8956
J. Phys. Chem. 1991, 95, 8956-8963
Temperature Dependence of the Ion Association between Hexaamminecobalt(III ) Ion and Monovalent Anions Haruhiko Yokoyama* and Hiroyuki Kon Department of Chemistry, Yokohama City University, Seto, Kanazawa- ku, Yokohama 236, Japan (Received: April 29, 1991; In Final Form: July 16, 1991) Conductivity measurements at temperatures between 0 and 50 O C were made for aqueous solutions of the chloride, bromide, iodide, nitrate, and perchlorate of hexaamminecobalt(II1)complex. The ion association constants (KA)obtained had minimum values at temperatures (rmin) characteristic of the anions. The fmin increased in the order CI- < Br- < I- < NO3- CI04and correlated with standard entropy and enthalpy of ion association. The order in the magnitude of KA among the salts was variously dependent on temperature, e.g., I- < C104- = Br- = CI- < NO3- at 0 OC and I- = C104- < Br- < NO3- = CI- at 25 OC, but, with increasing temperature, it seemed to approach the electrostatic prediction: C104- < I- < NO3- < Br- < CI-. The presence of tmin for the halides was explained to be due to the weak hydrations of the anions related to their structure-breaking properties. The remarkable increases of the K A valuesu with decreasing temperatures for the nitrate and the perchlorate and the relatively small positive entropy changes compared with those for the halides were ascribed to specific short-range interactions between ammine ligands of the complex and oxygen atoms of the anions in the contact ion pairs. Introduction
Wide temperature-range conductivity measurements for electrolyte solutions can give detailed information on ion-ion and ionsolvent interactions.'" From the conductivity measurements between 0 and 50 OC for aqueous potassium nitrate and potassium perchlorate solutions, we found that weak ion-ion interactions were present and that the ion association constants were minimized at characteristic temperatures.' These phenomena could not be explained soley by the electrostatic theories of ion association and were interpreted by assuming specific short-range interactions between the ions due to their weak hydrations. The ion associations between tris( 1 ,IO-phenanthroline)iron(II) ion and arenedisulfonate ions included not only usual electrostatic and hydrophobic interactions but also exothermic interactions between the aromatic ring of the anion and that of the ligand of the complex ion.2 The short-range interactions of cis-bis(ethy1enediamine)dinitrocobalt( 1 +) ion with (ethy1enediaminetetraacetato)cobaltate( I-) ion or (ethylenediamine)bis(malonato)cobaltate( 1-) ion was considered to be due to hydrogen bonding between hydrogen and oxygen atoms of the ligand^.^^^ Barthel and his coworkers6 discussed the effect of non-Coulombic forces on ion association of 1 :1 electrolytes using conductivity measurements of nonaqueous solutions at temperatures between -45 and 25 OC. The outer-sphere ion association of hexaamminecobalt(II1) ion, [Co(NH3)J3+, with various anions has been widely investigated by various methods,'-" but not including their temperature dependence or the nature of the interactions, although this complex is one of the simplest available. The UV spectrum changes in aqueous solutions of the iodide can be attributed to the formation of contact ion pairs in the outer sphere of the complex ion.I3 When the ions are in contact with each other, some specific short-range interactions may be involved. Exact conductivity measurements over a wide temperature range are expected to provide useful information concerning such interactions. In the present study, electric conductivities of aqueous solutions of the chloride, bromide, iodide, nitrate, and perchlorate of hex( I ) Yokoyama, H.;Ohta. T. Bull. Chem. Soc. Jpn. 1988,61, 3073. ( 2 ) Yokoyama, H.; Koyama, Y.; Masuda, Y. Chem. Leu. 1988, 1453. (3) Yokoyama, H.; Ohta, T. Bull. Chem. SOC.Jpn. 1989, 62, 345. (4) Yokoyama, H. Bull. Chem. Soc. Jpn. 1984, 57. 1304. ( 5 ) Yokoyama, H.; Nishimura. M. Bull. Chem. Soc. Jpn. 1985,58, 1094. (6) (a) Barthel, J.; Neueder, R.; Feuerlein, F.; Strasser, F.; Schmeer, G.; Iberl. L. J. Solution Chem. 1983, 12, 449. (b) Barthel, J.; Wachter, R.; Schmeer, G.; Hilbinger, H. J . Solution Chem. 1986, 15, 531. (7) Jenkins, 1. L.; Monk, C. B. J . Chem. SOC.1951, 68. (8) Tamamushi, R.; Isono, T.; Katayama, S . Bull. Chem. SOC.Jpn. 1967. 40, 334. (9) Katayama, S.;Tamamushi, R. Bull. Chem. SOC.Jpn. 1968,4/, 606. (IO) Takahashi, T.; Koiso, T. Bull. Chem. SOC.Jpn. 1978, 51, 1307. ( I I ) Elder, A.; Petrucci, S. Inorg. Chem. 1970, 9, 19. (12) Norden, B. Acto Chem. Scond. 1972, 26, 11 1. (13) Yokoyama, H.; Yamatera, H. Bull. Chem. Soc. Jpn. 1971,44, 1725.
0022-3654/91/2095-8956$02.50/0
TABLE I: Molalities of [Co(NH3)']X3 Solutions Used for Conductivity Measurements m, IO4 mol kg-' solution X = CI X = Br X = I X = NO3 X = CIO, I 1.9654 1.9562 1.9482 1.9305 1.9575 2 2.5789 2.5635 2.5497 2.5662 2.5616 3 3.2396 3.2501 3.2354 3.2422 3.2423 4 4.0411 4.0037 4.0004 3.9892 4.0074 4.8428 5 4.8668 4.8444 4.8268 4.8369 5.7138 5.7585 6 5.7800 5.1343 5.7681 I 6.7646 6.1538 6.7520 6.1762 6.7706 7.8332 1.8434 8 1.8682 1.8467 1.8458 9.0163 9.0261 9 9.0219 8.9782 9.0223 10 9.9251 10.0073 10.2628 10.2370 10.2618
aamminecobalt(II1) were measured a t temperatures between 0 and 50 OC and ion association constants calculated. From such data entropy and enthalpy changes can be estimated which enable the nature of the ion association and the hydration properties of the ions to be probed. The temperature dependence of the limiting molar conductivity of the complex ion is also discussed. Experimental Section Materials. Hexaamminecobalt(II1) chloride was prepared as
described in the l i t e r a t ~ r eand ' ~ recrystallized twice from water. The bromide, iodide, nitrate, and perchlorate of the complex were obtained by adding aqueous solutions of hydrobromic acid, potassium iodide, nitric acid, and perchloric acid, respectively, into solutions of the chloride and were reprecipitated. All of the salts were recrystallized at least twice from water. The absence of the chloride ion in the nitrate and in the perchlorate was ascertained by adding silver acetate to their aqueous solutions. All reagents used were of reagent grade (Wako Pure Chemical Industries). The preparation of the bromide and the iodide was made in a dark room. The complex salts obtained were air-dried and ascertained to be anhydrous, except for the nitrate, by the use of an Abderhalden dryer and by the Karl-Fischer method with an AQ-5 Aquacounter of Hiranuma Sangyo Co.; the number of waters of crystallization of the nitrate was 0.29. The molar extinction coefficients of the complex salts at A,, = 475 nm (a Hitachi 340 spectrophotometer was used) were confirmed to be in agreement with one another: their average value was 57.0 f 0.1 mol-' dm3 cm-I. The densities of the crystals at 25.0 OC were 1.71,2.34,2.19, 1.81, and 2.05 g cm-3 for the chloride, bromide, iodide, nitrate, and perchlorate, respectively. These values were determined by the density measurement for a mixture of organic liquids, having (14) Bjerrum, J.; McReynolds, J. P. Inorganic Syntheses; Fernelius, W. C., Ed.; Krieger: New York, 1978; p 216.
