3341
J. Phys. Chem. 1984, 88, 3341-3345
Conductometric Study of Some Metal( I I ) Perchlorates in Methanol Hidekazu Doe,* Toyokichi Kitagawa, Department of Chemistry, Faculty of Science, Osaka City University, Sumiyoshi- Ku, Osaka 558, Japan
and Kiyomi Sasabe Japan Food Research Laboratories, Suita, Osaka 564, Japan (Received: August 5. 1983; In Final Form: Jpnuary 17, 1984)
The ionic association constants of bivalent metal perchlorates, M(C10J2 (M2+ = Ca2+,Sr2+,Ba2+,Co2+,Ni2+,Cu2+,Zn2+, Cd2+),have been determined by conductometric measurements in methanol at 5, 15, 25, 35, and 45 " C . Only the constants for the ion pair of M2+-C10L, KIA, have been studied and the thermodynamic functions, mlAe and ASIAe, for the formation of that ion pair have also been obtained at 25 O C . The conductometric data were analyzed according to the Fuoss and Edelson method. The magnitude of KIA is in the order of Ba > Sr > Ca for alkaline-earth metals and in the order of Co > Ni > Zn for transition metals. The KIA values of Cd2+are similar to those of Zn2+,and those of Cu2+are large, deviating slightly from a smooth and monotonic decrease in KIA of the transition metals with atomic number. On the whole, the KIA values of the alkaline-earth metals are larger than those of the transition metals and so are the degrees of increases in K I Awith temperature with the exception of Cu2+. The KIA of Cu2+ shows a maximum temperature dependence. Both AHIAe and M l A efor all the salts, which are evaluated from their temperature dependences of KIA, are positive values and are in relatively good agreement with those calculated by Fuoss' theory on ionic association. That is to say, the ionic associations of these salts are the reactions of unfavorable enthalpy and favorable entropy changes in methanol. On the other hand, the Walden products, Aoq, of the salts, except for Cu(C10J2, decrease slightly with an increase in temperature at 5-45 O C .
Introduction In the studies of electrolytic solutions, it is often necessary to keep ionic strength, I , constant without affecting other chemical equilibria in the solutions. Popularly perchlorate salts have often been used to attain this purpose because of their great ability to dissociate into ions. In nonaqueous solvents with small dielectric constants-so-called low ionic media-however, even such perchlorate salts exhibit ionic associations to some extent. Actually some interference from the associations has been observed in our research studies of the formation of complexes in some nonaqueous solvents by using perchlorate salts to control the ionic It is only natural that this interference causes systematic errors in the chemical quantities we want to measure. Therefore, in order to remove the interference we have begun studying ionic associations in nonaquesous solvents by using the techniques of conductometry and other method^.^,^ Zinc halide complexes have relatively poor stabilities and they exhibit cooperativities at a step in their stepwise complexation in some solution^.^-^ Taking an interest in such cooperative phenomena, we have been studying the halide and thiocyanate complexes of Ni2+,CoZf,and Cuz+ in addition to ZnZ+by using Clodas an ionic medium. Thus, it has become necessary to investigate the ionic associations of these metal perchlorates in methanol. In addition, the transition metals have been compared with some alkaline-earth metals which are harder acids and weaker in solvating ability, in order to obtain some information on the conditions of the metal(I1) ions in methanol containing Clod-. Experimental Section Chemicals. Cobalt(I1) and nickel(I1) perchlorate hexahydrates were prepared from the corresponding nitrates, and copper(II), zinc(II), and cadmium(I1) perchlorate hexahydrates were from copper hydroxide and zinc and cadmium carbonates, respectively. (1) (a) Doe,H.; Matsui, M.; Shigematsu, T. Bull. Imt. Chem. Res., Kyoto Uniu. 1979,57, 343. (b) Doe, H.; Matsui, M.; Shigematsu, T. Ibid. 1980.58, 133. (2) Doe, H.; Matsui, M.; Shigematsu, T. Bull. Inst. Chem. Res., Kyoto Uniu. 1980, 58, 154. (3) (a) Doe, H.; Kitagawa, T. Inorg. Chem. 1982, 21,2272. (b) Doe, H.; Shibagaki, A.; Kitagawa, T. Ibid. 1983, 22, 1639. (4) Hoffmann, H. Pure Appl. Chem. 1975, 41, 327. (5) (a) Ahrland, S.;Bjork, N.-0. Acta Chem. S c a d . , Ser. A 1976,30,265. (b) Ahrland, S.; Bjork, N.-0.; Portanova, R. Ibid. 1975,30,270. (c) Ahrland, S . Pure Appl. Chem. 1979, 51, 2019.
