J. Phys. Chem. 1984,88, 3348-3356
3348
In effect, the ionization of benzoic acid has been arbitrarily chosen as a standard reaction type and u is defined on the basis of this standard. A positive u value for a substituent indicates that the substituent is a stronger electron attracter than hydrogen; substituents with negative u values are weaker electron attracters than hydrogen. We now apply the Hammett equation to the series of salts under investigation. However, before doing so, we shall show why this equation should hold. It is known that log K for a reaction is proportional to the standard free energy AGO. If we are considering the equilibrium constants associated with a given reaction series, we may rewrite the Hammett equation as log K = u log KO (13)
+
or in terms of free energy changes -AGO = RTu - AGOo
(14)
For a given reaction series at a given temperature T, AGOo is constant, and eq 14 is therefore of the form y=ax+b (15) The free energy changes associated with the reactions of the members of a series are thus linearly related to the respective values, and from a definition of u, linearly related to the standard free energies of the ionization of the correspondingly substituted benzoic acids. When applying eq 12 to the association phenomena in a series of substituted benzoate salts, then the more negative the value of u the more ionization takes place or the less association there is in the salts. We successfully applied7 this approach to a series of salts in an earlier investigation. One of the major purposes of this study was to apply the same approach to the various substituted hy-
TABLE VI: Hammett Function (a) for Ca- and Mg-Substituted Benzoate Salts ll
substituent (salt)
benzoate" 0-OH
(o-hydroxybenzoate)a
T,OC 25
35 45 25 35
45 rn-OH (m-h ydroxybenzoate)
3,5-di-OH (3,s-dihydroxybenzoate) 3,4,5-tri-OH (3,4,5-trihydroxybenzoate)
25
35 45 25
35 45 25
35 45
Ca 0.00 0.00 0.00
0.409 0.391 0.395 0.188 0.185
0.188 0.113 0.122 0.118 0.327 0.314 0.326
Mg 0.00 0.00 0.00
0.507 0.470 0.447 0.061 0.065 0.061 -0.121 -0.069 -0.054 0.389 0.351 0.342
OData for these two salts are taken from ref 7. droxybenzoates. Table VI shows the u values for the Ca and Mg salts under investigation and those of o-hydroxybenzoate obtained from ref 7. It is interesting to note that according to the Hammett function (a)approach (Table VI) the association phenomena in the Ca salts decreases in the order o-OH > 3,4,5-tri-OH > m-OH > 3,5-di-OH > benzoate and that for Mg salts in the following order o-OH > 3,4,5-tri-OH > m-OH > benzoate > 3,5-di-OH. These trends are exactly the same as observed for each of the Ca and Mg salts. This indeed suggestes once more that this approach for explaining the association phenomena of the Ca and Mg salts of aromatic salts is both fruitful and plausible.
Volume and Heat Capacity Changes upon Ionization of Water, Acetic Acid, n-Propylamine, and 4-Methylimidazoie in Water and 8 M Urea: Consequences of Ionization on Properties of Proteins Bernard Riedl and Carmel Jolicoeur* Department of Chemistry, UniversitP de Sherbrooke, Sherbrooke, Quebec, J1 K 2R1 Canada (Received: August 29, 1983: In Final Form: December 27, 1983)
The apparent molar volumes (&) and heat capacities (&) of acetic acid, n-propylamine, 4-methylimidazole, and salts of these compounds have been measured in water and in 8 M aqueous urea at 25 O C . From the infinite dilution values, GVo and & O , the changes in volume and heat capacity ( A P and ACpo)were calculated for various ionization and protonation reactions of interest in protein studies. For ionization reactions (e.g., water, acetic acid) both A P and AC O are strongly negative in water and considerably less so in 8 M urea. The correspondingvalues for the dissociation reaction otthe protonated bases (n-propylamine, 4-methylimidazole) are weak in water and also more positive in 8 M urea. These results, together with similar data for various iso-Coulombicreactions of the model compounds, are used to estimate the contribution of group ionization to V O and Cpovalues of several globular proteins in water and in 8 M urea. The model compound data also enable the calculation of P and Cpovariations upon acid-base titration of proteins in water and 8 M urea.
Introduction A detailed account of the thermodynamic properties of proteins in aqueous solutions still represents a formidable problem. Even for a well-characterized globular protein such as bovine chymotrypsinogen A, infinitely diluted in water, the physical and thermodynamical properties of the macromolecule still depend on many complex interactions, either among different portions of the macromolecule, or between the latter and other components of the surrounding medium: water, ions, and other organic solutes. While little is known on the thermodynamic consequences of each 0022-3654/84/2088-3348$01.50/0
type of interactions separately, the intermolecular effects obviously present a highly elusive situation because of the many contributing phenomena, typically, hydration of polar groups, hydration of apolar groups, varying degrees of solvent accessibility of the backbone and residues, ionization or protonation of the various polar groups, etc, Since no single experiment on proteins can provide an adequate understanding of these different contributions, the study of simple compounds which model some specific aspect of a protein (e.g., amino acid, peptides) can provide valuable quantitative estimates of contributions from particular constituents
Published 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984 3349
Ionization Effects on Protein Properties
TABLE I: Apparent Molar Volumes and Heat Capacities at Infinite Dilution in Water at 25 "Cb
bVO =
P,
cm' mol-' CH3COOH CHiCOONa n-C3H7NH2 n-C3H7NHyHCl (CH3)C3H4N2 (CHS)C,H4N**HCl H20 HCI" NaOH' NaC1"
51.85 (0.05) 39.24 (0.10) 72.71 (0.11) 87.16 (0.03) 76.86 (0.04) 93.96 (0.06) 17.998 17.89 -5.37 16.63
Bv 0.07 0.21 -0.18 -1.06 -0.16 -0.83
(0.07) (0.20) (0.18) (0.09) (0.11) (0.19)
&O = e;, J K-'mol-'
169.7 67.7 337.2 197.6 265.7 152.9 75.4 -124.7 -100.5 -83.7
(0.3) (0.8) (0.7) (0.8) (0.4)
BC -2.9 14.4 8.3 -19.0 -21.6 -25.7
(0.4) (1.6) (1.2) (2.6) (1.2) (1.3)
concn range, mol L-'
no. of
0.14-0.94 0.12-0.82 0.26-0.88 0.07-0.50 0.09-0.49 0.09-0.49
8 18 7 8 6 7
data
Reference 10. *Entries in parentheses are standard deviations.