0 1991 American Chemical Society
Ion Association of Hexaamminecobalt( 111) Complexes
TABLE II: Molar Concentrations of the [Co(NH3),]X3 Solutions Used for Conductivity Measurementso ~(24.95OCI, IO-'
solution
x = CI
X = Br
X=I
mol dm-, X = NO,
I 2 3 4 5 6 7 8 9
1.9596 2.5712 3.2299 4.0290 4.8522 5.7626 6.7441 7.8443 8.9944 9.8947
1.9504 2.5559 3.2404 3.9917 4.8282 5.7563 6.7333 7.8093 8.9886 9.9764
1.9424 2.5421 3.2257 3.9884 4.8297 5.7410 6.7313 7.8192 8.9981 10.2307
1.9248 2.5586 3.2325 3.9772 4.8122 5.7169 6.7555 7.8226 8.9505 10.2052
IO
x = CIO, 1.9517 2.5539 3.2326 3.9953 4.8222 5.7505 6.7498 7.8215 8.9941 10.2295
OMolar concentrations at 24.95 OC,c(24.95 "C), are shown: those a t the other temperatures ( f , "C) are given by c ( f ) = c(24.95 O C ) f ( f ) , whereflr) = 1.00279 (-0.01 "C), 1.00291 (5.04 "C),1.00264 (10.06 "C), 1.00204 (15.05 "C), 1.00115 (20.01 "C), 0.99863 (29.85 "C), 0.99706 (34.72 "C), 0.99532 (39.55 "C), 0.99340 (44.36 "C), and 0.991 34 (49.13 "C).
the same density as the crystals, whose compositions were adjusted to make the insoluble crystals float in the middle of mixed liquid. Solutions. All solutions were made by weight just before conductivity measurements. Corrections for the buoyancy by air were made with the weighed values for salts and water. The conductivity of water' used for the solutions was always lower than 1 X IO-' S cm-' at 25 OC after dissolved carbon dioxide was removed as described below. The molar solution concentrations were calculated by use of their estimated densities by assuming at each temperature the same increment with concentration as those observed at 25 OC as described previou~ly.~ The density measurements of solutions at 25 OC were carried out by using a vibrating-tube SS-D-200 twin-type densimeter of the Shibayama Scientific Co.' The density of water a t each temperature was obtained from an experimental equation given by Kell.lsb The molalities (m)and molar concentrations (c) of solutions are given in Tables 1 and 11, respectively. Conductivity Measurements. The conductivity measurements were made at 1 kHz with a Fuso 360 linear bridge conductometer in the manner described previously4 at 11 temperatures between 0 and 50 OC. The conductivity cell used was a four-necked flask with a 250-cm'capacity which was equippceedwith a thermistor, a nitrogen inlet, a magnetic stirrer, and two platinized platinum electrodes. The cell constant was 0.137 23 cm-' at 25 "C, and its change with temperature was corrected by using -0.0014% for the elevation of 1 OC.' Before the beginning of the measurement, dissolved carbon dioxide was removed by bubbling moistened nitrogen gas through the solution in the cell for about an hour. In any given solution the measurements were carried out by starting at 0 OC and elevating the temperature in steps of 5 OC. Throughout the measurements an atmosphere of nitrogen was maintained over the solution, and the solutions of the bromide and the iodide were protected from light. The resistance values were calibrated by use of a precision decade resistance box (Dekabox DB62, Elecro Scientific Industries; accuracy f0.02%). The complete measurements for one solution were accomplished in every case within 5 h after the preparation of the solution. The observed conductivities were corrected for the conductivity of the solvent and for the minor conductivity change considered to be due to the decomposition of the complex?*9which was about 0.01%on the molar conductivity at 0 OC and about 0.04% at 50 OC: the conductivity of the chloride solution was increased by 1.2 X 1 0 % m i d at 25 O C and 4.6 X 10% mi& at 45 OC. The reproducibility of the conductivity measurements was within 0.05%. The precision of the temperature measurements was *0.003 O C . The accuracy of the temperature was fO.O1 OC. (15) (a) Quoted through: Eisenbcrg. D.;Kauzmann, W. The Srrucrure and Properties of Water, Oxford-Clarendon Press: London, 1969. (b) Kell, G.S.J . Chem. Eng. Data 1967, 12, 6. (c) Malmberg, C. G.; Maryott, A. A. J. Res. Narl. Bur. Stand. 1956, 56, I .
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8957 Analysis of Conductivity Data
The observed molar conductivities of the complex salts, A(MX3/3),I6where M'+ is the complex ion and X- is the anion, are given in Table 111. The analysis was carried out in a similar manner as employed by Jenkins and Monk7 and other workers,&I0 although different theoretical equations for conductivities and activity coefficients were used in the present analysis. The only equilibrium considered below 0.001 mol dm-' was ion-pair formation [C0(NH3)6l3+ + X- + [CO(NH3)6]3+X-
(1)
where the other ion-ion interactions such as triple-ion formation were regarded to be negligible.17 The equilibrium constant (the ion association constant), KA, for eq 1 is written KA
=
- a)YMX/[ca(2
+ a)YdXI
(2)
where c is the molar concentration of the salt, a is the fraction of the free complex ion, and yM, yx, and yMxare the activity coefficients of M3+, X-, and M3+X-, respectively, which are represented by the Debye-Huckel equation'* log yi = -Azi21'/2/( 1
+ BUi")
(3)
where A and B have their usual meanings, zi is the ionic charge number, I is the ionic strength given by I = 3 4 1 a), and ai is the closest distance of approach of ions. From the additivity rule for ionic conductivities, the molar conductivity of the salt can be expressed
+
A(MX3/3) = a[X(M3+/3) + X(X-)] + 2(1 - a) X [ x ( M ~ + x - / ~ ) X ( X - ) ] / ~= ( Y A F ( M X ~ /+ ~ ) 2(1 - a ) b ~ ( M X X 2 / 2 ) / 3 (4)
+
where the X values are the ionic molar conductivities and AT (MXJ3) and hF(MXX2/2) correspond to the molar conductivities of hypothetical 3:l and 2:l electrolytes, respectively,I6 of which expressions can be theoretically given. While the Onsager limiting equation had been used in the previous the Robinson-Stokes equations were used here to provide a better fit to the datal9 AF(MX3/3) = [X"(M3+/3)
+ X"(X-)]
- S3111/2/(l+ Ba31I'/') (5)
A F ( M X X ~ / ~=) + B U ~ ~ I I /(6) *) [Xm(M3+X-/2) + X"(X-)] - S2111/2/(1 where the A" values are the limiting molar ionic conductivities and the S coefficients have their usual meaning^.'^ The theoretical expressions for S3I and SZlwere taken as those for the hypothetical states of a = 1 and a = 0, respectively. The ion association constants were determined by analyzing the conductivity data with eqs 2-6, fixing the values of (131,a21, and X"(X-), on the basis of the following assumptions. The values of 031 in eq 5 for the chloride, bromide, iodide, nitrate, and perchlorate were taken to be 4.91, 5.05, 5.26, 5.15, and 5.40 A, respectively, and were calculated from the crystallographic radii of CI- (1.81 A), Br- (1.95 A), and I- (2.16 A) presented by and the effective ionic radii of NO3- (2.05 A),' CIOC (2.30 ) , I and [ C O ( N H ~ ) ~(3.10 ] ~ + A) derived from their partial molar volumes by use of Glueckaufs equation;2',22the averaged
Pau1iY20
(16) The molar conductivities, A(MXl/3), X(M3+/3), etc., are equivalent to A(MXl)/3, X(M1+)/3, etc., respectively, and their values are identical with those of the equivalent conductivities. (17) At the maximum concentration (0.001 mol dm-]), the concentration ratio of the triple ion and the ion pair, [M"X-X-]/[M'+X-], is presumed to be about 0.01 by use of the formation constant of the triple ion (K,= [M1,+X'X']/[M1+X-]/[X-] = ca. 4 dm3 mol-')estimated from the ion association theories.26 This means that the ratio [M1+X-X-]/[M3+] docs not exceed 0.002. (18) Robinson, R. A.; Stokes, R. H.Electrolyre Solurions, 2nd ed.; Butterworths: London, 1959; Chapter 9. (19) Reference 18, Chapter 7. (20) Pauling, L. The Nature ofrhe Chemical Bond, 3rd ed.; Cornell Univ. Press: New York, 1960.