0022-3654/84/2088-3341$01.50/0
TABLE I: Densities, Viscosities, and Dielectric Constants of Methanol at 278.15-318.15 K 278.15 K 288.15 K 298.15 K 308.15 K 318.15 K
density, g cm-3 viscosity,
0.8050"
0.7958"
0.78656
0.7772"
0.7677'
0.7261
0.6244
0.5422
0.4742
0.4174
36.88
34.70
32.66
30.74
28.92
CP
dielectric constantb
"Calculated values. bFrom ref 10. Calcium(I1) perchlorate trihydrate and strontium(I1) perchlorate dihydrate were prepared from the corresponding carbonates. These perchlorate salts were made by neutralizing the corresponding starting materials with perchloric acid.6 Anhydrous barium(I1) perchlorate was a commercially available material (Wako, special grade). The perchlorate salts were purified by at least triple recrystallization from distilled water and were dried on a vacuum line over silica gel for several hours and were used to prepare stock solutions in methanol. The individual stock solutions were standardized by titration with EDTA. Methanol was dried over 3A molecular sieves and distilled fractionally. The electric conductivity of the purified methanol was 1.5 X lo-' f2-l cm-I and the water content was found to be 0.023 wt % by gas chromatography. All other chemicals were special-grade materials (Wako) . Physical Properties of Methanol. The density of 25 OC was determined by a vibrating densimeter (Model OlD, Sodev Inc., Sherbrooke, Canada) using chlorobenzene and methylcyclohexane as standards.' The accuracy of measurement was f 2 X low5g ~ m - ~Those . at the other temperatures were calculated from the equation of u = uo (1 alt azt2 a3t3)where u and u,, are the volumes of solvent at t and 0 OC, respectively. The values of a2 = 1.3635 X lod, expansion coefficients are a1= 1.1342 X and aj = 0.8741 X 10-8.s Viscosities were conventionally measured with an Ostwald viscometer. Water was used as a standard s u b ~ t a n c e . ~The
+
+
+
(6) Chemical Society of Japan. "Shin Jikken Kagaku Koza"; Maruzen: Tokyo, 1976; Vol. 8, Parts 1-3. (7) Tanaka, R. Netsu Sokutei 1979, 6, 2. (8) Chemical Society of Japan. "Kagaku-binran", 2nd ed.; Maruzen: Tokyo, 1975; Vol. Fundamentals, pp 687.
0 1984 American Chemical Society
3342 The Journal of Physical Chemistry, Vol. 88, No. 15, 1984
Doe et al.
TABLE 11: Limiting Equivalent Conductances (n-' cmz mol-') of M(Cl04)z and CIO, in Methanol at 278.15-318.15 K lim equiv conductance, Q-' cm2 mol-'
M
278.15 K 99.30 f 0.146 94.94 =k 0.1 18 101.95 f 0.145 99.22 f 0.123 99.82 f 0.041 98.12 f 0.102 96.57 f 0.089 98.51 f 0.103 52.9
Ca
Sr" Baa co Ni cu Zn Cd"
c104'a =5
288.15 K 115.25 f 0.167 110.23 f 0.150 118.37 f 0.210 114.81 f 0.099 115.53 f 0.067 113.78 f 0.125 111.72 f 0.108 114.16 f 0.119 61.2
298.15 K 132.12 f 0.205 126.45 f 0.199 135.62 f 0.205 131.45 f 0.103 132.23 f 0.066 130.56 f 0.123 127.88 f 0.126 130.51 f 0.132 70.1b
308.15 K 150.80 f 0.256 144.34 f 0.244 154.63 f 0.250 150.08 f 0.100 151.07 f 0.145 150.12 f 0.237 146.19 f 0.116 148.96 f 0.183 80.1
318.15 K 171.21 f 0.339 163.92 f 0.332 175.36 f 0.285 170.39 f 0.188 171.59 f 0.137 171.83 f 0.360 165.74 f 0.125 169.12 f 0.128 90.9