of proteins. This approach has been widely followed by using electrolytes, nonelectrolytes, amino acids, amino acid derivatives, and peptides' to provide basic thermodynamic data which, through additivity schemes or direct analogy, can be used to understand physical properties of proteins. In recent reports,2 an attempt was made to rationalize several aspects of volume and heat capacity changes for protein unfolding in concentrated urea solutions, drawing from data for a minimal series of homologous peptides. These results and other literature data for several electrolytes in water and urea solutions suggested that the solvation of ionic groups could exert a significant influence on the unfolding behavior of proteins in concentrated urea solutions. To clarify this point further, we examine here the partial molar volumes and heat capacities of several model ionizable compounds in water and concentrated urea solutions (8 M), in both their neutral and ionic forms. Following in part the work of Katz and Miller: the set of compounds chosen for this purpose was acetic acid, n-propylamine, and 4-methylimidazole which are taken to represent respectively the ionizable residues of glutamic (or aspartic) acid, lysine (or arginine), and histidine. Data for these compounds and their salts (sodium or hydrochloride salts), together with other results for HCl, NaOH, and H20enable the calculation of changes in volume and heat capacity for various ionization reactions. The data also provide a reasonable basis for calculating the contribution of various ionic groups to changes observed upon transferring a protein from water to urea solutions, or upon titration of a protein in water or in 8 M urea. Experimental Section Methods. The specific heat capacity per unit volume (cpv)of solutions were measured relative to water or to the appropriate mixed solvent, (cpvo)with a Picker differential flow microcalorimeter.4 The thermostat of the latter was set a t 25.00 OC and the temperature increment during the measurement was 2.0 OC; the mean temperature for all heat capacity data was then 26.0 O C . The solution densities (d)were obtained with a digital flow d e n ~ i m e t e r . ~The resolution limit in these experiments are respectively J K-' cm-3 on specific heat capacity and 2 X g cm-3 on densities. Materials. All solutions were prepared by weight with degassed and deionized distilled water. The urea, purchased from Fisher (Certified Reagent), was used after drying at 30 OC under vacuum over P205; no significant difference in the results could be found (1) For recent work see, for example, M. Y. Schrier, P. J. Turner, and E. E. Schrier, J. Phys. Chem., 79, 1391 (1975); S. Lapanje, J. S. Kerjanc, S. Glavnik, and S. Zibert, J. Chem. Thermodn., 10, 425 (1978); B. P. Kelley and T. H. Lilley, J. Chem. SOC.,Faraday Trans. 2, 74, 2779 (1978); K. Gekko, J. Biochem., 90, 1643 (1981); H. Schonert and L. Stroth, Biopolymers, 20,817 (1981); S.Cabani, G. Conti, N. Matteoli, and M. R. Tine, J. Chem. SOC.,Faraday Trans. I , 77, 2385 (1981); K. P. Prasad and J. C. Ahluwalia, Biopolymers, 19, 273 (1980). (2) 0.Enea and C. Jolicoeur, J. Phys. Chem. 86,3870 (1982); C. Jolicoeur and J. Boileau, Can. J . Chem., 56, 2707 (1978). (3) §. Katz and J. E. Miller, J . Phys. Chem., 75, 1120 (1971). (4) P. Picker, P. A. Leduc, P. R. Philip, and J. E. Desnoyers, J . Chem. Thermodn., 3,631 (1971). (5) P. Picker, E. Tremblay, and C. Jolicoeur, J. Solurion Chem., 3,377 (1974).
with solutions of recrystallized and unrecrystallized urea. Solutions of urea were used the day they were prepared, and solutions of urea containing basic compounds (amines, NaOH) were processed within hours, since urea solutions are affected, albeit slowly, by high P H . ~ Acetic acid purchased from Baker was distilled and its purity was assessed by acid-base titration as 299.7%; its water content was shown to be below 0.01% (Karl Fisher). Sodium acetate obtained from Baker was recrystallized in acetic acid and dried under vacuum until constant weight; its water content was below 0.02%. n-Propylamine (n-C3H7NH2)obtained from Baker was used as such (water content: 0.16%). n-Propylamine hydrochloride was purchased from Aldrich and used as such (water content below 0.02%). The HCl used was from Canlab and titrated as 36.88%. The NaOH (Fisher) was kept over P205under vacuum for several weeks before use; its carbonate content was determined by titration to below 0.01%. 4-Methylimidazole ((CH3)C3H4N2)was obtained from Aldrich and recrystallized from petroleum ether; its water content was 1.31%. Lastly, 4methylimidazole hydrochloride ((CH,)C,H4N2.HC1) was prepared by adding an equimolar quantity of HCl to a solution of 4methylimidazole; after drying, the product was recrystallized twice from a 4/ 1 chloroform-acetone mixture; the material titrated less than 0.01% water. Results The apparent molar volumes $v and heat capacities & were calculated from the solutions densities (the density of water at 25 OC was taken as 0.997 047 g cm-3 7, and specific heats (the specific heat of water was taken as 4.1793 J K-' g-' 8), using the standard expression^^,^
In eq 1 and 2, M2 is the molecular weight of the solute, c its molar concentration, d and cp', the solution density and volumetric specific heat; the zero subscripts for d and cp' refer to water or to the reference urea-water mixture. The c, d , cp', dv, and @c results are available as supplementary material. (See paragraph at end of text regarding supplementary material.) The c $ ~and +c values of neutral solutes were found to vary linearly with molar concentration over the range investigated here; hence, the results were fitted by least-squares methods to equations of the form 9v = 9vo+ Bvc
(3)
9c = 9co + Bcc
(4)
(6) S. Lapanje, "Physicochemical Aspects of Protein Denaturation", Wiley, New York, 1978, p 100. (7) G. §. Kell, J . Chem. Eng. Data, 12,66 (1967). (8) H. F. Stimson, Am. J. Phys., 23,614 (1955). (9) C. Jolicoeur, "Thermodynamic Flow Methods in Biochemistry: Calorimetry, Densimetry and Dilatometry" in Methods of Biochemical Analysis", D. Glick, Ed., Vol. 27, Wiley, New York, 1981.
