Jan., 1963
ROLEOF DISSOLVED TVVATER
I N PARTITION EQUILIBRIA O F
CARBOXYLIC ACIDS
187
the subclass behavior, expressible through Y(M,n,j), for both paraffins and olefins was shown to be represented by
From above we know that
that Zaj = 0, which states that the negative slopes balance out the positive slopes. This is quite evident in both sets of curves in Fig. 6. The data in Fig. 4, 5 , and 6 and in Table IV all dlemonstrate the rather extensive differences in detail between the characteristics of %-paraffin and n-termmal olefin spectra. Let us assume that the existence of the terminal double bond did not in any way affect the Idissociation mcchanism involving bonds apart from the double bond itself. With this assumption it would be possible to calculate much of the olefin spectra from the n-paraffin spectra as the effect of the double bond would be a mere stoichiometric change for many ions. The observed differences are much more profound than this and they indicate that the presence of the terminal olefin bond affects the whole molecule in its dissociation behavior. Conclusions The observations of above may be summarized as follows: (a) the spectra plotted as C ( M , n ) us. M of the n-terminal olefins are generically similar to those of the n-paraffins in demonstrating the universal maxima in the C3-C4 region with general decrease of intensities with increasing carbon number, (b) the Y(M,n) for nterminal olefins also depend linearly upon M , (c) the center of gravity of the C(M,n) plots are always higher for the olefins than for the corresponding paraffins, (d)
50
(e) the differences in subclass behavior between the two types of compounds show the invalidity of the postulate that the molecules first dissociate into CnH2n+lions and these in turn dissociate further into CnHZn,CnHan+ C,H2,-2, etc., ions, (f) the subclass differences between the olefins and paraffins show that the double bond in the olefins has a general effect on the dissociation pattern. that cannot be explained by a mere difference in stoichiometry, and (g) the subclass behavior for both types of compounds indicates that a molecule CMH2,w+2may first dissociate into CMH%,+l, C,H2,, CMH2,+ or CMH2,,+3 ions with further dissociations into ions of different n values but of the same stoichiometry; suitable changes in stoichiometry apply to the consideration of olefins. Although some speculation is offered relative to dissociation mechanisms, the main purpose of this work has been to find and describe mass spectral regularities that have regular dependence on M , n, or j , as used above. Such regularities must be quantitatively explained by the unimolecular theory as it develops and they serve to guide the development and to provide tests of validity. Acknowledgment.-Grateful acknowledgment is due to Dr. J. C. Schug for worthwhile discussions of this subject.
THE ROLE OF DISSOLVED WALTERIN PARTITION EQUILIBRIA OF CARBOXYLIC ACIDS BY SHERRILD. CHRISTIA4N,HAROLD E. AFFSPRUNG, AND
STANTON
A. TAYLOR
Department of Chemistry, Uniuersity of Oklahoma, Nornaun, Oklahoma Received August 16, 1966 ParLition and water solubility data have been obtained for the system water-benzene-acetic acid, with the object of calculating the extent of hydration of the acetic acid species in the benzene phase. Results are consistent with the assumption that a monomer hydrate, but no dimer hydrate, forms in the organic phase a t low acid concentrations. A general analytical treatment is presented for calculating hydration constants for solutes which associate in organic solvents.
Introduction The partition, or distribution, method has been widely used in the determination of dimerization constants of carboxylic acids in solvents only slightly miscible with ~ a t e r . l - ~I n using the method, it is commonly assumed that the presence of small amounts of dissolved water in the non-aqueous phase does not interfere with the association of the acid.l However, we have noticed that literature values of dimerization constants calculated from partition data frequently are lower than those reported for the same acids in the corresponding anhydrous solvents.5 (1) M. Davis and H. E. Hallam, J . Chem. Educ., 33, 322 (1956). (2) E. A. Moelwyn-Hughes, “Physical Chemistry,” Pergamon Press, Oxford, Second Revised Edition, 1961, pp. 1078-1080. (3) G. C. Pimentel and A. L. McClellan, “The Hydrogen Bond,” Freemzn and Company, San Francisco and London, 1960, pp. 45-49. (4) E. A. Moelwyn-Hughes, Trans. Chem. Soc., 850 (1940). ( 5 ) Reference 3, Appendix C, pp. 368-376.