A. bFrom ref 13.
TABLE III: Ionic Association Constants, KIA(M-I), of M(C104)2 in Methanol at 278.15-318.15 K
M
278.15 K
288.15 K
K I A ,M-' 298.15 K
308.15 K
318.15 K-
Ca
77.98 f 6.06 117.9 f 5.17 173.8 f 6.91 75.86 f 6.67 59.94 f 2.15 62.38 f 4.83 44.52 f 5.13 45.05 f 4.11
98.54 f 6.24 146.9 f 5.94 217.5 f 9.10 84.88 f 4.80 68.26 f 3.07 75.74 f 5.27 50.00 f 5.56 55.76 f 5.21
123.1 f 7.01 186.0 f 7.32 269.7 f 8.26 101.0 f 4.53 81.88 f 2.74 95.70 & 4.74 64.25 f 5.90 66.34 f 5.40
153.9 f 8.10 233.3 f 8.37 334.3 f 9.39 119.6 f 3.98 100.3 f 5.54 129.1 f 8.38 81.75 f 4.94 84.06 f 4.73
195.2 f 10.1 298.8 f 10.8 421.3 f 10.2 143.3 f 6.91 126.1 z!= 4.81 176.0 f 11.8 99.44 f 4.87 109.7 f 4.39
Sra Baa co Ni cu
Zn Cd"
'
temperature of the thermostat was controlled within the accuracy and precision of f0.05 and fO.O1 OC, respectively. The dielectric constants were cited from Albright and Gosting.Io The physical properties of methanol are summarized in Table I. Electric Conductances. The measurements were carried out with Yanagimoto Model MY-8 conductivity outfit and a type C cell. This closed cell was thermostated at the respective temperatures with an accuracy of > Kzk Therefore, they established a theory on the assumption that KIA >> K Z Aand proposed the following equation: AF =
A0
- XKIA/AO
(3)
where X F = ((1 -
cy2+AF(AF - Ao/2)
+ (A0 - X,J/2A)/(l + (A0 - Xo)/2Ao)
(9) Korosi, A.; Fabuss, B. K. Anal. Chem. 1968, 40, 157. (10) Albright, P. S.; Gosting, L. J. J . Am. Chem. SOC.1946, 68, 1061. (11) Fuoss, R. M.; Edelson, D. J . Am. Chem. SOC.1951, 73, 269.
where A and A. are the equivalent and the limiting equivalent conductances, respectively, Xo is the limiting equivalent conductance of C104-, 6 is Onsager's slope, divided by A. and c is the molar concentration of C10,. The ion activity coefficient of M2+, y2+, was estimated by the Debye-Huckel second approximation (eq 4). For the ion size parameter of M2+,a, we have assumed
+
log y = - A I Z , ~ ~ Z '1/ ~ /Ball/') (
(4)
the value of 5 %, for Sr2+, Ba2+, and Cd2+ and 6 %, for the other metal ions which are often adopted for those in water.I2 The value of X,is 70.1 Q-' cm2 mol-' in methanol at 25.0 OC.13 Since, however, we have no available data about the X{s at the other temperatures, we have calculated them on the basis of the value of 70.1. To begin with, the value of A. at a given temperature except 25 OC is calculated with an arbitrary estimate of Xo according to eq 3 that is solved for the two unknown parameters KIA and A. by an iterative procedure. In this way, we have determined the &'s of C O ( C ~ O ~ Ni(C104)2, )~, and ZYI(C~O~)~ at the temperature. Then, the second estimate of Xo is calculated by mutiplying the ratio of the mean value of their A{s at the temperature to that at 25.0 "C by 70.1. The above procedure is then iterated until Xo becomes a constant value. It is not then necessary that Xo be determined very accurately, partly because the KIA's, that we can evaluate, involve relatively large errors and partly because Xo does not control the values of KIA and A. strongly. With the Xo value evaluated by averaging the data for C O ( C ~ O Ni(C10J2, ~)~, and Zn(C104)2,the KIA and A. of the other M(C104)zare determined at the temperatures except for 25 "C. Figure 1 shows the plots according to eq 3 for Co2+,Ni2+,Cu2+, and ZnZt systems at 25 "C. The results from such plots are summarized in Tables I1 and 111. The values of X,are also given in Table 11. The errors in the tables are the standard deviations. The standard enthalpy changes, AHIAe, of the reaction of eq 1 at 25.0 "C are closely related to the tangents of plots of In KIA against T I at the temperature, as expressed by the equation of d(ln K)/d(T') = -AZP/R. In order to evaluate the AHlA*,we have fitted the equation of AGIAe = -RT(ln KIA) = A + BT + C p to the KIA values and computed the optimum values of A , B, and C by the least-squares method.14 Then, AHIAeis A - C p (12) Kielland, J. J. Am. Chem. SOC.1937, 59, 1675. (13) Conway, B. E. "Electrochemical Data"; Elsevier: Amsterdam, 1952. (14) Fujishiro, R.; Wada, G.;Tamamushi, R. 'Yoeki-no-seishitsu"; Tokyo-kagaku-dojin: Tokyo, 1968; Vol. 2, pp 58, 121.