3350 The Journal of Physical Chemistry, Vol. 88, No. 15, 1984
Riedl and Jolicouer
__
TABLE II: Apparent Molar Volumes and Heat Capacities at Infinite Dilution in 8 M Urea at 25 "Cb
dv" = t", cm3 mol-' CH,COOH CH,COONa n-C3H7NHz n-C3H7NHZ*HCl (CH3)C3H4N2 (CH3)C,H4NZ*HCl H2O HCI NaOH NaCP
52.57 44.36 74.07 89.84 77.47 95.63 17.95 20.50 2.30 20.91
(0.06) (0.05) (0.03) (0.08) (0.02) (0.05) (0.03) (0.03) (0.07)
&" =
BV 0.34 -0.56 -0.01 -1.36 ,0.26 -0.67 0.01 -0.84 -0.67
c;,
J K-I mol-'
(0.08) (0.18) (0.07) (0.22) (0.05) (0.29) (0.01) (0.04) (0.15)
165.6 (0.3) 144.6 (0.7) 252.9 (0.4) 198.1 (0.9) 218.4 (0.3) 193.7 (1.1) 72.8 (0.2) 5.3 (0.6) 43.7 (0.4)
BC -1 .O (0.4) 2.8 (2.7) 2.8 (0.9) -22.5 (2.5) -1.1 (0.9) -24.2 (5.9) 0.01 (0.07) -44.3 (0.8) 5.1 (0.8) 24.77
concn range,
no. of
data
mol L-'
0.21-1.08 0.06-0.40 0.15-0.68 0.12-0.54 0.14-0.50 0.07-0.29 0.45-4.4 0.13-0.45 0.08-0.67
7 7 7 8 6 6 5 6 8
7.99 7.99 8.01 7.92 7.97 7.95 7.99 7.99 7.99
mol L-'
Cure,,
"Reference 13. bEntries in parentheses are standard deviations. The &O, dCo,Bv, and Bc parameters obtained for the nonionic solutes in water and 8 M urea are given in Tables I and I1 together with standard deviations and concentrations ranges investigated. When judged from the results of other workers,lOJ1no significant correction was required for ionization (acid dissociation or base protonation) over the concentration range examined here. For dissociated 1:l electrolytes at low concentrations in water, the apparent molar volume and heat capacity usually vary according to"
& = d v D+ 1 . 8 6 5 ~ ' /+~ Bvc dc = +c0
+ 28.95~~1'+ BCC
(5) (6)
The 4' and B parameters obtained for the ionic compounds in water and urea 8 M from least-squares fit of the data to eq 5 and 6 are also collected in Tables I and I1 (at infinite dilution, the apparent molar values are identical with partial molar values which will be used throughout the text). In obtaining the doand B terms for these solutes, we assumed that the coefficients in c1I2, which represent the Debye-Huckel limiting law, were the same in aqueous urea as in water. The hypothesis of identical contributions from long-range electrostatic effects in water and in aqueous urea solutions was also used by other investigator^'^ on the basis of the similarity in dielectric constants of these solvents. Although this assumption remains to be fully assessed from accurate measurements of the temperature and pressure dependences of the dielectric constant of 8 M urea, the consequences are not expected to be significant when the data extend to sufficiently low concentration, as in the present case. For acetic acid and sodium acetate in water, comparison of our data with other literature data yields excellent agreement as shown below.
Discussion Limiting Partial Molar Volumes (P)and Heat Capacities in Water and 8 M Urea. The thermodynamic functions P and basically reflect two contributions: the intrinSic property of the solute (e.g., gas phase) and the consequences of solute-solvent interactions. For simple electrolytes, such as NaC1,13-14 relevant data are available on suitable reference state (gas phase or pure crystal); hence, solvation contributions can be evaluated with some confidence (in spite of fundamental problems regarding the values of ionic radii in solution). For such electrolytes, transfer from the gas phase to aqueous solutions occurs with a large reduction in both volume and heat capacity, typical
(cpo) cpo
(10) G. C. Allred and E. M. Wolley, J . Chem. Thermodyn., 13, 147 (1981); see also P. P. Singh, E. M. Wolley, K. G. McCurdy, and L. G. Hepler, Can. J . Chem., 54, 3315 (1976). (11) G. C. Allred and E. W. Wolley, J . Chem. Thermodyn., 13, 155 (1981). (12) J. W. Larson, K. G. Zeeb, and L. G. Hepler, Can. J . Chem., 60, 141 ( 1982). (13) N. Desrosiers, G. Perron, J. G. Mathieson, B. E. Conway, and J. E. Desnoyers, J . Solution Chem., 3, 781 (1974). (14) J. E. Desnoyers and C. Jolicoeur, 'Hydration Phenomena and the Thermodynamic Properties of Ions" in "Modern Aspects of Electrochemistry", Vol. V, J. O'M. Bockris and B. E. Conway, Ed., Butterworths, New York, 1969.
TABLE 111: Apparent Molar Volumes and Heat Capacities of Transfer from Water to 8 M Urea at 25 "C At",,,
cm3 mol-' CH3COOH CH3COONa n-C3H7NH2 n-C3H7NH2.HC1 (CH3)C3H4N2 (CH3)C3H,NZ*HCl H2O HCI NaOH NaCl
0.72 (0.1 1) 5.12 (0.15) 1.36 (0.14) 2.68 (0.11) 0.61 (0.06) 1.67 (0.11) -0.01 2.61 7.67 4.28
ACp'tr,
J K-'mol-' -4.2 76.9 -84.3 0.5 -47.2 40.8 -2.5 130.0 144.2 108.5
(0.5) (1.5) (1.1) (1.1) (1.5)
'Entries in parentheses are sums of standard deviations on P in water and in 8 M urea. of strong Coulombic solute-solvent interactions, accompanied by local perturbation of residual solvent s t r ~ c t u r e . ' ~ J ~For the complex molecules and molecular ions investigated here, the lack of appropriate reference state data prevents a reliable separation of the P and cpo data into their intrinsic and solvation contribution. In such cases, it is more convenient and informative to examine thermodynamic functions describing the transfer of the solute from water (W) and 8 M urea (U) as APt,(W+U) = P ( U ) - P ( W )
(7)
where Y stands for V or Cp. In such transfers, it can be safely assumed that solute intramolecular effects will not contribute significantly to AT,,, so the latter reflects only differences in the solvation contributions in the two solvents; the same assumption will also hold for macromolecules provided no marked conformational changes occur upon the transfer. The transfer A P and values were calculated from the data in Tables I and I1 and the results are given in Table 111. The A T D t are r positive for all compounds investigated here, except for water itself for which A T " , is essentially zero. As noted earlier,* the volume data are not particularly incisive toward solvation effects in these systems, since both apolar and ionic solutes exhibit positive values of ATtr.3,13917The observations from the present data are consistent with reports of previous studies in that simple electrolytes (HCl, NaOH, NaCl) exhibit the largest Apt,, while the uncharged compounds (acetic acid, n-propylamine, and 4-methylimidazole) yield the lowest A T , , . The ionic forms of the latter exhibit values close to those of simple electrolytes. It may thus be concluded that, for the ionic forms of the compounds studied here, as well as for the amino acid and peptides reported previously,' A T t , is dominated by electrostatic solvation effects. The larger P of ions in 8 M urea compared to water presumably reflects the loss of the structure-breaking effects such
Acpo
(15) J. L. Fortier, P. R. Philip, and J. E. Desnoyers, J . Solution Chem., 3, 523 (1974). (16) J. L. Fortier, P. A. Leduc, and J. E. Desnoyers, J . Solution Chem., 3, 323 (1974). (17) C . deviser, G. Perron, and J. E. Desnoyers, J . Am. Chem. SOC.,99, 5894 (1977).