A plausible explanation for this discrepancy in dimerization constants is that dissolved water reacts with the acid monomer to form a hydra.te. To test this theory, we decided to measure the solubility of water in benzene as a function of the concentration of dissolved acetic acid. The Karl Fischer method was employed to analyze for water. Equilibrium concentrations of acetic acid in the benzene phase and in the aqueous phase were determined using standard alkali. We observed that the total concentration of water in the benzene phase increases significantly as tota.1 acid concentration is increased. Theory Our solubility data can be explained on the basis of the assumption that the only species present as solutes in the benzene phase are CH&OOH, (CHICOOH)2, HaO, and CH3COOH.H,O (monomer hydrate). The
S. D. CHRISTIAN, H. E. AFFSPRUNG,AND S. A. TAYLOR
188
VOl. 67
centration of about 1.7 M in the aqueous phase. Although the water solubility data scatter to a certain extent, the increase in water concentra,tion in the organic phase is striking and parallels the increase in acid concentration.
0.04 1
0.03
TABLE I PARTITION AND WATER SOLUBILITY DATA'
0.02 P
1'
0 0.0152 .0206 .0294 .0474 .0691
& I
0.01
0 0
0.2
0.4
1.4
1.0 1.2 (mole/l.).
0.8
0.6
C:
1.6
1.8
Fig. 1.-Dependence of 2 and Y on CT. 2 values: X, a t 35'; 0 a t 15". Y values: a t 35'; 0 at 15".
+
formal concentration of acetic acid in benzene can be expressed as = CAb
+
+
a
b
(1) and the formal concentration of water in benzene may be written ajs fAb
2CA:
+
CAW
(2) where C A ~ CA,), C W ~ and , CAW^ represent the molarities of the species CHaCOOH, (CHaCOOH),, H.0, and CHaCOOH.HzO, respectively, in the benzene phase a t equilibrium. Further, the equilibrium quotients fWb
K2 =
Kh
CA,~/CA~~,
=
= CAWb
CWb
b w C A W ~ / C A ~ C WK~ ,D = CA /CA
(3)
should remain constant in dilute solutions; where C A represents the concentration of acetic acid monomer in the aqueous phase, K z and Kh are the acid dimerization constant and acid monomer hydration constant in benzene, and KD is the distribution constant for the acid monomer. Combining equations 1, 2, and 3, we may write
- fWb
+ CWb = y = K D $. ~ K K2cAW D ~ (4)
CAW
and fAb/CAW
=
z = K D + KhCwbKn + ~KD'K~CA"(5)
~
fwb
CAW
fAb
Ej
At 15' 0 0.709 0.851 1,047 1.366 1.680
At 35' 0 0 0,0187 0,700 .0248 ,836 .0249 .841 ,0355 1.048 .Ob49 1.361 All concentrations in mole/liter.
0.0265 .0287 .0280 .0291 .0307 .0310
0.0465 .0485 .0488 ,0495 .0490 ,0527
As a test of the hydration theory, the data are plotted in Fig. 1in the form Y us. C A and ~ Z vs. C A ~ . It can be seen that a t each temperature the Y and Z points define nearly parallel curves; consequently, in curvefitting data at each temperature, the curves were forced to have equal slopes. Table I1 summarizes results calculated from the parameters of these straight lines. Except for the additive constant KhcWbKD, eq. 5 is identical with the expression commonly applied in treating partition data to obtain K2 and K D . Neglecting KhCWbKD in comparison with KD, one could Calculate an apparent dimerization constant from the relation
KZaPParent = slope/24ntercept2
(6)
where the slope and intercept are obtained from a plot of Z us. CAW. However, in the present instance, an examination of Fig. 1 reveals that K ~ c w ~ K is not D small compared to KD; and as a result, the partition method leads to a value of the dimerization constant that is too low. Values of K P P a r e n t calculated from the present data by means of eq. 6, and dimerization constants reported by Davies, ed aL,' (from partition data) are included in Table I1 for comparison. Note that Kz values TABLE I1
where Y and Z are defined in terms of measurable CURVE PARAMETERS AND CALCULATED EQUILIBRIUM CONSTANTSO ~ Z us. concentrations.6 Note that plots of Y us. C A and 15 35 t, "C, C A W should be linear, with a common slope of ~ K D ~ K ~ Slope . from Fig. 1 0,0203 0.0205 However, the intercept obtained from a plot of Z US. Intercept from Fig. 1 0,0067 0.0121 CAW should exceed that determined from a plot o€ Y us. 2 curve .0041 .0091 Y curve C A by ~ the constant K ~ c w ~ K D . .0265 .0464 c w b (mole/l.) Results 26 7.1 Kh (l./mole) Table I contains the partition and solubility data for 0.0041 0.0091 KD 605 125 the system water-benzene-acetic acid at 15 and 35'. K 2 (l./mole) K Z a ~ p a r e n(l./mole) t from eq. 6 225 70 The upper limit of the concentration of acid in the orK 2 8 P ~ 8 r e n t(I./mole) from ref. 7 200 (extrap81 ganic phase is about 0.07 M, corresponding to a con(6) In dilute solutions, cwbshould be constant and equal to the solubility of water i n pure benzene a t the given temperature. Also, C A (the ~ acid monomer concentration in the aqueous phase) is equal t o the formal concentration of acetic acid in water minus the ooncentration of thc acetate ion, which can be computed from the ionization constant.
