3345
J . Phys. Chem. 1984,88, 3345-3348
of the physical properties of methanol. The present study has been partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture.
proaches M2+ more closely in the alkaline-earth-metal systems than in the transition-metal systems. Therefore, there is a pronounced relation between AGIAe and Ache in the alkalineearth-metal systems.
Registry No. Ca(C104)2,13477-36-6;Sr(C104)2,13450-97-0;Ba13465-95-7;CO(CIO~)~, 13455-31-7;Ni(C104)2, 13637-71-3; CU(CIO~)~, 13770-18-8;Zn(C104)2, 13637-61-1;Cd(C104)2, 13760-37-7.
Acknowledgment. We thank Dr. Reiji Tanaka of Osaka City University for his very kind help and advice in the measurements
Thermodynamics of Ion Association in Aqueous Solutions of Calcium- and Magnesium-Substituted Hydroxybenzoates Using an Ion-Selective Electrode Technique Mostafa M. Emara,* Nazik A. Farid,? Ahmed M. Wasfi, Mohie M. Bahr, and Hassan M. Abd-Elbary Department of Chemistry, Faculty of Science, Al- Azhar University, Nasr City, Cairo, Egypt (Received: August 9, 1983; In Final Form: December 8, 1983)
The stoichiometricion-association constants,K, for Ca and Mg salts of m-hydroxy-, 3,5-dihydroxy-, and 3,4,5-trihydroxybenzoates have been measured at 25, 35, and 45 OC in aqueous NaCl or tetramethylammonium chloride solutions with a divalent ion electrode. The K values were converted to the infinite dilution, KA, values by standard activity coefficient methods. The value for o-hydroxybenzoateis included from a previous investigation and the general behavior of the association phenomena in the substituted hydroxybenozate was discussed. The trend in the K A values could not be explained on the basis of the pK, values of the parent organic acids of the corresponding salts for both Ca and Mg. However, it was possible to explain the results by using the Hammett, (r, function approach. Also, the thermodynamic parameters AGO, AHO, and ASo for ion pair formation of all salts were obtained.
prepared from 1 mol of sodium carbonate (AR) and 2 mol of the corresponding acids; for example
Introduction The use of ion-selective electrodes in the study of ion association in aqueous solution has been reviewedl very recently. In the past few years we have been concerned with carrying out measurements on the ion association phenomena of some important Ca and Mg salts using this novel t e c h n i q ~ e . ~ - ~ In some cases it was necessary to investigate the corresponding sodium salts, especially for organic sah6v7 In a few cases it was found that association took place between Na ions and the organic ligandsS8 To our surprise, for most of the organic salts we have investigated so far, formates, acetates, propionates, butyrates, benzoates, o-toluates, o-chlorobenzoates, and salycilates, there were no systematic good measurements available in the literature. Also it was found that no simple explanation could be offered for the association of the Ca and Mg salts of aromatic acids. However, we were able to find a reasonable approach to explain the thermodynamic behavior, the Hammett function approach.1° Hammett applied his approach to the dissociation phenomena of substituted benzoic acids. However, we have used it for the association phenomena of the substituted benzoate salts. The fact that it did succeed in explaining the results for o-toluate and o-chlorobenzoate caused us to carry out this present study on the substituted hydroxybenzoates, namely, the Ca and Mg salts of m-hydroxy-, 3,5-dihydroxy-, and 3,4,5-trihydroxybenzoate. Combining these results with those obtained earlier7 for calcium and magnesium benzoate and o-hydroxybenzoate gave a reasonable series for testing the Hammett function approach.