8958 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
Yokoyama and Kon
TABLE III: Molar Conductivities in Aqueous Solutions' A(MX3/3), S cm2 mol-I, at temperatureb
solution
11
12
t3
14
t5
t6
11
t8
t9
110
111
183.47 181.91 180.43 178.60 177.19 175.56 173.99 172.71 171.15 170.13
200.77 199.07 197.42 195.41 193.85 191.92 190.31 188.79 187.16 185.98
218.36 216.50 214.72 212.47 210.70 208.74 206.92 205.06 203.46 202.12
236.29 234.29 232.32 229.79 228.00 225.74 223.64 221.93 219.92 218.42
254.49 252.29 250.12 247.43 245.48 242.99 240.78 238.86 236.68 235.07
186.06 184.49 182.94 181.38 179.76 178.20 176.84 175.42 173.94 172.85
203.43 201.69 199.98 198.27 196.48 194.74 193.24 191.69 190.06 188.85
221.08 219.18 217.30 215.41 213.45 21 1.63 209.91 208.22 206.41 205.09
239.05 236.98 234.95 232.88 230.73 228.67 226.86 225.00 223.04 22 I .58
257.27 255.02 252.81 250.54 248.22 245.96 244.00 241.97 239.84 238.31
[Co(NH3)61C13
I 2 3 4 5 6 7 8 9
IO
89.08 88.38 87.71 86.89 86.23 85.48 84.77 84.16 83.44 82.97
103.40 102.58 101.81 100.84 100.07 99.19 98.37 97.64 96.8 1 96.23
118.37 117.42 116.51 1 15.39 114.51 113.51 I 12.56 111.69 110.76 1 10.09
133.91 132.83 131.79 130.5 1 129.52 128.36 127.27 126.31 125.19 124.49
149.98 148.76 147.56 146.11 145.01 143.64 142.45 141.34 140.14 139.30
166.5 1 165.14 163.80 162.18 160.90 159.45 158.06 156.85 155.49 154.54
91.10 90.38 89.65 88.93 88.16 87.41 86.77 86.1 1 85.41 84.89
105.56 104.72 103.87 103.03 102.12 101.26 100.51 99.75 98.93 98.33
120.64 1 19.67 1 18.70 1 17.72 116.68 1 1 5.70 1 14.84 1 13.96 1 1 3.02 1 12.33
136.28 135.18 134.07 132.96 131.78 130.66 129.68 128.68 127.61 126.84
152.44 151.20 149.93 148.69 147.37 146.11 145.01 143.88 142.67 141.79
90.68 89.93 89.29 88.66 87.94 87.26 86.62 85.91 85.27 84.67
105.03 104.16 103.42 102.68 101.83 101.05 100.31 99.48 98.74 98.05
120.00 119.01 118.15 117.29 116.32 1 15.44 114.58 1 13.63 1 12.79 1 12.00
135.53 134.42 133.43 132.45 131.35 130.35 129.37 128.30 127.35 126.44
151.58 150.32 149.19 148.10 146.87 145.74 144.64 143.43 142.36 141.35
168.07 166.67 165.40 164.17 162.81 161.54 160.30 158.95 157.77 156.65
184.96 183.36 182.00 180.63 179.11 177.70 176.35 174.86 173.55 172.29
202.19 200.43 198.93 197.42 195.74 194.22 192.71 191.07 189.62 188.23
219.71 217.80 216.15 2 14.47 2 12.64 210.97 209.31 207.53 205.94 204.41
237.53 235.47 233.66 23 1.83 229.89 228.03 226.20 224.28 222.51 220.84
255.61 253.36 25 1.44 249.40 247.33 245.31 243.30 241.22 239.29 237.50
87.96 87.18 86.44 85.73 85.00 84. I8 83.41 82.73 8 I .98 8 1.30
101.75 100.84 99.99 99.17 98.32 97.39 96.51 95.72 94.86 94.08
116.12 1 15.08 114.12 113.19 112.21 111.16 110.15 109.26 108.29 107.39
131.01 129.84 128.76 127.69 126.61 125.42 124.28 123.29 122.19 121.18
[Co(NH3)61(NO313 146.40 162.20 145.08 160.73 143.86 159.37 142.67 158.05 141.47 156.72 140.13 155.23 138.86 153.83 137.75 152.61 136.53 151.24 135.40 149.99
178.38 176.77 175.25 173.80 172.34 170.69 169.13 167.79 166.29 164.91
194.90 193.10 191.45 189.84 188.26 186.44 184.75 183.28 181.63 180.11
211.69 209.71 207.93 206.17 204.44 202.44 200.59 199.00 197.20 195.52
228.79 226.63 224.69 222.76 220.89 218.71 216.70 214.99 213.02 211.18
246.09 243.76 241.67 239.56 237.58 235.18 233.00 231.13 229.03 227.04
85.05 84.41 83.70 82.95 82.33 8 I .72 80.98 80.23 79.63 78.96
98.57 97.83 97.01 96.15 95.42 94.61 93.82 93.02 92.34 91.56
1 12.68
127.32 126.37 125.32 124.2 1 123.28 122.26 121.23 120.21 119.32 118.35
141.39 140.22 138.99 137.94 136.82 135.65 134.50 133.48 132.44
173.98 172.63 171.18 169.74 168.44 166.99 165.66 164.22 162.99 161.72
190.26 188.77 187.19 185.62 184.17 182.61 181.15 179.55 178.14 176.83
206.83 205.20 203.45 201.78 200.19 198.47 196.88 195.13 193.62 192.17
223.69 221.90 220.00 218.23 2 16.49 214.63 212.91 210.99 209.30 207.78
240.75 238.83 236.78 234.89 232.97 230.97 229.13 227.03 225.17 223.56
[Co(NH,)6i Br3
1 2 3 4 5 6 7 8 9
IO
169.04 167.66 166.24 164.84 163.38 161.97 160.73 159.48 158.12 157.15
[Co(NH3)6113
1
2 3 4 5 6 7 8 9
IO 1 2 3 4 5 6 7 8 9
IO 1 2 3 4 5 6 7 8 9
IO
I 1 1.82 1 10.90 109.93 109.09 108.18 107.27 106.36 105.53 104.71
@Seeref 16. bThe temperatures ( t , "C) are as follows: t , = -0.01. t9
= 39.55, r,o = 44.36, and t , , = 49.13.
t2 =
156.82 155.50 154.17 153.00 I5 I .69 150.46 149.18 148.11 146.90
5.04, t a = 10.06, t 4 = 15.05, t5 = 20.01, t6 = 24.95, t, = 29.85, t8 = 34.72,
(7)
where X"(25 OC),a, 6,and c are constants depending on the ions. The values of these parameters for the anions used have been given,lJ3 and are shown in Table IV. Although the limiting molar conductivity of the complex ion, X"(M3+/3), could be estimated from the analysis of the conductivity data, those of ion pairs, X"(M3+X-/2), were virtually impossible to estimate experimentally and were assumed to be equal to (2/3)A'(M3+/3) as suggested In this treatment the following asin the previous sumptions are included: Stokes lawz4is valid for representing the
(21) Glueckauf, E. Trans. Faraday Soc. 1965, 61, 914. (22) Yokoyama, H.;Mochida, M.; Koyama. Y. Bull. Chem. Soc. Jpn. 1B8, 61, 3445.