olated)
a
All concentrations in mole/liter.
(7) M. Davies, P.Jones,D. Patniak, and E. A. Moelwyn-Hughes, J . Chem. SOC.,1248 (1951).
Jan., 1963
ROLEOF DISSOLVED WATERIN PARTITION EQUILIBRIA OF CARBOXYLIC ACIDS
obtained by the preceding analysis are greater by a factor of 2 or 3 than the apparent constants. Discussion The results given here cast serious doubt on the reliability of the conventional partition method as a means of determining association constafits. We believe that systematic studies of the variation in water solubility with acid concentration in the organic phase should be undertaken in order that available partition data may be re-evaluated with due regard being given to hydration. We also wish to emphasize that the presence of tiny amounts of dissolved water can lead to erroneous reeults in the case of other methods for determining a,ssociation constants for carboxylic acids. In fact, we suspect that a major reason for the lack of agreement between various literature values of associstion constants of carboxylic acids in solution is that small, variable amounts of dissolved water have been present in most of the systems investigated. Since both the monomer and the dimer of many polar solutes rnay be expected to hydrate, an extended treatment of data which would allow the determination of the extent of hydration of each species is desirable. We may develop equations analogous to 1 through 5, without making the restrictive assumption that the monomer monohydrate is the only hydrated species in the organic phase. If both the monomer and the dimer form hydrates, with formulas AWj and A2Wk, respeotively, the hydration constants may be defined by the relations Khi = CAwjb/CAbCwb'
and Khz = C A , ~ W ~ / C bz A Cwb k
(7)
The following equations then rnay be developed in a manner similar to the development of relations 4 and 5
and
~ A ~ / C = A ~2
1.89
= KD(f ~ KhiCwb') f
K D ' ( ~ Kf~2Kh2Cwbk)Ctlw (9) These equations indicate that even in the more complex situations where both the monomer and the dimer form hydrates, plots of Y and 2 vs. C A should ~ be linear. If the monomer hydrates, the intercept of the 2 plot will exceed that of the Y plot by the constant jKDKhlcwb'; and if the dimer hydrates, the slope of the 2 plot will exceed that of the Y plot by the constant ~ K D ~ K w c w ~ ~ . In order to determine j and k uniquely, further data would be required. We anticipate that plots of 2 and Y similar to those in Fig. 1will prove to be of great utility in the interpretation of partition data for carboxylic acids and other polar solutes. These plots can be classified into these four types 2 = slope Y; intercept 2 = intercept Y. No hydration of either A or Az occurs. Type 2 4 l o p e 2 = slope Y ; intercept 2 > intercept
Type l-Slope
Y . Hydration of A, but not of AS, occurs. 2 > slope Y ; intercept 2 = intercept Y . Hydration of Az,but not of A, occurs. Type 4-Slope 2 > slope Y ; intercept 2 > intercept Y . Hydration of both A2 and A occurs.
Type 3-Slope
Type 1 plots may be expected only in systems where the solute is not capable of forming hydrogen bonds. The data presented in this paper indicate that systems containing acetic acid, and perhaps other carboxylic acids, yield type 2 plots. In general, it is expected that the majority of systems will be characterized by type 4 plots; and that type 2 and 3 plots will result when hydration of either the monomer or the dimer predorninates. Currently we are investigating other systenns involving amides, carboxylic acids, and phenols, and in each case we find that the solubility of water in the nonpolar solvent is greatly increased by the presence of small concentrations of the polar solute. Acknowledgment.-This work was supported in part by the National Institutes of Health, and in part by the Research Corporation.