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984 3351
Ionization Effects on Protein Properties
Volume and Heat Capacity Changes for Various Ionic Reactions in Water and 8 M Urea at 25 "Cg A P , cm3 mol-' ACno,J reaction water 8 M urea water H,O OH- + Ht -22.2" -15.2 (0.2) -216.8' CH,COOH CH,COO- + Ht -11.5 (0.2) -7.8 (0.2j -143.0 (1.5) -10.3e -8.7e 73.8 10.7 7.4 CH3COOH OH- ---* CH3COO- + HzO -128' -16.3' H3P04 ---* HZPOL Ht -220' -25.9' H2P0c HP0:Ht -242' Po43- Ht HP0:-28.7' -247' HCOc C03'- + Ht PhOH PhO- Ht -209' n-PrNH3' n-PrNHz + Ht 3.4 (0.1) 4.7 (0.1) 14.9 (4.5) Tris.Ht Tris Ht 3.6de 3.7e 25.6 19.9 231.7 n-PrNHgt OH- n-PrNH2 H 2 0 25.1f 4-MeImid.Ht 4-MeImid Ht 0.8 (0.1) 2.3 (0.1) -1 1.9 (3.3) Imid.Ht Imid H+ 2.75' 1.7' 4-MeImid.Ht OH 4-MeImid H20 17.5 204.9 23.0 209d NH4+ NH3 Ht
TABLE I V -
K-l
mol-[
- -
--
+
+ + + + +
-- -+ - -+ + - +
+
+
+
8 M urea -48.7 (1.4) -40.5 ( i s j
8.2
60.1 (2.0) 108.8 29.9 (2.0) 78.6
'Reference 10. bReference 12. CReference21. dReference 11. eReference 3. fReference 41. gNumbers in parentheses are the combined standard deviations for reactants and products. ions exert in water13 and, as well, poorer molecular packing in TABLE V Comparison of Various Quantities Obtained in This Work the mixed urea-water solvation shell. with Literature Values (in Water, 25 "C) The transfer heat capacities, ACpa(W+U), are considerably more sensitive to solvation effects than the corresponding volume P(CH3COOH) 39.24 (39.26)' 67.7(67.7,"67.8*) changes; ACpot,are usually found to be positive for simple elecP(CH3COONa) 51.85 (52.01,"51.9') 169.7 (169.7,"165b) trolytes and negative for apolar (hydrophobic) m o l e ~ u l e s . ~ J ~ J ~ P(n-C3H7NH2) 73.28 (74.12e) 304.4 (327') The ACpat, data in Table I11 show large positive values for all APi(CH3COOH) -11.46 (-11.19') -143.0 (-143') simple electrolytes and negative values for the un-ionized forms APdiss-14.9 (-31') of acetic acid, 4-methylimidazole, and n-propylamine, decreasing (n-C3H7NHIt) in that order. With the negative values being associated to the Reference 11. 'Reference 22. 'Reference 23. dReference 24. hydrophobic residues (loss of hydrophobic hydration in 8 M urea), e Reference 25. f Reference 26. the ACpat, results are consistent with the relative hydrophobic character of the neutral compounds. The parent electrolytes of Acid. The standard processes of interest with regards to water the latter exhibit, as expected, larger AC values by an increment and acetic acid are the ionization reactions ranging between 80 and 90 J K-' mol- I V. Although we refer to the compounds studied here as "models" of ionizable residues on proteins, the transfer A P and ACpa of these compounds (neutral or ionic forms) should not be used directly to calculate side-chains contributions to A P and ACpa in (W+U) protein transfer. The compounds studied here are only suggested to model the effects associated with the polar (or ionic) groups; solvation of the apolar moiety may be quite different for the model compounds and for residues attached to the polypeptide backbone. Hence, only those changes related to the ionizable groups and ionization processes of proteins may be realistically derivable from the model compound data. Side-chain contributions to A p t , and A ~ p a t can , be estimated from differences between transfer values for amino acids and glycine; such differences yield negative ACpat, for the side chains of lysine, aspartic acid, and histidine, but the absolute values are significantly lower than those of the model compounds investigated here.'* This observation is consistent with a less efficient hydration of the hydrophobic moiety of the residues when attached to the glycyl unit. Finally, it is interesting to note from the data in Table I11 that ACpatr of HzO from the pure liquid to 8 M urea solutions is only -2.5 J K-I mol-' although the water/urea ratio at 8 M urea is down to -4, and, thus, the characteristic structure of liquid water must be virtually destroyed. This appears as additional support to the suggestion that the high heat capacity of water is due, largely, to its extensive hydrogen-bond conne~tivity,'~ additional contributions due to characteristic local fluctuations of liquid water being relatively small.20 Volume and Heat Capacity Changes for Ionization Processes in Water and 8 M Urea. ( a ) Dissociation of Water and Acetic (18) To be submitted for publication. (19)M.Oguni and C. A. Angell, J. Chem. Phys., 73, 1948 (1980). (20) R.Lumry, E.Battistel, and C . Joiicoeur,Faraday Symp. Chem. Soc.,
17,93 (1982).
HzO(liq) CH,COOH(aq)
-
H+(aq) + OH-(aq) CH,COO-(aq)
(8)
+ H+(aq)
(9)
Under the conditions of most studies and of the present work, the changes in volume and heat capacity upon ionization ( A T , and AC,",) are best obtained through appropriate combinations of acid-base reactions, in this case NaOH
+ HCl
CH3COOH + NaOH
-
+ H20 CH3COONa + H 2 0 NaCl
(10) (1 1)
Since and Ce0values are additive in their ionic components, the A T i and ACpoivalues are then obtained in water and in urea solutions according to AP,(H~O) = P ( N a 0 H ) + P ( H C 1 ) - P ( H 2 0 ) - P ( N a C 1 ) (12) APi(AcOH) = F'(Ac0Na)
+ P ( H 2 0 ) + A P i ( H 2 0 )P(Ac0H)
- P ( N a 0 H ) (13)
where AcOH and AcO- represent acetic acid and the acetate ion, respectively. With this particular combination of reactions, prior knowledge of data for ionization of water is required to calculate A P i and ACpoiof acetic acid. For the latter, an alternate reaction may be considered CH,COOH
+ NaCl
-
CH3COONa
+ HC1
(14)
for which A P i ( A c O H ) is (eq 12 and 13) AP,(ACOH) = P ( A c 0 N a ) + P ( H C 1 ) - P ( A c 0 H ) - P ( N a C 1 ) (15) Using the data in Tables I and 11, we calculated A T i and ACpa, for water and acetic acid, in water and in aqueous urea 8 M, with the results given in Table IV; in Tables IV and V, we compared the present values in water with previous results and with data
3352 The Journal of Physical Chemistry, Vol. 88, No. 15, 1984
Riedl and Jolicouer
TABLE VI: Ionizable Groups of Several Globular Proteins: Chymotrypsinogen A (CGN); 8-Lactoglobulin (8-LG); Lysozyme (Lys); Myoglobin (Mb) ~
~~
~~
~
no. of groups in
group arginine,
amino acid" pK,
CGN~
8-LGe
Lysb
Mbb
12.5
4
6
11
4
aspartic acid, -COOH cysteine, -S-H glutamic acid, -COOH
3.9 8.3 4.3
8
21
0
2
8 0
6.0
5 2
30 4
2
histidine,
1
6 0 13 12
4.5 (4.4-4.6) (8.5-8.8) 4.5 (4.4-4.6) 6.5 (6.5-7.0)
14 2 1 1
30 8 2 2
6 3 1 1
19 3 1 1
10 (10.0-10.2) (9.6-10) 8.0 (9.02) 3.7 (3.72)
-NH-C
p& in proteind 12.5 (7-12)
/ "2
qNH+ I
lysine, -NHSt tyrosine (u-NH,' (u-COOH
10.8 10.9
"Reference 29. bReference30. eReference 31. dValuesin parentheses are as quoted in ref 29; single values (mean) were used in the calculations.