(23) Harned, H. S.;Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold: New York, 1958; p 233. (24) Reference 18, Chapter 2.
value of the partial molar volume of the complex ion at infinite dilution was estimated to be 55.9 f 0.9 cm3 mol-' at 25 OC from the densities of the solutions used for the conductivity measurements. The same values were assumed also for aZ1in eq 6 . The X"(X-) for the anions at a given temperature (t in "C) was estimated from
X'(X-) = X"(25 "C)+ a(t - 25)
+ b(t - 25)2 + c ( t - 25).'
The Journal of Physical Chemisrry, Vol. 95, No. 22, 1991 8959
Ion Association of Hexaamminecobalt(II1) Complexes TABLE I V Parameter Values in Equation 7 for Limiting Molar Conductivities of Ions, X-(X-) and X'(MW/3)' a, 6 X IO', c X IOs, X"(25
"C), S c m 2
s cm2
ion
CI-
mol-'
76.35 78.17 BrI76.90 NO; 71.60 CIOi 67.20 [CO(NH~)~]'+99.56 a Equation
K-'
Scm2 mol-' K-2
Scm2 mol-' K-3
1.5404 1.5437 1.5099 1.3670 1.3159 2.0729
4.650 4.470 4.375 3.776 3.833 7.212
-1.29 -2.30 -2.17 -0.35 -0.59 -3.30
mol-'
b 1.75 -
ref, 23 23 23 1 1
1.70-
2 T
"4 t
this work
7 was used also to express the temperature dependence of
X"(M3+/3).
molar conductivities of the complex ion and the ion pairs and the Stokes radii of M3+ and M3+X- are approximately equal. The calculations for the determination of KA and X"(M3+/3) were achieved by the least-squares method through minimizing u, where uz = x[A(obsd) - A(calcd)lZ/(n - 2), as described previously.4 The values of dielectric constant (e) of water at given temperatures in theoretical equations were estimated by use of an empirical equation of Malmberg-MaryottlSC and those of viscosity of water (v0) were obtained from the interpolation with literature values between 0 and 50 0C.15925
Results and Discussion Ion Association Constants and Their Temperature Dependence. The ion association constants (KA) obtained are summarized in Table V and compared to the predictions of the ion association theoriesXJ7 which assumed a simple Coulomb interaction between hard sphere ions in a continuous medium. The values of log KA are plotted vs temperature ( I ) in Figure 1. These plots give smooth curves. Except for the chloride each curve has a minimum at a different temperature, tmin,characteristic of the salt. The relative order of magnitude of log KA for the salts depends on the temperature. The observed temperature range cannot be explained by simple electrostatic t h e o r i e ~ , *which ~ * ~ ~predict that the ion association is enhanced with decreasing a and endothermic in water as demonstrated later (Table VIII). The behavior at temperatures higher than 50 OC obtained by an extrapolation of the curves in Figure 1 seems to be in agreement with the theoretical prediction~.~~.~' The log KA temperature dependence can be reproduced by a quadratic equation in I
- 55 . 1
0
10
20 30 t lac
40
50
Figure 1. Temperature dependence of the ion association constants of the chloride ( O ) , bromide (A),iodide ( O ) , nitrate (O), and perchlorate (A).
= 29.9 and 35.6 "C),respectively, although the magnitude of KA for the chloride and perchlorate in the present system is reverse to that of K N 0 3 < KClO, at a temperature between 0 and 50 OC.'
The following ion association constants at 25 O C have been reported in the literatures: KA(25 OC)/dm3 mol-' = 31 or 35 (X = Cl),7J' 45 (X = Br)? 24 (X = I)? 43 (X = NO3)? and 25 (X = These values are about 13 units (except for the bromide) smaller than those in Table V. This is attributable mainly to the use of the Onsager limiting conductivity equation in the previous studies. If that equation and the limiting equation of Debye-Huckel for the activity coefficient are used for the present analysis, we get values that are about 17 units smaller than those in Table V: KA(25 OC)/dm3 mol-' = 34.1 f 1.4 (X = CI),30.4 f 1.7 (X = Br), 20.3 f 1.4 (X = I), 32.8 f 1.0 (X = NO3), and 19.6 f 1.3 (X = CIO,). The differences from the literature values except for the chloride may be mainly due to the fact that Katayama and Tamamushi9 used the Guggenheim equation of the activity coefficient and extrapolated log KA values obtained at different concentrations for these salts to I = 0. The use of the limiting theoretical equations leads also to the different tmin values shifted by about 10-1 5 OC to higher temperatures than log KA = P ( t - ?,in)' + 1% KA(min) (8) those shown in Table VI. where p , tmin,and log KA(min)are constants; their values obtained Many extended theoretical conductivity equations for the unare summarized in Table VI. The reproduced log KA values are symmetrical electrolyte have been presented, but there is no drawn with solid lines in Figure 1. All p values obtained are of complete equation yet. The Robinson-Stokes equation used for the order of 10-SK-z,characteristic of ionic equilibria in water,28.29 the analysis should be better than the Onsager limiting equation and are comparable to those previously obtained for KN03, but may not necessarily be the best one. However, the relative KClO,, and K2S04: p / 1 WSK-*= 2.9, 5. I , and 3.9, respecti~ely.~.~ changes in the ion association constant and in its temperature The tminvalues for the nitrate and the perchlorate given in Table dependence should be insensitive to the theoretical equation used. VI are about 10 ' C higher than those for KNO, and KCIO4 (Imin The assumed a values in the theoretical equations have some arbitrariness. However, even if the errors in a were *1 A, the resulting KA values are changed only by f 3 dm3 mol-' for each (25) Reference 18; p 457. case, increased with increasing a. The tminvalues were changed (26) (a) Ebcling, W. Z . Phys. Chem. ( k i p z i g ) 1968, 238,400. (b) Yokoyama, H.; Yamatera, H. Bull. Chem. Soc. Jpn. 1975,48, 1770, 3002. The by f 2 OC, decreasing with increasing a. The uncertainties actheoretical equation for a symmetrical electrolytehas been derived by different companied by the assumption of Xm(M3+X-/2)= (2/3)h"(M3+/3) ways will be discussed later. Entropy and Enthalpy Changes of Ion Association. The fol( S ~ N A ~ ~ / 1 0 0 0 ) 5 6 * ' / ( ( + 2 n 2)!(2n I)) KA lowing expressions for the standard entropies and enthalpies of n- I ion association in aqueous solutions, ASaso(aq)and AH,,"(aq), where 6 = Ir+z-l&/(4m&Ta).We assumed this equation to be useful for the can be derived from eq 8: approximate estimation of the ion association constant for an unsymmetrical electrolyte. (27) Bjerrum, N. Kgl. Danske Videnskab.Selskab. 1926, 7 , No. 9. The theoretical e uation is given by KA = ( 4 ~ N , / l 0 0 0 ) ( a b ) ~ Q (where b ) , Q(6) = I: exp(x)/j dx. (28) Harned, H. S.;Embree, N. D. J . Am. Chem. Soc. 1934, 56, 1050. (29) Gurney, R.W. Ionic Processes in Solution;Dover Publications: New York, 1953; Chapter 7.