COOH
I
I
CO,
+
HO ,
(N.B. In the above salts we used sodium carbonate in the preparation and avoided sodium hydroxide to limit salt formation due to the carboxylic group.) Calcium chloride was from Cambrian chemicals. Magnesium chloride was a Merk reagent. Sodium chloride was a B.D.H. reagent. Solutions. Stock solutions of the above three salts were prepared with deionized distilled water. The exact concentration of each salt was determined by a flame photometer. Stock solutions of calcium chloride and magnesium chloride were prepared with deionized distilled water. The exact concentrations were determined with an ion-exchange resin procedure. Procedure. The divalent electrode was calibrated with standard calcium or magnesium chloride solutions as a reference. Sodium chloride was used to fix the ionic strength for both the reference and test solutions for m-hydroxybenzoate and 3,5-di(1) M.M.Emara, Ion. Sel. Electrode Rev., 4, 143 (1982). (2) M.M. Emara, C. T. Lin, and G. Atkinson, Bull. SOC.Chim. Fr., 5-6, 173 (1980). (3) M. M. Emara, N. A. Farid, and C. T. Lin, J . Chem. Ed., 56, 620 ( 1 979) -,(4) M.M.Emara, N. A. Farid, and G. Atkinson, Anal. Lert. All, 797 (1978). ( 5 ) M. M.Emara and N. A. Farid, Egypt. J . Chem., 22, 89 (1979). (6) M.M.Emara, N. A. Farid, and A. M. Wasfi, Electrochim. Acta, 26, 1705 (1981). (7) M.M.Emara, N. A. Farid, and A. M. Wasfi, Electrochim. Acta, 27, 647 (1982). (8) M. M. Emara, N. A. Farid, A. M. Wasfi, and H. M.Abd Elbary, submitted to Electrochim. Acta. (9) G. Atkinson, M.M. Emara, and R. Fernandez-Prini, J. Phys. Chem., 78, 1913 (1974). (10)L. P. Hammett, “Physical Organic Chemistry”, 2nd ed, McGraw-Hill, New York. 1970.
Experimental Section
\ - -
Apparatus. The potential measurements were made with a Radiometer Model P H M62 digital pH-mV meter equipped with a divalent cation membrane electrode (Orion Model 92-32) together with a single junction reference electrode (Orion Model 90-01). These two electrodes were immersed in a double-jacketed cell thermostated at the correct temperature. Materials. The sodium salts of m-hydroxybenzoic acid, 3,5dihydroxybenzoic acid, and 3,4,5-trihydroxybenzoic acid were ‘Egyptian Petroleum Research Institute, Nasr City, Cairo, Egypt.
0022-3654/84/2088-3345$01.50/0 0 1984 American Chemical Societv , , I
COONa
-
3346 The Journal of Physical Chemistry, Vol. 88, No. 15, 1984 TABLE I: pK, Values of the Parent Aromatic Acids for Salts Used in This Study at 25 O C
acid o-hydroxybenzoic acid 3,5-dihydroxybenzoic acid rn-hydroxybenzoic acid 3,4,5-trihydroxybenzoicacid benzoic acid
PKa 1 3.00 4.06 4.08 4.41 4.70
PKa2
+ A-
where [NaA] is the concentration of ion pairs, [Na+If is the concentration of free sodium ions, and [A-], is the concentration of free ligand ions. Assume the following: [ M 2 + ]= ~ [M2+]f+ [MA']
(9 9.93
MA+
+ [MA'] + [NaA] [NA+IT = [Na2+If+ [NaA]
[A-]T = [A-],
(ii) (iii)
hydroxybenzoate only. For 3,4,5-trihydroxybenzoate,tetramethylammonium chloride was used to fix the ionic strength for both the reference and test solutions. A linear calibration curve was obtained for the plot of emf against log activity of the corresponding ion giving the correct Nernst slope. Several measurements at each ionic strength were carried out at the proper temperature to give an average value for the stoichiometric constants. The measurements were carried out at 25, 35, and 45 "C. The proper Ca or Mg salts are obtained by mixing the sodium salts with calcium or magnesium chlorides in 2:l ratio. However, the concentration of the Ca or Mg organic salts never exceeded 0.20 M to assure the formation of 1:l ion pairs only. Mathematical Model. The association of CaZ+or Mg2+with m-hydroxybenzoate and 3,5-dihydroxybenzoate can be mono- or bidentate depending on the conditions of the experiment. For monodentate binding Mz+
Emara et al.