for various other ionization processes. The results reported here for ionization of acetic acid (in water) are in excellent agreement with results of previous work." Also, the present Pidata in water and 8 M urea are in reasonable agreement with the data of Katz et ale3,allowing for differences in the compounds studied and in the conditions of the experiments. In water, the large negative values of A T i and ACpoi of H 2 0 or CH,COOH are readily understood as due to Coulombic iondipole interactions and to the "structure-breaking" influence of the ionic species.I4 If, as ~uggested,'~ ion structure-breaking effects are depressed in urea-water mixtures, less negative A P i and A C g i are expected in the presence of urea, as observed. Other contributions to A P i and ACpoi due to changes in dielectric constant' or molecular packing effects (size and shape of solvent molecules) cannot be ruled out, but for ACpoi at least, these are not expected to be dominant. Also, to first order, the strong ion-dipole interactions should not be very sensitive to temperature or to the chemical nature of the solvent dipole; hence contributions from such interactions to ACpoiwill be weak and not strongly dependent on solvent composition. This view appears well supported from data for electrolytes in nonaqueous solvent^.^' With regards to ionization processes of proteins, an obvious consequence of the acid ionization data in Table IV is that the dissociation of protein carboxylic groups in water will lead to a large decrease of Cpo of the protein. The same process occurring in 8 M urea will yield much weaker negative Cpochanges so that the transfer of the ionization process (all species) from water to 8 M urea will lead to a significant increase in Cpoof the protein; judging from the data for acetic acid, one would expect that the contribution of each ionizing group will be of the order of 100 J K-I mol-'. Such estimates are, however, relevant only to unbuffered systems; in the presence of buffers (external or internal to the protein), additional reactions will need to be considered. ( b ) Proton Dissociation from n-Propylammonium and 4Methylimidazolium Zons. The standard proton dissociation reaction of interest here for the conjugate acid (BH+) of an organic base (B) is
cpo
-
+
BH+ B H+ (16) The data obtained for the neutral and ionic forms (HCl salts) of (21) P. D. Bolton, F. M. Hall, and I. H. Reece, Spectrochim. Acta, 22, 1149 (1966). (22) J. Konicek and I. Wadso, Acta Chem. Scand., 25, 1541 (1971). (23) M. C. Cox, D. H. Everett, D. A. Landsman, and R. I. Mum, J . Chem. SOC.B, 1373 (1968). (24) P. A. Leduc and J. E. Desnoyers, Can. J . Chem., 51, 2993 (1973). (25) S. Cabani, G. Conti, and L. Lepori, J . Phys. Chem., 78,1020 (1974). (26) S. Cabani, P. Gianni, J. Mollica, and L. Lepori, J . Solution Chem., 10, 563 (1981). (27) R. Zana, G. Perron, and J. E. Desnoyers, J . Solution Chem., 8, 729 (1979); R. N. French and C. M. Criss, ibid., 11, 625 (1982); D. Mirejovsky and E. M. Amett, J . Am. Chem. SOC.,105, 1112 (1983).
n-propylamine and 4-methylimidazole (Table I and 11) then allow calculation of the dissociation quantities ( A p d i s s and ACpodss) as A p d i s s = P ( B ) i- P ( H C 1 ) - p(B.HC1) (17) The A p d i s s and ACpodissvalues for proton dissociation from npropylammonium and 4-methylimidazolium in water and 8 M urea are reported in Table IV. These reactions, compared to the acid ionzation processes, occur with relatively weak A P and Acpo changes especially in water. This is readily understood from the discussion above, since the proton dissociation is carried out a t constant ionic charge (iso-Coulombic process) and, thus, the cp contributions from ion-solvation interactions largely cancel. However, the trend observed when comparing A P d , and ACpodisr in water and in 8 M urea is the same as that found with the acid ionization reactions: increased A P and ACpo values in 8 M urea. For ACpodns,an important part of the increment is readily traced to proton solvation effects, as evidenced by the large positive ACPok of HC1 from water to 8 M urea (Table 111). From the above results, the protonation of basic protein residues in water (arginine, lysine, histidine, and terminal amino groups) must be expected to occur with a weak change in heat capacity, as also suggested from previous data;28on the same grounds, base protonation in 8 M urea will occur with a significant negative ACpo. These results together with the acid ionization data enable some estimate of the P and Cpochanges occurring upon internal acid-base neutralization of proteins (e.g., at the isoelectric point) as discussed below. Finally, in comparing thermodynamic data for dissociation of carboxylic acids and protonation of nitrogen bases, it should be generally more appropriate to examine the following proton transfer reactions: RCOOH
-
+ OH-
RNH3'
RCOO-
RNHZ
+ H20
+ H+
(19) Both processes are carried out at constant ionic charge (isoCoulombically) so the resulting A P and ACpo will not be dominated by ionization effects. A comparison of A V and ACpo for such reactions is illustrated in Table I for the systems investigated here, in water and urea 8 M; indeed, the thermodynamic quantities corresponding to reactions 18 and 19 appear more closely related (sign and magnitude) than in comparisons involving the standard acid dissociation values. Application to Protein Results. The model compound data reported here may be used to examine two aspects of P and Cpo changes related to protein ionization. First, the total contribution from all ionization processes of a protein at its isoelectric point (28) S. Cabani, E. Matteoli, and E. Selli, J . Chem. Soc., Faraday Trans. I , 75, 363 (1979).
Ionization Effects on Protein Properties
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984 3353
TABLE VII: 9"and CpoResults for Chymotrypsinogen A and &Lactoglobulin P or A P , om3 mol''
cpoor A c p o , J K-'
0-LG
CGN
Experimental Valuesn 17.9 x 103 27.4 x 103 18.3 x 103 27.1 x 103 0.2, x 103 0.3, x 103
native protein in water protein in 8 M urea water 8 M urea transfer
-
total contribution from ionization at isoelectric pH in water same as above in 8 M urea total contribution of group ionization to the transfer (water 8 M urea) values
-
-209
Calculated Ouantities . . -596
-175 34
-500 101
mol-'
CGN
0-LG
38.3 x 103 61.0 x 103 22.7 x 103
56.3 x 103 86.5 x 103 30.2 x 103
-2.2 x 103
-6.6 X lo3
x 103 x 103
-4.1 X 10' 2.5 x 103
-1.4 0.8
Values measured in our laboratory, to be published.