ASssO(aq) = 2.303R(log KA(,,,in)+ p(31 - tmin + 546.3)(1 - fmin)) (9) AHaso(aq) = 4.605pR(r
+ 273.15)*(t - fmin)
(10)
The values of ASaSo(aq)and Maso (as) at several temperatures
Yokoyama and Kon
8960 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
TABLE V Ion Association Constants (K,)between [Co(NH3),p and Anions and Limiting Molar Conductidties of [Co(NH,),P, X'(M*/3) K,,, dm3 mol-' theoretical KA valuesb A"( M3+/3): r, O c S cm2 mol-! x = CI X = Br X=I X = NO, X = C104 E-Y-Yc Bjerrumd -0.0 I 52.76 f 0.09 48.1 f 1 . 1 47.8 f 1.2 39.8 f 1.2 58.2 f 0.8 46.6 f 1.3 30.7-26.8 41.9-36.2 47.2 f 1.3 39.0 f 1 . 1 55.9 f 0.7 44.6 f 1.0 31.3-27.3 42.8-37.0 61.31 f 0.15 48.5 f 1.0 5.04 70.30 f 0.19 79.68 f 0.22 89.43 f 0.23 99.46 f 0.25 109.79 f 0.25 120.36 f 0.25 131.14 f 0.27 142.15 f 0.29 153.33 f 0.35
10.06 15.05 20.01 24.95 29.85 34.72 39.55 44.36 49.13
48.7 f 49.1 f 50.0 f 50.5 f 51.5 f 53.2 f 54.3 f 56.1 f 56.8 f
1.0 1.1 1.2 1.1 1.4 1.5 1.4 1.7 1.6
46.8 f 46.8 f 46.8 f 47.0 f 47.3 f 47.9 f 48.5 f 49.4 f 50.4 f
1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.4
38.4 f 38.0 f 37.8 f 37.9 f 37.7 f 37.9 f 38.3 f 38.8 f 39.3 f
1.0 1.0 1.0 1.0 1.2 1.2 1.1 1.0 1.0
54.0 f 0.7 52.5 f 0.7 51.3 f 0.7 50.4 f 0.7 49.9 f 0.7 49.4 f 0.8 49.5 f 0.9 49.7 f 0.9 50.0 f 1.0
42.9 f 0.8 41.0 f 0.9 39.9 f 0.9 38.6 f 0.9 37.8 f 0.7 37.5 i 0.7 37.0 f 0.7 36.7 f 0.7 36.6 f 0.7
43.8-37.8 44.8-38.8 46.0-39.7 47.2-40.8 48.4-41.9 49.8-43.1 5 1.3-44.4 52.8-45.7 54.4-47.1
32.0-27.9 32.8-28.6 33.6-29.3 34.5-30.0 35.4-30.8 36.4-31.7 37.5-32.6 38.6-3 3.5 39.8-34.5
OAveraged values of X"(M3+/3) obtained from each system. bCalculated by assuming a = 4.91-5.40 A. cTheories of Ebeling2&and Yokoyama and Yamatera.26b "Reference 27.
TABLE VI: Values of Parameters in Equation 8 Representing the Temperature Dependence of Ion Association Constants between ICo(NH&P+ and Anions p x 105, anion CIBrI-
K-2
2.51 f 0.34 3.1 I f 0.07 3.38 0.14 4.76 0.08 4.50 f 0.22
* *
NO; CIOL
tmin? "C -6.1 f 4.1 16.8 f 0.2 25.9 f 0.1 38.6 0.3 48.5 f 1.2
*
log KA(min) 1.681 f 0.003 1.670 f 0.001 1.577 f 0.001 1.694 f 0.001 1.564 f 0.001
are given in Tables VI1 and VI11 with their uncertaintiesg0and are compared with the theoretical value^.^' The errors arising from the assumption for X"(Mg+X-/2) will be discussed later. The uncertainties in ASaso(aq) and AHaso(aq) accompanied by the i l - A deviations in a were within f l J K-'mol-' and f0.2 kJ mol-', respectively, for the chloride and the bromide and within f 2 J K-'mol-l and *0.5 kJ mol-', respectively, for the other salts. The ASUo(aq) and AHm0(aq)values were slightly increased with increasing a except for AHaso(aq)at the higher temperatures for the chloride and bromide. The following discussion will be made with these uncertainties considered. The experimental values of AS,"(aq) and AH,O(aq) are both in the order chloride > bromide > iodide > nitrate > perchlorate a t given temperatures and are significantly smaller than the corresponding theoretical values except for the chloride. With decreasing temperature, the discrepancies from the theoretical values become large and the experimental AHaso(aq) values become negative at temperatures below tmin. The characteristic temperature dependence of the ion association constant is largely owing to different tmindependence of the anions. The tmincorrelates (30)The experimental errors of AS,"(aq) and AHUo(aq),6(ASas0(aq)) and 6(AHuo(aq)), were estimated with the standard deviation of log KA, u(log KA),derived by the least-squares fitting with eq 8, presuming the relations 6(AH,,O(aq)) = 2.303R(t + 273.1S)2(2u(10gK,,)/(30 - It - 251)) and 6(AS,,"(aq)) = 2.303Ru(log KA) + 6(AHa,0(aq))/(t + 273.15), where the values of u(1og K~)/lo-' were 2.37, 0.46, 0.98, 0.53, and 1.56 for chloride, bromide, iodide, nitrate, and perchlorate, respectively. (31) The theoretical values were calculated by the expressions of AHUo(aq) and A.Spso(aq)derived from the theoretical equations of KA26-2' AH,,O(aq) = - b R p ( T '
+ d In r/dr)(d
ASaSo(aq)= R In KA
In KA/db)
+ TIAH,,O(aq)
where in the E-Y-Y theory26 d In KJdb
-2
t ,
,
--34:, -10
,
,
,
IO 20 30 t m i IT
0
/t, 50
40
"
[2b2"+'/{(2n + 1)!(2n "-1
- l ) l ] / n-[ fI L ~ ~ ~ / { (+2 n2)!(2n
- I)}]
and in the Bjerrum theory2' d In KA/db = 36-1 + exp(b)b4Q(b)-l The theoretical AH,,"(aq) values in water are always positive because of d In KA/db > 0 and (TI+ d In c / d n < 0.