(1)
From the above assumption we can derive the following: [A-lf = [A-]T - [MA']
+ [NaA]
From eq 8 [NaA1 = K(NaA)[Na+lf[A-lf but [NaA] = [ N ~ + ]-T [Na+If
so [Na+lT - [Na+lf [A-I, =
K(NaA)[Naflf[A-lf
[Na+lT - [Na+lf K(NaA) INa+1f
substituting for [A-If in eq 6 yields K(MA+)=
[M2+1T- [M2+lf
where M2+ may be Ca2+or Mg2+, and A- may be m-hydroxybenzoate or 3,5-dihydroxybenzoate. The thermodynamic association constant KA is given by K(MA+)=
(3) where K is the stoichiometric association constant. f* is the mean activity coefficients of the corresponding species. If we assume that f*(MA+) = fh(A-), then eq 3 becomes KA = K/fh(M2')
(4)
In the above two salts there was no need to consider the association between sodium and the corresponding anion since no association takes place.s But for 3,4,5-trihydroxybenzoatewe found as shown in our previous works that there was association between the above anion and the sodium ion. The association of Ca2+ and Mg2+ with 3,4,5-trihydroxybenzoate can be mono- or bidentate depending on the conditions of the experiment. For the monodentate binding M2+
+ A-
MA+
(5)
where M2+ may be CaZ+or MgZ+,and A- is 3,4,5-trihydroxybenzoate. The stoichiometric association constant is
where [MA+] is the concentration of ion pairs, [MZ+]fis the concentration of free metal ions, and [A-If is the concentration of free ligand ions. Owing to the association with sodium Na+
+ A- + NaA
the stoichiometric association constant with sodium is
(7)
K(NaA)[Na+lf([M2+lT- [Mz+lfj [MZ+l!4[Na+1,- tNa+lfl
(9)
Since the conditions of the experiments permit only the first association to take place, the thermodynamic association constant (KA) can be calculated as follow:
where K is the stoichiometric association constant, and fA(Mz+) is the mean activity coefficient of the corresponding metal ion. Effect of Hydrolysis. It is well-known that both the anion and cation of each of these organic salts can be hydrolyzed in specific pH ranges. In this study the pH was fixed at a value to eliminate cationic hydrolysis. However, anionic hydrolysis could not be avoided and was corrected for by using the dissociation constants of the corresponding organic acid at the corresponding temperature. The corrected stoichiometric association constants, K,,,, were calculated with the following equation: K,,, = K( 1
+
F)
where [H'] is the concentration of hydrogen ions in solution, and Ka is the dissociation constant of the organic acids (Table I). The thermodynamic association constant reported in Tables IV and V are obtained directly from the K,,, shown in Tables I1 and 111. KA values are therefore in the corrected form. Results and Discussion Looking at the obtained data one can deduce the following. (i) The associations in Ca aromatic salts (m-hydroxybenzoate, 3;5-dihydroxybenzoate, and 3,4,5-trihydroxybenzoate)are generally greater than the corresponding Mg salts. We know that from an electrostatic point of view ion association decreases as the cation size increases. Accordingly, one would have expected more stable Mg than Ca ion pairs. However, the stability of ion pairs decreased in the order CaZ+ > Mgz+ for all ligands under
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984 3347
Ion Association in Substituted Benzoates TABLE II: Stoichiometric Association Constants of Ca Salts Using CaCI, as a Standard Solution in Aoueous NaCl and
strength,
M
m-hydroxybenzoate'
0.15 0.20 0.25 0.30
13.05 11.95 10.88 10.00
0.15 0.20 0.25 0.30
14.15 12.78 11.76 10.19
0.15 0.20 0.25 0.30
15.02 13.80 12.37 10.85
3,5-dihydroxybenzoate'
T = 25 'C 10.99 10.14 9.15 8.35
3,4,5-trihydroxybenzoateb 16.16 15.94 15.57 15.27 17.04 16.66 16.21 15.64
T = 45 'C
@
In aqueous NaCl.
12.56 11.78 10.50 9.47
benzoate 3,5-dihydroxybenzoate 3,4,5-trihydroxybenzoate benzoateu
T = 35 'C 12.10 11.37 9.91 8.87
TABLE IV: Thermodynamic Parameters of Ca Salts at Various Temoeratures
19.36 18.57 17.17 16.35
o-hydroxybenzoate" (salycilate)
~
M
m-hydroxybenzoate'
0.15 0.20 0.25 0.30
6.59 6.16 5.62 4.95
3,5-dihydroxybenzoate' T = 25 OC 4.73 4.40 3.52 3.19
0.15 0.20 0.25 0.30
7.55 7.20 6.5 1 6.21
T = 35 'C 5.75 5.49 4.75 4.11
0.15 0.20 0.25 0.30
8.59 7.80 7.10 6.68
3,4,5-trihydroxybenzoateb 12.72 12.48 12.25 12.06 13.68 13.65 13.03 12.40
T = 45 'C
@
In aqueous NaC1.