can be calculated in water and in urea. Second, variations in protein P and 2'1, due to ionization can be predicted as a function of pH. These two aspects are explored below for several globular proteins, for which the distribution of pK,'s of ionizable groups are given in Table VI. In the calculations described below, mean pKa values observed for proteins were used, and the number of groups and their pK, were assumed identical in water and in 8 M urea. The titration data available for proteins and model compounds in aqueous urea show significant pKa shifts,32but such variations would only affect minor features of the results described below. Also, the contributions from cysteine and tyrosine residues have been neglected for lack of appropriate model compound data. To check the consistency of the calculations and the significance of the assumptions used here, we computed the total protein charge as a function of pH for chymotrypsinogen A and @-lactoglobulin in the pH range 4-10. The calculations predict the isoelectric pH values within half a pH unit and the agreement between calculated and experimental curves is sufficient to warrant the qualitative conclusions derived below. ( a ) Ionization Contributions to P and of Proteins. The of proteins overall influence of group ionization on P and can be obtained by hypothetically reversing all ionization processes at the isoelectric pH. This simply involves calculating the number of charged groups of each category (Table VI) and summing A P and AC,' values for the corresponding reactions, Le., of the type H+ RCOOH and RNH3+ R N H 2 H+, or RCOOinternal neutralization RCOO- RNH3+ RCOOH RNH2 Additionally, in the case of AC,', one may consider possible "relaxational" C, contributions, i.e., due to equilibrium shift of the ionization reaction^;^^^^^ calculations of such contributions for coupled ionization processes show these to be only a few J K-' mol-' for each group, hence small compared to effects resulting from ionization.35 Using the data in Tables IV and VI, we computed the total A P and AC," associated with the "uncharging" of chymotrypsinogen A and @-lactoglobulin; the results are reported in Table VI1 together with experimental data for these proteins in water and 8 M urea. As expected from the model compound results, the calculated of the proteins contribution due to group ionization on P and is negative in water and in 8 M urea, and much weaker (approximately half) in the latter solvent. As suggested earlier,2 the magnitude of group ionization effects appears as a significant
e,'
+
-
+
e,'
--
+ +
e,'
(29) C. R. Cantor and P. R. Schimmel, "Biophysical Chemistry", W. A. Freeman, San Francisco, 1980, p 4950. (30) H. A. Sober, Ed., "Handbook of Biochemistry", CRC Press, Cleveland, 1970. (31) W. G.Gordon, J. J. Barch, and E. B. Kalan, J. Biol. Chem., 236,3907 (1961). (32) M. A. Marini and C. Wunsch, Biochemistry, 2, 1454 (1963); 0. F. Schafer, Ber. Bunsenges. Phys. Chem., 80, 529 (1976). (33) E. W. Wolley and L. G.Hepler, Can. J. Chem., 55, 168 (1977). (34) C. Jolicoeur, L. L. Lemelin, and R. Lapalme, J. Phys. Chem., 83, 2806 (1979). (35) E. Battistel, R. Lumry, and C. Jolicoeur, to be submitted for publication.
fraction of either the total quantities (Pand epo) of proteins or their transfer function from water to 8 M urea. Clearly, such effects must be accounted for in interpreting the molecular basis of thermodynamic data for protein unfolding in urea solutions. In fact, because of extensive solvent exposure of ionic groups, changes in the interactions involving these groups upon addition of urea may play an important role in the early events leading to protein unfolding.2 The dependence of P and of proteins upon urea concentration is currently being investigated. ( b ) p H Dependence of P and of Proteins. The variation in P and of proteins as function of ionic charge (pH) can also be calculated from the model compound data. For interpretive purposes, one would ideally like to obtain in this way the charge dependence of P and e," of the biopolymer, independently of all counterions. However, this would require ionic values of P and Cpo which are not yet fully established in water (especially and completely unknown in 8 M urea. Short of such ionic data, the changes in protein P and C' with pH may be calculated as they would be observable in titration experiments. Again, this involves calculating the fraction of each type of ionized groups as a function of pH, and summing the contributions from the appropriate reactions. In the case of acid or base titrations from the isoelectric point, the relevant reactions are predominantly acid titration, RCOOH+ RCOOH, and base titration, RNH3+ + OH- RNHz + HzO. The results of calculations following this scheme would correspond to P and Cpochanges obtained in a differential experiment involving (protein + solvent) against solvent, the solvent being a dilute acid or base. Such calculations are illustrated below for chymotrypsinogen A, (CGN), @-lactoglobulin(@-LG),lysozyme, and myoglobin and the results compared with experimental data as available. The predicted influence of ionization reactions (upon acid-base of CGN and @-LGin water and in 8 titration) on P and M urea is illustrated in Figure 1. On these plots, the ordinate zero is set at the isoelectric point (experimental) of the protein in water. Over a range of p H values between 4 and 10, changes in P of proteins is predicted to occur within a few hundred cm3 mol-', somewhat less pronounced in urea than in water. A similar pattern is predicted for in this case with much lower variations in urea than in water. Interpretation of these effects must be viewed within the various limitations inherent to the calculations (assumptions regarding pKa values, the solvent accessibility of all ionizable groups, the adequacy of the model compounds, neglect of tyrosyl residues); however, the shape of these curves and the order of magnitudes of the effects predicted for these two widely different proteins should be reliable and useful in assessing the consequences of ionization on protein properties. A detailed comparison with experimental data is possible for volume changes using the results of Katz and co-workers3' and Kauzmann and c o - w ~ r k e r s . ~ ~
c,'
e,'
c,'
e,')
+
-
-
e,'
c,",
(36) A. L. Lehninger, "Biochemistry", Worth, NY, 1975, p 162. (37) (a) S. Katz and T. J. Ferris, Biochemistry, 5, 3246 (1966); (b) S.Katz and J. E. Miller, ibid., 10, 3569 (1971); (c) J. Phys. Chem., 76, 2778 (1972).
3354 The Journal of Physical Chemistry, Vol. 88, No. 15, 1984
Riedl and Jolicouer LYSOZYME
A CHYMOTRYPSINOGENA
2
aV(ion) lo2cm3 moil
- CALCULATED -- EXPERIMENTAL 1200
1 0
800
-1
"0
2
I ,
>
I
a
LOO
2-1 0 3
5
MOLES H' BOUND/105g
Figure 2. Calculated and experimental volume of ionization of lysozyme in water and in 8 M urea as a function of number of moles of H t or OHbound. Experimental values taken from ref 37b.