10
Figure 2. Correlations of tminwith ASas0(aq) (open symbols) and AH,"(aq) (solid symbols) at 25 "C.
v NO3-
2ol u 4 ClO,
30
40
50 -As
60
70
80
90
X 3 / J K-lmol-'
Figure 3. Relationship between -Mh"(X-)and ASuo(aq) at 25 O C . Solid symbols for the nitrate (v) and the perchlorate (e) represent hypothetical values presumed from the relationship between A&,"(X-) and re[' (see text). The solid line is drawn for the halides, and the dashed line is its extrapolation.
with AHaso(aq) and ASaso(aq) as demonstrated in Figure 2. To clarify what physical meanings in the thermodynamic parameters obtained, we considered the following hypothetical cycle composed of three steps for the ion association in an aqueous solution: M3+(gas) + X-(gas)
=
1
t
step 1
M3+(aq)
t
+ X-(aq)
M3+X-(gas)
-
J
step 3
M3+X-(aq)
The first step is the transfer of the free ions from aqueous solution to gas phase (dehydration process), the second step is the ion association process in the gas phase, and the third step is the transfer of the ion pair from gas phase into water (hydration
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8961
Ion Association of Hexaamminecobalt(II1) Complexes
TABLE VII: Standard Entropies of the Ion Association in Aqueous Solutions, ASMo(aq),at Several Temperatures ASUo(aq),J K-'mol-' theoretical valuesa 1, OC x = CI X = Br X=I X = NO3 x = CIO, E-Y-Yb Bjerrum 16.4 f 0.6 10.7 f 1.7 38.6-37.3 41.3-40.2 28.2 f 0.5 23.0 f 1 . 1 5.0 35.2 f 2.6 26.2 f 0.6 20.6 f 0.3 14.3 i 0.9 40.6-39.2 43.3-42.2 15.0 38.3 f 1.4 31.4 i 0.3 18.4 f 0.7 42.7-41.3 45.3-44.3 25.0 41.6 f 1.0 34.9 f 0.2 29.9 f 0.4 25.2 f 0.2 35.0 45.2 f 1.5 38.9 f 0.3 33.9 f 0.6 30.4 i 0.4 23.0 f 1.0 44.9-43.4 47.4-46.4 36.2 f 0.7 28.1 f 2.0 47.1-45.5 49.5-48.5 45.0 49.1 f 2.9 43.1 f 0.6 38.3 f 1.2
'Calculated by assuming u = 4.91-5.40 A (see ref 31). bTheoriesof Ebeling2&and Yokoyama and Yamatera.26b TABLE VIM: Standard Enthalpies of the Ion Association in Aqwous Solutions, AH,O(aq), at Several Temperatures
A&O(aq), kJ mol-' 1,
OC
5.0 15.0 25.0 35.0 45.0
x = CI
X = Br
0.8 f 0.7 1.7 f 0.4 2.7 f 0.3 3.8 f 0.5 5.0 f 0.9
- 1 . 1 f 0.2 -0.2 f 0.1 0.9 f 0.1 2.1 f 0.1
- 0 . 1 f 0.1 1 . 1 f 0.2
3.4 f 0.2
2.5 f 0.4
X=I -2.1 f 0.3 -1.2 f 0.2
X = NO3
x = ClO,
-4.7 f 0.2 -3.6 f 0.1 -2.2 f 0.1 -0.6 f 0.1 1.2 f 0.2
-5.8 -4.8 -3.6 -2.2 -0.6
f 0.5 f 0.3 i 0.2
theoretical valuesa E-Y-Yb Bjerrum
f 0.3
2.77-2.72 3.3 5-3.28 3.96-3.88 4.62-4.51
f 0.6
5.3 1-5. I8
2.79-2.83 3.36-3.40 3.96-4.00 4.59-4.64 5.26-5.30
'Calculated by assuming a = 4.91-5.40 A (see ref 31). bTheoriesof Ebeling2&and Yokoyama and Yamatera.26b TABLE I X Values of AS,'(Gas), AS,'(Cas), AS,+,"(Gas), and AS,O(Gas) at 25 OC for the Contact Ion-Pair Formation of [Co(NH3),p with Anions in the Gas Phase Calculated without Any Consideration for Their Intrinsic Rotational and Vibrational Entropy Changes" AS,,,'(gas), AS,O(gas), &bo(@S),b J K-'mol-' ASMo(gas),CJ K-'mol-' anion J K-'mol-' J K-'mol-' n=2 n = 12 n = 30 n=2 n = 12 n = 30 c1-150.9 83.7 18.9 9.2 5.6 -48.3 -58.0 -6 1.6 -158.5 89.2 21.7 11.9 8.1 -47.6 -57.4 -61.2 Br-162.1 92.2 23.4 13.5 9.7 -46.5 -56.4 -60.2 I21.2 11.4 7.7 -47.2 -57.0 -60.7 -1 56.4 88.0 NO; -160.3 91.5 23.2 13.3 9.4 -45.6 -55.5 CIOi -59.4
"The values of AStramo(gas),hS,,'(gas), and ASvibo(gas)were calculated according to the manner described in refs 33 and 34. bThe interionic vibration was approximated as the harmonic one having the mutual potential energy given by V ( r ) = -lz+z-l$/4m$ + bo/?, where z+ and z- are the ionic charge numbers of the cation and the anion, co is the permittivity of vacuum, r is the interionic distance, and bo and n are constants. The ~ a ~ ~p~isp ~the ' ~reduced ~, mass. The calculations expression for the corresponding vibrational frequency, v, becomes Y = {(n - I ) ~ z + ~ ~ ) e ~ / 1 6 ? r ~ cwhere + ASvibo(gas). were made by assuming three n values as shown. CASmo(gas)= ASlmnso(gas)+ ASSmlo(gas) process). The AS,"(aq) and AHaso(aq) observed for the ion association in an aqueous solution therefore can be expressed sa:(aq)
= o(M3+X-) - hShy0(M3+)- Uhyo(x-) + ASaso(gas) = PAShy' + Maso(gas) (11)
+
AHaSo(aq)= AHhyo(M3+X-)- AHhyo(M3+)- AHhyo(x-) AHuO(gas) = AAHhyO+ AH,O(gas) (12) where &yo and m h y o are the standard hydration entropy and enthalpy and are both negative quantities. APShyoand A M h O are usually positive because of the decrease in hydration of the ion pairs compared to that of the free ions. ASaso(gas) and AH,,O(gas) are the standard entropy and enthalpy of ion association in the gas phase which are negative because of losses of thermal motion of the ions and because of lowering of mutual electrostatic potential energies accompanied by the ion association. It is clear from eq 12 that the sign of MaSo(aq)is dependent on whether AAHhyoor AHaSo(gas)is larger at a given temperature and that from eq 11 the positive ASaso(aq)indicates A s h y o > -AS,,O(gas) > 0 in the observed temperature range. COrrdeHOIIbetween AS,O(aq) and Ashyo(x-) for the Halides. At 25 OC ASaso(aq) for the halide is decreased with decreasing -A&, "(x-) as shown in Figure 3 where the following values of Uh:(x-) in the literature32 were used: -87, -70, and -47 J K-1 mol-! for CI-, Br-, and I-, respectively. However, the difference in ASUo(aq)between any two halides is considerably smaller than that in -MhYo(X-). This indicates that the sum of AShyo(M3+X-) (32) Marcus, Y. Ion Soloation; Wiley: New York, 1985; Chapter 5.
