of Non-Electrolyte Solutions," Pergamon Press, New York, N. y., 1964. H. C. Van Ness and R. V. Mrazek, AlChE J , , 5,209 (1959). D. V. Fenby, G. J. Billing, and D. B. Smythe, J. Chem. Thermodyn.. 5, 49 (1973). C . M. Huggins, G. C. Pimentei, and J. N. Shoolery, J. Chem. Phys., 23,1244 (1955). C. J. Creswell and A. L. Ailred, J. Phys. Chem., 66, 1469 (1962). B. 8. Howard, C. F. JumDer. and M. T. Emerson, J . Mol. Spectrosc,, 10, 117 (1963). R . Philippe, J. Jose, and P. Clechet, 8uli. Chim. SOC. F r . . 2866 119711 \ . _ . . / .
(16)
E. R. Kearns, J . Phys. Chem., 65, 314 (1961)