-
-* 1
(FERRIIMYOGLOBIN
-CALCULATED - -EXPERIMENTAL
isoelectric point
I
4
10
8
6
MOLES OH- BOUNDIIO g
PH Av( ion)
o3
B
-
/3 LACTOGLOBULlN
1 cm3 mor'
/
'1
ACp(ion) kJK mol-'
lG0 MOLES H'
BO BOUNOl 10 g
0
80 160 5 MOLES OH- BOUNDllO g
Figure 3. Calculated and experimental values of ionization of ferrimyoglobin in water and in 8 M urea as a function of number of moles of H+ or OH- bound to the charged sites. Experimental values taken from ref 38. I n Figures 2 a n d 3 w e illustrate the reported experimental volume changes for both acid and basic titrations of lysozyme a n d myoglobin i n water a n d 8 M urea. T h e results are shown here
cpo
Figure 1. Calculated variations in P and of chymotrypsinogen A and P-lactoglobulin as function of pH in water and in 8 M urea. P and CPoof the protein are taken as zero at the isoelectric pH of the protein in water (taken from ref 36). The P and curves in 8 M urea are also positioned from the isoelectric pH, displaced from the curves in water by the total calculated differences in ionization contributions in water and urea 8 M (last line in Table VII).
cpo
(38) S . Katz, J. K. Crissman, and J. A. Beall, J. Biol. Chem., 248, 4840 (1973). (39) E. Battistel, R. Lumry, and G. Jolicoeur, work in progress. (40) J. Rasper and W. Kauzmann, J . Am. Chem. Soc., 84, 1771 (1962). (41) W. Kauzmann, A. Bcdansky, and J. Rasper, J . Am. Chem. SOC.,84, 1777 (1962).
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984 3355
Ionization Effects on Protein Properties (FERRI~MYOGLOBIN
---
GOO
CALCULATED
- EXPERIMENTAL 400
200
0
m0 7
\
E O
>
a
-2oc
0
40
80
120
1GO
5
MOLES H’ BOUND/ 10 g
Figure 4. pH mediated conformation transition in ferrimyoglobin as evidenced by volume changes upon proton binding; see text for details of the calculated curve.
in the framework used by Katz et al.,37 that is, AV for lo5 g of proteins plotted against number of moles of bound H+ or OH-. For experimental purposes, this may be prefereable since it yields near linear volume variations. In calculated curves, however, the region near zero moles bound (H’, OH-) would not yield a sharp break since the calculated H+ and OH- binding curves as function of pH overlap somewhat near neutral pH40 due to ionization of histidyl residues; this overlap is not illustrated in Figures 2 and 3, although histidyl residues were included in the calculations. The comparisons illustrated in Figure 2 for lysozyme shows rather close similarity between calculated and experimental volume changes, especially in the acid region. In the basic titration, the calculated slopes (AV/mol OH- bound) are lower than the experimental ones as would be expected if part of the groups were not titratable. In 8 M urea, the calculated vs. experimental agreement is closer, again as expected if additional titratable groups became exposed in the presence of urea. (For lysozyme, however, we have found no report of buried, nontitratable, groups in the basic region). Considering the limits of the assumptions, the calculations based on model compounds indicate quite satisfactorily that the volume change of lysozyme as function of pH is largely dominated by electrostatic effects; protein structural changes and other solvation effects can only be inferred from small differences in the slopes of the binding curves. For example, since the difference in the predicted OH- binding curves in water and in 8 M urea is not found experimentally, it may be inferred that other solvation effects and protein conformational changes contribute to the differences in the binding volume behavior. In cases where protein conformational changes lead to the exposure of new ionizable groups, volume effects may appear quite large as with myoglobin illustrated below. The calculated H+ and OH- binding curves for ferrimyoglobin are compared (Figure 3) to the experimental data reported by Katz and c o - w o r k e r ~ the ; ~ ~ calculated curves assume that all hystidine residues are titratable and neglect ionizable residues on the heme group. For this protein, the experimental volume changes in the acid region are qualitatively different from the predicted ones, indicating important structural changes in the protein. The observed volume behavior in the acid region has been interpreted by Katz et aL3* as originating from the exposure of “masked”
histidyl groups due to a structural transformation of the protein when proton binding exceeds 40 mol of H+/105 g of protein. Similarly, in the basic region, a structural transition was invoked to explain the volume behavior in 8 M urea when more than 50 mol of OH-/105 g of protein are bound, although no detailed explanation could be advanced. The volume changes occurring in the acid titration of ferrimyoglobin are examined in greater detail in Figure 4, where, calculations using the model compound data can help visualize the magnitude of volume changes expected from the sudden exposure of buried titratable groups (6 imidazole/mol of myoglobin) as proposed by Katz and c o - w o r k e r ~ .The ~ ~ initial portion of the calculated curve illustrates a continuous volume increase due to protonation of carboxylate groups. The sudden exposure and protonation of the hystidyl residues at 40 mol of H+ bound results in a marked volume decrease, followed by increasing volume for protonation of residual carboxylates. The S-shape curve found experimentally is significantly less pronounced than the idealized situation depicted by the calculations for a number of reasons, such as, progressive rather than instantaneous exposure of buried imidazoles, differences in the acid-base properties of the groups titrated, buffering from the various coupled equilibria, etc. Nonetheless, the calculations confirm that, although the S-shape experimental volume curve is a consequence of a structural transition of the protein, the magnitude of the related volume effects are dominated by ionization reactions. A comparison of calculated and experimental cpo changes lacks corresponding Cpodata for proteins as function of pH. However, in ongoing studies with human hemoglobin A (oxy and deoxy) in water (compared in a framework consistent with the present in water exhibits a weak calculations), it was found that maximum near the protein isoelectric pH.39 In this case, the model compound predictions (Figure 1) would thus rule out ionization effects as the origin of such a maximum.
cpo
Conclusions The main conclusions derived from this work may be summarized as follows. For ionization reactions, large negative A T l and ACpo! are observed in water which originate in the hydration of the ionic species; the magnitude of the corresponding changes in 8 M urea are much lower, which is consistent with the behavior of electrolytes in these solvent systems. Iso-Coulombic reactions, such as proton transfer, occur with much weaker A P and ACpo changes, and thus appear better suited for comparison of reactions involving organic acids and bases. With the data from the model compounds investigated (acetic acid, n-propylamine, and 4-methylimidazole), the contribution of charged groups to A P and ACpo for the transfer of proteins from water to 8 M urea was calculated (at the isoelectric point) and shown to be a sizeable fraction of the total functions. These results will be exploited later in attempts to unravel changes in protein 1“ and Cpoas a function of urea concentration. The model compound data allow qualitative predictions of P and Cpovariations of proteins as functions of pH. P changes calculated over a broad pH range agree reasonably well with experimental data, provided no gross structural transition occurs in the protein as function of pH (e.g., lysozyme), indicating that protein volume changes as function of pH are largley governed by ionic reactions. The calculated and experimental P titration curves lie closer together in 8 M urea than in water suggesting that the protein behavior is more accurately described from model compound data in 8 M urea. Strong departure of the calculated P binding curves (H+ or OH-) can also be understood qualitatively from the model compound data. The latter can help distinguish the relative magnitude of volume effects associated with ionic reactions and with other phenomena (conformational changes, solvation effects) when a protein undergoes a pH-dependent transition. Acknowledgment. The authors gratefully acknowledge financial support of this work by the Natural Sciences and Engineering Research Council and the “MinistZre de 1’Education du QuEbec”.
J. Phys. Chem. 1984,88, 3356-3359
3356
The assistance of Diane Desrochers in many of the measurements is also acknowledged with pleasure.