and ASao(gas) is in the order of chloride < bromide < iodide < 0 from eq 11: the sums are estimated to be in turn -403, -393, and -375 J K-' mol-' at 25 OC, considering AShyo([Co(NH3)6]3+) The "'(gas) is approximately identical = -358 J K-' with the sum of the translational, rotational, and vibrational entropy changes by the ion association (AS-O(gas), ASmo(gas), and .M~bo(gas),respectively), of which values at 25 OC and 0.101 MPa for the contact ion pairs having interionic distances of a!! were roughly estimated and are shown in Table IX. In this calculation the intrinsic rotational and vibrational entropies of the complex ion were assumed to be not changed by the ion association. The sums of their values (= hS,O(gas)), also shown in Table IX, are close to one another among the halides: the differences are within 2 J K-' mol-'. This means that the order Mhyo(M3+CI-)< hShyo(M3+Br-) < u?hy0(M3+I-) < 0 exists. ) This - l order c ( ois,similar , $ !to&A < '(Br-) < &?hyo(I-) < 0, although the differences in A,!&,,,"(M'+&-) among the halides are somewhat smaller than those in aShyo(X-),and indicates that the intrinsic hydration properties of the halide ions are kept considerably after their ion-pair formation with the [ C O ( N H ~ ) ~ ] ~ + ion. The ion pairs formed by the ion association include not only the contact ones but also the solvent-separated ones, since the respective ion-pair formation constants for [ C O ( N H ~ ) ~ ] ~at+ 25 IO C (ionic strength = 0.06) have been experimentally determined through spectrophotometric measurements and the fraction of the solvent-separated ion pairs in all ion pairs was estimated to be 0.60 f 0.07.13The similarity between the order in AShyo(M3+X-) and that in hshyo(x-) may be largely owing to the presence of the solvent-separated ion pairs, regardless of the use of the values of ASaso(gas) for the contact ion pair in the above discussion: (33) Loewenschuss, A.; Marcus, Y. Chem. Rev. 1984,84, 89. (34) Lewis, G. N.; Randall, M. Thermodynamics; Pitzer, K. S.,Brewer, L., Eds.;McGraw-Hill: New York, 1961; Chapter 27.
8962 The Journal of Physical Chemistry, Vol. 95, No. 22, I99'1
+
assuming a31 2rH20as the interionic distance, where 2rH20is the diameter of a water molecule equal to 2.8 A, we can get values smaller by 12-13 J K-I mol-' as -ASaso(gas) for the solventseparated ion pair relative to those for the contact ion pair given in Table IX. Although more strict values of ASaso(gas) might be estimated by considering the presence of the solvent-separated ion pair, the order in AShyo(M3+X-)and its correlation with mhy0(X-) discussed above will not be changed because, among the anions, the fraction of the solvent-separated ion pair will not be so much different and the values of AS,,O(gas) are expected to be similar. Further discussion about Mhyo(M3+X-)is difficult because the values of ASviba(gas)in AS,O(gas), as shown in Table IX, depend on the n value in the potential energy equation which is given in footnote b of Table IX. Marcus32 estimated the contribution due to the structurebreaking effect in ahy0(X-): 12, 29, and 51 J K-' mol-' at 25 OC, respectively, for chloride, bromide, and iodide ions. The considerably smaller AS,,"(aq) values obtained for the halides except the chloride, compared with the theoretical ones (Table VII),31 may be related to their weak hydrations attributable to such structure-breaking properties. The large differences between the experimental and the theoretical ASaso(aq) values at 5 OC for the bromide and the iodide suggest that these anions extensively act as structure breakers in water having higher structure at such a lower temperature. Similar features are found also in the M,O(aq) values shown in Table VIII. The weak hydrations of the anions are considered to lead to small or negative values of AHaso(aq)at lower temperatures and to the increase of the ion association constants for the bromide and the iodide with decreasing temperature below tmin. The apparent agreement of the ion association behavior extrapolated to higher temperatures over 50 OC with the theoretical prediction suggests that the model of continuous medium having a dielectric constant of pure solvent assumed on the theoretical consideration of ion association becomes apparently effective with lowering of water structure with increasing temperature. Specific Entropy Loss in Ion Associations of the Nitrate and the Perchlorate. Although the -Mhy"(X-) values of the nitrate and the perchlorate ions32are 77 and 59 J K-'mol-', similar to those of the halide ions, the ASUo(aq) values obtained for the salts of the former ions are significantly smaller compared with those for the halides as shown in Figure 3. The differences in ASso(aq) are attributable to those in the sum of AShyo(M3+X-)and ASSo(gas) in eq 11, mainly in ASao(gas) because Mhy0(M3+X-) is presumed to be correlated to &yo(x-). The values of PSaso(gas) for the nitrate and the perchlorate can be approximately estimated in a similar way as made for the halides on the assumption that the intrinsic rotational and vibrational entropies of the complex ion and the oxoacid ion (NO3- or Clod-) are not changed by the ion association. However, such AS,O(gas) values, close to those for the halides as shown in Table IX, cannot explain the differences in ASaro(aq). The nitrate and perchlorate ions have considerably large intrinsic rotational entropies, S,O(gas), and also relatively small vibrational entropies, Svibo(gas):SroIo(gas)(J K-' mol-') = 81.' for NO3and 83.9 for CIO,-; Svibo(gas)(J K-' mol-') = 3.6 for NO3- and 12.8 for C104- at 25 0C.35 If their rotational motions are partly restricted by the ion association, it leads to partial losses of their intrinsic rotational entropies and then to small AS,O(gas) values, compared with those shown in Table IX. The excess entropy loss can be estimated by assuming that the relationship between ASa:(aq) and -A&,,"(X-) for the halides drawn with a solid line in Figure 3 is effective also for the hypothetical ion association between the complex ion and the oxoacid ions, which is not accompanied by the changes of the intrinsic entropies of the anions. In this estimation we should consider that the intrinsic rotational entropies of the oxoacid ions may be partly lost already in their hydration process because the k&hy0(x-) values are somewhat (35) Calculated by use of the interatomic distances or the vibrational frequencies given in ref 33 according to the manner described in refs 33 and 34.
Yokoyama and Kon more negative than those expected from a comparison with the halide ions on the effective ionic radii of the ions (ref): the relationship in L$shyo(x-) is CI-< NO3- < Br- < c10,- < 1- < o, while, in ref,CI- < Br- < NO< < 1- < Clod-. If the hypothetical hydration entropies for the oxoacid ions and the hypothetical ASso(aq) on their ion association with the complex ion, including no loss in their intrinsic rotational entropies, can be estimated from the relationship between uhy:(x-) and re{' and from that between ASaro(aq)and Mhy0(x ) for the halide ions, respectively, we can indicate the hypothetical hshyq(x-) and AS,"(aq) values for the oxoacid ions in Figure 3 with solid symbols. The differences between the hypothetical and the observed ASh "(X-) correspond to those between SrOto(gas)and SrOlo(aq)and give SroIo(aq)= 63 and 59 J K-'mol-' for the nitrate and perchlorate ions, respectively. In Figure 3 it is obvious that the observed AS,O(aq) values for the nitrate and the perchlorate are still smaller than the hypothetical ones. The remaining differences in ASaso(aq) are 7 J K-' mol-] for the nitrate and 10 J K-' mol-' for the perchlorate, which are about 11% and 17% of SrOto(aq)for NO< and C104-, respectively. These entropy losses may be attributable to the rotational ones of the oxoacid ions associated with the [ C O ( N H , ) ~ ]ion, ~ + since the &,'(gas) values for these anions are relatively small and their changes by the ion association, if present, will be negligible. The [Co(NH3)6]3+ion has the intrinsic vibrational entropy (435.2J K-' and the intrinsic rotational entropy (128.' J K-'mol-')3s including the contribution from free rotations around the Co-N bond axes (34.3J K-' Even if their changes by the ion association are not negligibly small, their differences may be small between the halides and the nitrate or the perchlorate. If the above entropy losses are mainly due to the formation of the contact ion pairs and their fractions in all the ion pairs are 0.4 as demonstrated for the iodide,I3 about 28% and 42% of SroIo(aq)for nitrate and perchlorate ions, respectively, are lost in the contact ion pairs. The AHaSo(aq)values observed for the nitrate and the perchlorate are also significantly smaller by 2.6 and 3.3 kJ mol-' at 25 OC, respectively, than those expected from a similar comparison with the halides as made for AS,O(aq). These differences cannot be explained only by the rotational enthalpy losses of the oxoacid ions by the ion association because the maximum losses are not considered to exceed 0.4, and 0.63 kJ mol-' for the nitrate and the perchlorate, corresponding to 11% and 17% of their rotational enthalpies (3RT/2), respectively. This suggests that some exothermic short-range interactions between the oxoacid ions and the complex ion are present, probably within the contact ion pair. Specific Interactions between the Complex Ion and the Oxoacid Ions. The restrictions in the rotational motion of the oxoacid ions described above are expected to be unfavorable for the ion association and to reduce the resulting ion association constants, because the rotational free energies of the oxoacid ions (-Grol = R T In Q,,,> 0, where Q,,,is the rotational partition function) and -AGaso(gas) in the following equation should be somewhat decreased and it leads to the decrease of -AGaSo(aq): AGasO (aq) = AGhyo(M3+X-)- AGhyo(M3+)- AGhyo(X-) + AG,O(gas) (13)
The subscripts and the terms in parentheses have the same meanings as in eqs 11 and 12. The relationship between -ACaSo(aq) and -AGhyo(X-)32 at 25 O C is shown in Figure 4, where the contribution from the entropy loss in the hydration process of the oxoacid ions, described above, to AGhyo(x-) is minor. The AG,O(aq) values for the nitrate and the perchlorate are more negative than those expected from the relationship among the halides as shown in Figure 4. This is opposite to the above expectation from the rotational restrictions and indicates that AG,O(gas) values for the nitrate or the perchlorate include excess free energy due to some specific interactions as suggested above. With decreasing temperature the ion association constants for the nitrate and the perchlorate are rapidly increased and the order of magnitudue of K becomes nitrate >> chloride = bromide = perchlorate >> iodide at 0 OC. Although we cannot exactly discuss
Ion Association of Hexaamminecobalt(II1) Complexes
200
250 -AG$X?/kJ
300
350
mol-'
Figure 4. Relationship between -AGhyo(X-) and -AG,,'(aq) at 25 'C. The sol.id line is drawn for the halides, and the dashed line is its extrapolation.