6.89 6.00 5.38 4.89
15.36 14.50 14.32 13.39
In tetramethylammonium chloride.
investigation. The lower stability of the Mg2+ ion pairs compared with Ca2+ is due to mainly to an unfavorable enthalpy term; the order of decreasingly favorable enthalpies is CaZ+> Mg2+. It is assumed from the various experiments of the relaxation methods on systems similar to those under investigationg that association takes place with the hydrated cations, in which the water is arranged more easily around the ions with smaller size and then the enthalpies decrease with increasing size. The association is then accompanied by the loss of hydration, resulting in an increase in the disorder of the system. Entropy changes will be greater with smaller cations. These are most likely the reasons behind the higher values for the thermodynamic association constants of Ca over the Mg salts. (ii) In all salts under investigation, the thermodynamic association constants increased as the temperature increased, which indicates that these association processes are endothermic. (iii) We include the data obtained from our previous investigation7 on the o-hydroxybenzoate and para-substituted benzoate (Tables IV and V) and then try to generalize the behavior of the association phenomena in the substituted hydroxybenzoate salts of both Ca and Mg. For Ca salts we observe that association
9.07 9.53 8.19 8.69 9.11 9.41 9.82 10.37 7.52 7.98 8.36 9.87 10.28 10.78
2.34 2.34 2.34 2.34 2.34 2.17 2.17 2.17 2.10 2.10 2.10 1.57 1.57 1.57
37.0 37.3 35.4 35.8 36.0 38.9 39.0 39.4 32.3 32.7 32.9 38.4 38.4 38.8
TABLE V: Thermodynamic Parameters of Mg Salts a t Various Temoeratures
In tetramethylammonium chloride.
TABLE III: Stoichiometric Association Constants of Mg Salts Using MgCI, as a Standard Solution in Aqueous NaCl and Tetramethylammonium Chloride at Various Temperatures and Ionic Strengths K,,, L M-' ionic
34.44 36.66 27.24 29.77 3 1.24 44.56 46.38 50.47 21.00 22.50 23.80 53.90 55.30 59.10
"Data for these two salts are taken from ref 7.
salt
strength,
35 45 25 35 45 25 35 45 25 35 45 25 35 45
m-hydroxybenzoate 3,5-dihydroxybenzoate 3,4,5-trihydroxybenzoate benzoatea o-hydroxybenzoate@ (salycilate)
T. "C 25 35 45 25 35 45 25 35 45 25 35 45 25 35 45
KA -AGO, M-I kJ mol-' 14.05 6.56 16.51 7.19 18.19 7.69 9.23 5.56 12.11 6.40 13.95 6.98 29.91 8.44 31.86 8.86 34.75 9.41 12.20 6.19 14.20 6.77 15.80 7.27 39.20 9.07 41.90 9.57 44.20 9.99
AS',
AH', kJ mol-'
J (mol K)-I
4.51 4.51 4.51 6.48 6.48 6.48 2.68 2.68 2.68 4.35 4.35 4.35 2.04 2.04 2.04
37.2 38.0 38.4 40.4 41.8 42.3 37.3 37.5 38.0 35.3 36.1 36.5 37.3 37.7 37.9
'Data for these two salts are taken from ref 7.
decreases in the order o-OH > 3,4,5-tri-OH > rn-OH > 3,5-di-OH > benzoate. However, for the Mg salts the observed trend is o-OH > 3,4,5-tri-OH > m-OH > benzoate > 3,5-di-OH. In order to explain such behavior, two main approaches were used in our previous investigation and will be applied here once again. In the first approach we make use of the well-known pK, values (Table I) for the corresponding parent acids of the salts under investigation. According to these values, one would expect that both Ca and Mg behave similarly and the association phenomena decreases in the order o-OH > 3,5-di-OH > m-OH > 3,4,5-tri-OH > benzoate which by no means is the observed results from either the calcium- or the magnesium-substituted hydroxybenzoates. If, on the other hand, we apply the second approach, namely, the linear free energy relationship (LFER), the following results. The Hammett'O eq 12 relates structure to the equilibrium constants for the reactions of substituted benzene derivatives. The Hammett relationship which is been applied to acids and in some cases to salts (e.g., substituted benzyl chlorides) stipulates that the equilibrium constant associated with the reaction of any one of the substituted acids or salts may be determined from the corresponding equilibrium constant of the parent acid or salt, if a parameter known as Hammett u function is known. This parameter is characteristic only of the substituent and represents the ability of the group to attract or repel electrons by a combination of its inductive (I) or resonance (R) effects where K and KOare the stability constants of the substituted benzoic acids, respectively.
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
