NOTES
2801
has a high value. If the association constant for solutesolvent interaction is much higher than the solventsolvent association constant, eq. 3 is also applicable to the dimerization of initially solvent-bonded monomers, provided the temperature dependence of the apparent absorptivity is taken into consideration. Figure 1B leads to the following numerical values: T = 298OK., Eobsd = 0.184 1. mole-l cm.-I, K', = 4.1 (mole fraction)-l; T = 318O, Eobad = 0.246, K', = 4.2; T = 338O, Eobsd = 0.295, K', = 4.0. The variation of K', is within experimental accuracy. Standard methods lead to: AH = 0 0.5 kcal./mole, AS' = 3 =t0.5 e.u. for the dimerization of initially solvent-bonded monomers. The entropy value refers t o a standard state defined in mole fractions.
+
Diwcussion The results suggest that the energy required to break amide-ether hydrogen bonds is approximately equal to the energy of formation of amideamide bonds. The relatively high value of the association constant is thus a consequence of a positive standard entropy change upon dimerization. While the system is far too complex for a detailed discussion of entropy relations, a brief qualitative consideration might provide some insight. The "monomeric" system involves two particles schematically represented by: 2 X (amidedioxane). Upon dimerization, one amide-amide dimer (with two H bonds) and two free solvent molecules are formed, i.e., the total number of particles is increased. At sufficiently high concentration, the positive value of ASo results in a considerable number of NH---O=C bonds being formed without a net change in enthalpy. The value of K', reported here is about 1/725 times the value given by Tsuboil for dimerization of 6-valerolactam in carbon tetrachloride solution (Kc(cc4, 26') = 280 moles/l.; Kz(Cc4,26") = 2900 (mole fraction) -l), reflecting the strong competition between dimerization and solvent interaction in the studied system. The experimental data, as presented in Figure lA, re-emphasize the necessity31sto determine the temperature dependence of apparent absorptivity values if thermodynamic quantities are deduced from absorbance measurements in complex systems. Our results also lend support to the conclusiongthat the anharmonicity of X H stretching fundamentals is reduced by hydrogen bonding.lO (9) See ref. 5, p. 114. (10) The overtone frequency in dioxane solution is very close to the overtone frequency in CCla solution. The fundamental frequency is substantially lower in dioxane solution.
Ion-Pair Formation in Aqueous Solutions
of Butylammonium Isobutyratel
by Irving M. Klotz and Henry A. DePhillips, Jr.2 Departmnt o j Chemistry, Northweatern University, Evanston, Illinois (Received February 8, 1966)
Among the noncovalent bonds which may participate in the fixation of conformation in protein molecules one must include the possibility of electrostatic interactions between pendant -NH3+ and -COO- side chains. From the physicochemical behavior of simple ions in aqueous solution there are indicationsa that ion-pair formation, such as [-NH3+. .-OOC-], does not occur to any detectable extent except at very high concentrations. Nevertheless, no direct measurements have been available for a system of an ammonium and carboxylate group suitable as amodel for potential interactions among protein side chains. We have now found that optical measurements in the near-infrared, similar to those used previously to study amide hydrogen bonds,4 do give an insight into ion-pair formation between n-butylammonium and isobutyrate ions. In essence we have used the overtone infrared region to measure the equilibrium constant for the reaction
-
CdHsNH3+
+ C3H7COO[ C ~ H ~ N HC3H,COO] S, +*-
(1)
From the equilibrium constant, established a t three temperatures, the free energy, enthalpy, and entropy of ion-pair interactions may be calculated.
Experimental Preparation of Solutions. Spectra were examined in the region of 1.5 p rather than in the fundamental range so as to minimize complications due to the absorption by water, the solvent. As in previous work a reference cell was prepared containing the same amount of water as the sample cell but with a solute, (1) This investigation was supported in part by a grant (GM-09280) from the National Institute of General Medical Sciences, Public Health Service. It was also assisted by support made available by a Public Health Service Training Grant (No. 5T1-GM-626) from the National Institute of General Medical Sciences. (2) Predoctoral Fellow of the U. S. Public Health Service, 19611963. (3) I. M.Klotz, Brookhaven S y n p . Biol., 13, 26 (1960). (4) I. M. Elotz and J. S. Franzen, J. Am. Chem. Soc., 84, 3461 (1962).
Volume 69, Number 8 August 1966
2802
optically transparent a t the wave length of interest, in place of the butylammonium butyrate in the sample cell. A series of reference solutions of potassium isobutyrate in water was prepared, their densities were determined, and their water concentrations were calculated. A graph of density (or composition) vs. water content of the reference solutions was then drawn. Thereafter a sample solution was made from accurately known weights of n-butylammonium butyrate and water; the density of this solution was determined and the concentration of water therein was calculated. Inspection of the graph for reference solutions then revealed what composition to create to have an accurately balanced filler for the reference cell. Densities. Measurements were made with a Weldtype pycnometer of 7-cc. volume. Samples were introduced with a hypodermic needle. All densities were determined at 25.00 f 0.05'. Spectra. Absorption spectra in the 1.4-1.7-p range were recorded with a Cary spectrophotometer, Model 14R. The cell compartment in the spectrophotometer was thermostated and the temperature within the absorption cells was checked periodically with a thermistor probe. Quartz absorption cells were used. Materials. n-Butylamine and isobutyric acid of reagent grade were purchased from Fisher Scientific Co. The salt butylammonium isobutyrate was obtained by slowly mixing amine and acid in a large beaker with rapid stirring. A slight excess of amine was used to assure complete reaction. Dry nitrogen was bubbled through the liquid for 2 hr. to remove excess amine. A spectrum of the final product revealed no absorption at 1.53 p, where pure butylamine exhibits an intense absorption. Potassium isobutyrate was prepared by neutralizing isobutyric acid with potassium hydroxide. Carbon tetrachloride was Fisher Spectranalyzed grade.