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984
Metal(I1) Perchlorates in Methanol
\
1251
1
2
6
4 X
1
Figure 1. Fuoss and Edelson plots for the metal(I1) perchlorates at 25 "C: (0)Co(I1); ( 0 )Ni(I1); (0)Cu(I1); (A) Zn(I1).
I
I
\ 3.0 3.5 T-' x
lo3
Figure 2. In K,, vs. T1 plots for the metal(I1) perchlorates: (0)Sr(I1); (e)Cu(I1); ( 0 )C O W ) ; ( 0 )Cd(I1).
TABLE I V Results of Thermodynamic Functions for Ion Pairs of M2+-C10L in Methanol at 298.15 K
AHIAe,
M
kJ/mol
Ca Sr" Bao
16.85 f 1.52 17.19 f 0.93 16.29 f 0.79 12.12 f 1.58 13.95 f 0.93 19.46 f 1.67 15.53 f 2.09 16.36 f 1.69
Co Ni Cu
Zn Cd" " a .- 5
3343
.aslAe?
J/(K mol) 96.5 f 101.1 101.2 f 79.0 f 83.4 f 103.3 f 86.8 f 89.8 f
*
5.11 3.14 2.65 5.30 3.14 5.61 7.07 5.72
-GAe, kJ/mol 11.93 f 0.141 12.95 f 0.098 13.88 f 0.076 11.44 f 0.111 10.92 f 0.083 11.31 f 0.123 10.32 f 0.228 10.40 f 0.202
A.
and ASIAe is -B - 2CT. The representative plots of In K I A against T 1are shown in Figure 2. The figure involves curves calculated with the optimum A , B, and C. The values of MIAe and ASIAe are summarized in Table IV with their standard deviations. The deviations of MIAe are calculated with those of K I A in the same way the deviation of a slope in the linear least-squares method is calculated, because - A H I A e / Ris the slope of the tangent line (at 25.0 "C) of a curve in Figure 2. The deviations of ASIAe are calculated from those of MIAe according to the propagation rule of errors.
Discussion As shown in Table 11, the & values of all the salts are relatively similar, and the values are in a reasonable range expected from
1
I
I
I
I
I
I
1
Sr Bcr Co Ni Cu Zn Cd Figure 3. Graphical summary of the ionic association constants of the metal(I1) perchlorates: (0) 5, (0)15, ( 0 ) 25, ( 0 ) 35, ( 0 ) 45 OC. Co
some literature source^.^,^^,^^ However, it seems that the values of Ba(C104)2 are slightly large even after several careful recrystallizations. We are unable to find any outstanding tendencies in the A. values. However, there is a common characteristic in Walden products, Aoo, that, except for C U ( C ~ O the ~ ) ~Aov , values of M(C104)2decrease with an increase in temperature at 5-45 OC. The degrees of decrease in Aoo are very small; they are about 1% decreases on going from 5 to 45 OC. The no?of C U ( C ~ O ~ ) ~ also decreases very slowly till 25 OC, but then it breaks into an increase above 25 OC. The decreases in hoq with temperature, which are often found in the data for water solution^,'^ will probably be interpreted as a thermal expansion of the solvent sheath (which envelopes an ion and moves with it by ion-solvent interactions), that is, the expansion of a solvated ion, because of the activation of solvent molecules forming the sheath. In contrast to the hovalues, there are very marked characteristics in the K I A values (Table 111). In order to show the characteristics clearly, Figure 3 has been prepared. Now, some of them can be interpreted with one concept fairly well. In general, all the ionic species involved in eq 1 are solvated to various extents. In this work, it will be necessary to call attention to the solvations of M2+ and MC104+. It has been found that there is a close relationship between the K I A values and the strength of solvation of M2+; that is, the stronger M2+ is solvated, the weaker the association between M2+ and C104- becomes in methanol. From ion solvation free energies and free energies of transfer of metal ions in water and methanol, it will be certain that the M2+solvation free energies of these metal ions in methanol are a little larger than those in water (about 50 kJ/mol), though not all the data for the metal ions are available in methanol.I6 Thus, the K I A values will be discussed in light of M2+ hydration free energies at 25 OC.I7 The M2+ hydration free energies, Ache, steadily decrease in theorder of Ba (-1317 kJ/mol) > Sr > Ca > Cd (-1799 kJ/mol), and then those of the first-row transition-metal ions are similar to each other, in the order of Co (-2004 kJ/mol) > Zn > Ni > Cu (-2080 kJ/mol) at 25 O C . I 7 The K I A values also steadily decrease in