,,-
Registry N ~ . CH,COOH, 64-19.7; C H ~ C O O N ~127-09-3; , C,H,NH,, 107-10-8;n-C3H,",.HC1, 556-53-6; ( C H , ) C ~ H ~822,, 36-6; (CH,)C,H,N,.HCl, 23187-14-6; H20, 7732-18-5; HC1,7647-01-0;
NaOH, 1310-73-2;NaCl, 7647-14-5;chymotrypsinogen A, 9035-75-0;
lysozyme, 9001-63-2;urea, 57-13-6.
Supplementary Material Available: The concentrations, densities, and specific heats of the binary and ternary solutions investigated here, along with 4" and values of the solutes a t each concentration, are reported (5 pages). Ordering information is available on any current masthead page.
Aqueous Solubility of Trls(acetylacetonato)chromium(I I I ) Manabu Yamamoto Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan (Received: September 12, 1983; In Final Form: January 24, 1984)
The aqueous solubility of tris(acetylacetonato)chromium(III) was measured from 5 to 75 "C and has a minimum at 45 OC. By the scaled particle theory (SPT), a hard-sphere diameter of 8.97 %, was estimated from the heat of solution and the partial molar volume, and a Lennard-Jones parameter of 616 K was also determined from the solubility at 25 OC. With these parameters, solubilities could be estimated by the SPT. Throughout the temperature range, a major part of the large negative entropy and of the large positive heat capacity of solution was contributed by the cavity formation term. From a comparison of the temperature dependences of the cavity formation term and other terms for the aqueous solution with those for a carbon tetrachloride solution, it was confirmed that the specificity of aqueous solubilities is due to the cavity formation term.
Introduction @-Diketonesform a variety of metal chelates with various metal ions1 and have been used widely for the separation or purification of metals by solvent e ~ t r a c t i o n . ~Solvent ,~ extraction of metal @-diketonatesand also the gel chromatographic behavior of metal acetyla~etonates~-~ may be explained by regular solution theory in terms of the solubility parameters of organic solvents, though the thermodynamic properties of tris(acety1acetonate) complexes in aqueous solutions have been scarcely studied. Moreover, it is not appropriate to apply regular solution theory for the explanation of the thermodynamic properties of aqueous solution. Recently it was found that partial optical resolution of tris(acetylacetonato) chelates such as C r ( a ~ a cor ) ~Co(acac)3 could be accomplished through the hydrophobic interactions with optically active metal chelate ions of tris(phenanthroline)nickel(II) by solvent extraction' and salting-in chromatography.8 In consideration of these phenomena and also in comparison with the behavior of simple gases in solution it is of interest to study aqueous solutions of these metal chelates. In the present study, choosing C r ( a ~ a c as ) ~a model of a large, rigid, and nearly spherical solute, solubilities were measured over the temperature range from 5 to 75 "C and compared with those calculated by the scaled particle theory (SPT).9s'0 Specificity of the aqueous solubilities of nonpolar solutes is also explained by comparing observed and calculated thermodynamic parameters of solution. ~~~~
~
(1) Mehrotra, R. C.; Bohra, R.; Gaur, D. P. "Metal @-Diketonatesand Allied Derivatives"; Academic Press: London, 1978. (2) Morisson G. H.; Freiser, H. "Solvent Extraction in Analytical Chemistry"; Wiley: New York, 1957. (3) Stary, J. "The Solvent Extraction of Metal Chelates"; Pargamon Press: New York, 1957. (4) Yamamoto, Y.; Yamamoto, M.; Ebisui, S.; Takagi, T.; Hashimoto, H.; Izuhara, M. Anal. Lett. 1973, 6, 451. (5) Yamamoto, M.; Yamamoto, Y. Anal. Chim. Acta 1976, 87, 375. (6) Saitoh, K.; Satoh, M.; Suzuki, N.; J . Chromatogr. 1974, 92, 291. (7) Iwamoto, E.; Yamamoto, M.; Yamamoto, Y.; Inorg. Nucl. Chem. Lett. 1977, 13, 399. ( 8 ) Yamamoto, M.; Iwamoto, E.; Kozasa, A.; Takemoto, K.; Yamamoto, Y.; Tatehata, A. Inorg. Nucl. Chem. Lett. 1980, 16, 71. (9) Reiss, H. Adv. Chem. Phys. 1966, 9, 1. (10) Pierotti, R. A. Chem. Rev. 1976, 76, 717.
0022-3654/84/2088-3356$01.50/0
TABLE I: Parameters for the Solubility Equations
eq 2 eq 3
iw,
A
B
-1.5384 X 105 -2.0253 X
3.2254 X 102 6.3810 X 102
1.0200
105
-4.3976 103
C
-2.5884 103
X
X
Though SPT is not a pure molecular theory" and there is some inaccuracy in the estimation of the absolute values of thermodynamic properties of cavity formation,I2 it is useful to estimate solution behaviors of various solutes with a minimum number of parameters. SPT has been applied successfully to calculate the thermodynamic functions of solution of g a ~ e s ' ~ and - ' ~ also for more complex solutes to explain the thermodynamic properties of transfer,I6-'* salt effect^,'^-^^ or hydrophobic interaction.22 Except for a few cases,16,18,23,24 it was limited to the study at a fixed and low temperature. Here the applicability of SPT over a broad temperature range is also examined.
Experimental Section Cr(acac), was prepared according to the literature25and purified by sublimation at 100 "C under reduced pressure of 1 mmHg25 (Calcd for C r ( a ~ a c ) ~C, : 51.57%; H, 6.08%. Found: C, 51.56 (1 1) Ben-Naim, A. "Water and Aqueous Solutions"; Plenum Press: New York, 1974; Chapter 7. (12) Crovetto, R.; Fernandez-Prini, R.; Japas, M. L. J . Phys. Chem. 1982, 86, 4096. (13) Pierotti, R. A. J . Phys. Chem. 1965, 69, 281. (14) Wilhelm, E.; Battino, R.; J . Chem. Thermodyn. 1972, 3, 379. (15) Wilhelm, E.; Battino, R.; J . Chem. Phys. 1972, 56, 563. (16) Philip, P. R.; Jolicoeur, C. J . Solution Chem. 1975, 4, 105. (17) Desrosiers, N.; Desnoyers, J. E. Can. J . Chem. 1976, 54, 3800. (18) Lucas, M. J. Phys. Chem. 1972, 76, 4030. (19) Shoor, S. K.; Gubbins, K. E. J . Phys. Chem. 1969, 73, 498. (20) Masterton, W. L.; Lee, T. P. J. Phys. Chem. 1970, 74, 1776. (21) Lucas, M.; deTropriann, A. J. Phys. Chem. 1971, 75, 1803. (22) Ben-Naim, A,; Tenne, R. J . Chem. Phys. 1977, 67, 627. (23) Lucas, M. J. Phys. Chem. 1973, 77, 2479. (24) Hirata, T.; Arakawa, K.; Bull. Chem. SOC.Jpn. 1973, 46, 3367. (25) Moeller, T., Ed. In "Inorganic Syntheses"; McGraw-Hill: New York, 1957; Vol. 5, p 130.
0 1984 American Chemical Society