Results Water itself shows a broad region of absorption in the near-infrared with a peak at about 1.46 p at room temperature. Addition of n-butylammonium isobutyrate to water changes the absorption spectrum. Such a change may reflect two contributions, however: (1) the solute absorbs in this region; and (2) the solute changes the absorption spectrum of water because it perturbs the structure of the ~ o l v e n t . ~ To compensate for the second effect we have used potassium isobutyrate in the reference cell. This salt, being present at approximately the same concentration as the butylammonium isobutyrate in the sample cell, should have approximately the same ionic The Journal of Physical Chemistry
NOTES
I
'
1500
1550 1600 Wave length, mp.
1650
Figure 1. The upper curve is the difference spectrum in the near-infrared region (1510-1650 mp) for a n aqueous solution of n-butylammonium isobutyrate us. a n aqueous solution of potassium isobutyrate containing the same molarity of water: concentration of butylammonium isobutyrate, 3.389 M ; temperature, 25.0'. The lower line shows the balance between cells with identical contents.
perturbing effect on the solvent. A typical difference spectrum is illustrated in Figure 1 and shows a peak at 1.56 p. Since this is the general range in which the overtone absorption of N-H groups usually appears, it seem reasonable to assume that the intensity of the difference spectrum at 1.56 p reflects the concentration and state of the CH3CH2CH2CH2NH3+group. If there is no change in state, the molecular extinction coefficient should be essentially constant. If a large change in extinction coefficient is observed it seems reasonable to attribute it to ion-pair formation. On this basis one can measure the equilibrium constant from changes in absorbance at 1.56 p. For the equilibrium of eq. 1, an association constant, K , may be written as
where a is the fraction of total butylammonium isobutyrate in the form of free ions and Ct is the total molar concentration of salt. (Strictly speaking this equation gives only the equilibrium quotient since activity coefficients are not included). Spectrophotometric measurements provide the information for the evaluation of a. In a solution containing free ions and ion pairs, the absorbance, A , may be expressed as
A
=
+
(3) where L represents the extinction coeficient and 1 is the optical path length. In view of the definition of a, it follows that (EionsCions
€ion pairCion pair)l
( 5 ) That salts affect the infrared spectrum of water hm long been known in the literature. For a recent description of some of these effects see I. M. Klotz, Federation PTOC., 24, 5-24 (1965).
NOTES
2803
500 400
from which we obtain a =
eobsd
- €ion pair
€ions
-
€ion pair
(5)
$8 300 200
The value of Cobad, which is in essence defined by the second part of eq. 4, is obtained from the measured value of A for a solution of known Ct of butylammonium butyrate. Since in increasingly dilute solutions, ion pairs would tend toward complete dissociation, €ions can be evaluated from lim
Ct-tO
(6)
cobad = €ions
Such an extrapolation is illustrated in Figure 2. The values found for €ions were 524,413, and 310 mole-' at 1.3, 25.0, and 49.8', respectively. The determination of €ion pair is generally more difficult. However, butylammonium isobutyrate is a liquid at room temperature, and we have assumed that lim Ct+-
Eobsd = €ion pair
=
€pura liq
(7)
The spectrum of the pure liquid was examined at each temperature, with potassium isobutyrate mixed with carbon tetrachloride in the reference cell. The extinction coefficient calculated at 1.56 p is small, 25 mole-I. Since this is near zero, and there is some uncertainty in regard to compensation by the contents of the reference cell, we have arbitrarily set €ion pair equal to zero. The uncertainty in K due to this procedure is about 5%. Knowing e at the extrema, a and then the apparent association constant K may be computed from experimental values of Eobsd vs. Ct. As is evident from Figure 2, most of the salt exists as ions until the concentration of water is greatly reduced so that ion pairs must be formed. In the range of 1-3 M butylammonium isobutyrate, a varies from 0.96 to 0.7, i e . , the salt is overwhelmingly present as ions. Association constants are thus very uncertain but vary from about 0.02 at low concentrations to 0.2 near 3 M . At 25' a rough extrapolation to infinite dilution was attempted and it led to K = 0.03. From an equilibrium constant alone one cannot tell much about the nature of the interaction in these ion
100
1.0
2.0
4.0
3.0 Cl
.
5.0
Figure 2. Observed extinction coefficients at 1.56 p as a function of total (molar) concentration of n-butylammonium isobutyrate in water.
pairs. Nevertheless, since the observed K is an order of magnitude greater than that for an N-He *O=C hydrogen bond in an aqueous ~ o l v e n tit, ~seems likely that electrostatic interactions are contributing to the stability of the ion pair. The uncertainty in association constant was too great to permit a direct computation of hH' from the temperature dependence of In K. However, by a procedure analogous to that used previously for hydrogen-bonding amides in water4one can show that
b In Cions bT )P+
(
AH" =
-RT2
(8)
i e . , one can compute the enthalpy from the temperature dependence of Cionaat constant a. By this method a AHo of - 1 kcal. mole-l was obtained. I n summary then, for the ionic association of eq. 1, at,25' AF" = 2.1 kcal. mole-' AHo = - 1 kcal. mole-'
A S = -10 gibbs mole-l As one might expect from other ion associations, AS" has a negative value, presumably because some water molecules are released, and A H o is near zero. It is no surprise then that AFO for ion-pair formation is unfavorable. As the results in Figure 2 show most directly, only at high molar concentrations of butylammonium isobutyrate, where the water concentration is severely reduced, do the ions tend to become appreciably associated.
Volume 69,Number 8 August 1966