the order Ba > S r > Ca > Cd, and there is a good linear relationship between AGIA' (=-RT In K I A ) and Ache as shown in Figure 4. On the other hand, the A G I A e values of the firest-row transition-metal ions, in spite of their smaller Ache than Cd2+'s, are about as large as, or a little smaller than, that of Cd". As shown in Figure 4,there is no relationship between A G I A e and (15 ) Jan,, G. J.; Tomkins, R. P. T. "Nonaqueous Electrolytes Handbook"; Academic Press: New York, 1972; Vol 1. (16) Burgess, J. "Metal Ions in Solution"; Ellis HoFwood: Chichester, 1978; Chapter 7. (17) Rosseinsky, D R. Chem Rev. 1965, 65, 467
3344
The Journal of Physical Chemistry, Vol. 88, No. 15, 19‘84 14-
-
13-
2.. \
2 +12:-
5 a
3 t
11 -
- 2 -
IO 1.5
1 -A
~,-,,-,xlO-~( kJ/md 1
2
Figure 4. Correlation between the ionic association and the M(I1) ion hydration free energies for the metal perchlorates at 25 OC: (0) Ca(I1); ( e )Sr(I1); (0)Ba(I1); (0) Co(I1); (E) Ni(I1); (a) Cu(I1); (H) Zn(I1); (A) Cd(I1). Error arrows indicate f a .
AGhe in the range of AGhe less than that of Cd2+. Hence, it is first thought that the solvation energies of ions are a very important factor in controlling ionic associations effectively, when the solvations of the ions are weak to some extent. On the contrary, when ions have the solvation energies below a critical value and are stably solvated to a certain extent, the magnitude of K I A is mainly controlled by some other factors which are not as effective as that from the solvation energies. In our systems (M2+-C104- in methanol), the critical value of AGhe is about -1800 to -1700 kJ/mol. We do not know what physical picture of the ion pair of M2+-C104- can explain these results well. As shown in the results of X-ray diffraction it seems that though the primary solvent molecules (which directly interact and bond with an ion) of the alkaline-earth metal ions are not aligned in an orderly manner in water, six water molecules are aligned in order around the transition-metal ions except Cu2+with an octahedral structure. A Jahn-Teller distorted octahedron has been observed for the structure of the primary hydration shell of Cu2+.19 These structures of solvation observed in water solutions will probably appear in methanol solutions ~imilarly.~ Thus, it will be inferred that the primary solvation shells of the transition-metal ions, which have smaller solvation free energies than the critical value and have relatively firm shell structures, are not deformed very much by ion pairing. That is to say, the main species in such systems may be a so-called solvent-separated ion pair.21 As shown later, by using the solvent-separated value, 7.4 A, for the M2+-C104distance of the transition-metal systems, AGIAe are calculated by Fuoss’ theoryz2 to be in fair agreement with the experimental values (Table IV). As for the alkaline-earth metals, on the other hand, ClO, may enter into the soft primary solvation shell of M2+ having a large solvation free energy (a weak solvation), or a part of C104- ions forming the ion pairs with M2+ ions may be substituted for solvent molecules in the primary solvation shells and the others may be outside the shells. Here, we have to describe the trend in the KIAvalues of the first-row transition metals (Figure 3). As is clear in the figure, the K I A tends to decrease with atomic number, but only the K I A values of Cu2+ are exceptionally large in the trend. Though we cannot correctly explain the decreasing trend in K I A now, we think that the large KIAvalues of Cuz+are related to the Jahn-Teller ~~~
~
(18) (a) Albright, J. N. J. Chem. Phys. 1972, 56, 3783. (b) Licheri, G.; Piccaluga, G.; Pinna, G. Ibid. 1975, 63, 4412. (c) Hewish, N. A,; Neilson, G. W.; Enderby, J. E. Nature (London) 1982, 297, 138. (19) (a) Ohtaki, H.; Yamaguchi, T.; Maeda, M. Bull. Chem. SOC.Jpn. 1976, 49, 701. (b) Magini, M. J. Chem. Phys. 1981, 7 , 2523. (20) Ohtaki, H.; Maeda, M.; Ito, S.Bull. Chem. SOC.Jpn. 1974, 47, 2217. (21) Matesich, S.M. A.; Nadas, J. A.; Evans, D. F. J. Phys. Chem. 1970, 74, 4568. (22) Fuoss, R. M. J . Am. Chem. SOC.1958, 80, 5059.
Doe et al. distortion of its hydration shell. There will be two possible explanations; the first one is that a ClO,- ion can approach very closely from an equatorial side where the bonds between Cu2+ and its four primary solvent molecules, equatorial bonds, are strong and short, and the second one is that a C104- ion attacks one of two axial solvent molecules which are bound to Cu2+weakly with a long Cuz+-solvent distance, axial bonds. The second explanation suggests that there is some probability of the substitution of C10, for the axial solvent. The large values of AHIAe and ASIAefor Cu2+(Table IV) may also indicate that the ion pairing weakens the axial bonds considerably. According to the results of thermodynamic functions in Table IV, we will discuss the ionic associations in more detail. If we consider that from a rudimentary standpoint the ion pair is formed with only the action of the Coulombic force in a continuum medium, both the values of A I P and ASe of the ion-pair formation will be negative. In general, however, the solvation of ions is weakened as soon as the ion pair is formed. This situation turns out to increase in both A P and ASe. Therefore, all the experimental values of AHIAeand ASIAein Table IV are positive. On the other hand, these thermodnamic functions can be theoretically calculated by Fuoss’ electrostatic theory on ionic association.22 The distance between M2+ and C10,- is necessary to perform the calculation. Then the following estimation will be possible for the distance of the first-row transition metals in methanol. If the distance between a central M2+ ion and the oxygen atom involved in the primary methanol molecules, a M2+-oxygen distance of the solvated M2+, is about 2.1 A b analogy with that in waterlg and the radius of C H 3 0 H is 2.5 from its molecular volume, the radius of M(CH,0H),2+ is 4.6 A. The radius of C104- is about 2.8 A from the sum of 1.43 A for C1-0 distancez3and 1.4 for the van der Waals radius of the oxygen atom.24 Thus, if the ion pair is perfectly separated with the primary solvent molecules, the distance between M2+and C104- is about 7.4 A. At this distance, the calculated AHiA’, ASIAe, and AGiAe are 9.4 kJ/mol, 70.2 J/(K mol), and -1 1.5 kJ/mol, respectively. In comparison with the results in Table IV, it is very surprising that his theory has predicted the thermodynamic functions reasonably well. It is especially interesting that his rudimentary theory has given AHIAeand ASIAepositive values. When one calculates and Me of an ion-pair formation with his theory, one needs data on the temperature dependence of dielectric constants, d(ln E)/d(ln T ) . According to the experimental values of d(ln c)/d(ln T), there are few solvents which make the theoretical values of A P and/or ASe negative. Though, for instance, is negative when d(ln c)/d(ln r ) > -1-almost all of the solvents used for the investigation of electrolytic solutions do not meet the requirment-the d(ln c)/d(ln T ) value of methanol is -1.816. As already mentioned, because the solvation of ions is weakened by ion pairing, the values of A P and ASe become large, That is to say, his theory has unconsciously predicted that the ionic solvation is weakened by ion pairing because of some complicated physical meaning involved in the temperature dependence of dielectric constants. In addition, the fact that his theory predicts well the values of AHIAeand ASIAe may mean that there is a relation between dielectric constants and the strength of the ionic solvation in methanol. Though there are still several characteristics in the results in Table IV, we will need too many data to explain them. At least, however, we will be able to form an opinion for the difference between the alkaline earths and the transition metals except Cu2+. On the average, AHIAe and ASIAe of the alkaline-earth metals are larger than those of the transition metals in spite of the fact that the alkaline-earth metals form more stable ion pairs. This means that the alkaline-earth metals greatly weaken the solvation of M2+caused by the formation of MC104+ in comparison with the transition metals. In any event, it is evident that C104- exhibits stronger interaction with the primary solvent molecules and ap-
i
(23) Michelsen, K . Acta Chem. Scand. 1952, 6, 1289. (24) Pauling, L. “The Nature of the Chemical Bond”, 3rd ed.; Cornell University Press: Ithaca, NY, 1960.
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
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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
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