the reason for such an order because there is no available information on thermodynamic parameters for the ionic hydration at such lower temperatures, specific short-range interactions between the oxoacid ions and the complex ion are considered to be strengthened with decreasing temperature. The most probable short-range interaction is the hydrogen bonding between the hydrogen atoms of NH3 ligands of the [ C O ( N H ~ ) ~ion ] ~ and + the oxygen atoms of the oxoacid ions. In this case it may be important that the two or three oxygen atoms of the anions may concern the hydrogen bonding at the same time. This will lead to considerably large ion association constants at lower temperatures. Limiting Molar Conductivities of the Complex Ion and Their Temperature Dependence. The limiting molar conductivities of the complex ion, A"(M3+/3), determined from each system were averaged and are shown in Table V. The same quadratic equation as eq 7 was used for expressing their temperature dependence. The parameter values obtained are shown in Table IV and could be used to reproduce the experimental A"(M3+/3) within an average deviation of f0.02 S cm2 mol-'. The Stokes radius of [ C O ( N H ~ ) ~ ]r,, ~ +is, calculated to be 2.6-2.9 A from the limiting molar conductivities between 0 and 50 OC. This r, value is somewhat smaller than the effective ionic radius of the complex ion (ref = 3.10 A). The value of d In (A"vo)/dT at 25 OC can be evaluated to be -1.95 X IC3K-I. The relation r, < refand the negative d In (A"qo)/dT indicate that the [ C O ( N H ~ ) ~ion ] ~ +is a structure breaker in water. Its structure-braking effect is weaker than that of potassium or chloride ions but stronger than that of sodium ion, because the above value of d In (A"vo)/dT for the [Co(NH3)6]3+ion is more positive than -3.28 X tV3K-l for potassium ion or -2.61 X IO-' K-'for chloride ion but more negative than -1.01 X K-' for sodium ion.36 We presume that the ion pairs have also a similar structurebreaking effect as the free complex ion has, although its strength may be somewhat increased by the ion associations with the structure-breaking anions. Examination of the Assumption for Limiting Molar Conductivities of the Ion Pairs and Estimation of Possible Uncertainties in the Results. Monk discussed the ratios of the limiting molar conductivities between similar complex ions [M( 1)'1 and M(2)Q] having different charges3' and showed that the value of A"[M(2)z*/~zz~] usually could be approximated to that of (Iz21/ Izll)A"[M( l ) z ~ / ~ . z lFrom ~ ] . analogy with this relation Jenkins and Monk assumed A"( [Co(NH3),I3+X-/2) = (2/3)A"( [Co(NH3)6]3+/3)to obtain the ion association constants? Actually, (36) Calculated from eq 7 by use of the.parameter values given in ref 23. (37) Monk, C. B. Elecrrolytic Dissociarion; Academic Press: London, 1961; Chapter 8.
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8963 the value of Am( [Co(N02)(NH3),12+/2)at 25 O C can be calculated to be 64.9 or 62.9 S cmz mol-' from those of A0([Co(NO2)(NH3)5]S0,/2) given in the l i t e r a t ~ r ewith ~ ~ , A"(S042-/2) ~~ = 79.84 S cm2 mol-',3 and calculated to be 65.8 S cm2 mol-' from A"( [CO(NO,)(NH,),]CI,/~):~ the ratios of A"( [Co(N02)(NH3),I2+/2) to A"( [Co(NH3),13+/3) become 0.652,0.632, and 0.661 S cm2 mol-', respectively, which are near 2/3. Fuoss and Edelson also made the same treatment on the analysis for a 2:l electrolyte in nonaqueous Most conductivity studies of the ion association on unsymmetrical electrolytes have been essentially carried out according to the manner of Jenkins and Monk7 or Fuoss and EdelsonU4 In the present study the same treatment was also made for A"( [ C O ( N H ~ ) ~ ] ' + X - /assuming ~), that the Stokes radii of the ion pairs were equal to that of the free complex ion. Although the effective radii (ref) of the ion pairs, ref= 3.29, 3.34, 3.42, 3.37, and 3.47 for the chloride, bromide, iodide, nitrate, and perchlorate, respectively, estimated from the sum of the van der Waals volumes of the complex ion and the anions, Cuo(ion), on the assumption of zuo(ion) = 47rrer3/3, are somewhat larger than ref = 3.10 A for the complex ion and will reduce somewhat the mobility of the complex in solution, this effect will be more or less compensated by an opposite effect caused by the increase in the structure-breaking effect of the complex ion, expected from its association with the structure-breaker anions. We will demonstrate how the results are changed when the values of A"( [Co(NH3)J3+X-/2) are deviated from (2/3)A"([CO(NH3)6]''/3). If the deviation is within *lo%, the changes in the values of tmin,ASaso(aq),and AH,O(aq) from the present results are comparably small to their experimental errors, although the values of KA are changed within 7-8%, where they were increased with increasing A"( [ C O ( N H ~ ) ~ ] ~and + / ~vice ) versa. These uncertainties do not entirely affect the discussion in the present study. If the deviation is extremely large, e.g., Am( [Co(NH3)613+X-/2) = ( 1/2)A"( [cO(NH3)6]"/3) (Case 1) Or x"([CO(NH,),]~+/~) (case 2), the results are changed as follows: the values of KA are decreased by 15-1 6% in case 1 and increased by 52-60% in case 2; trninvalues are increased by 0.5-0.7 'C (case 1) and decreased by 1.2-2.5 OC (case 2); AS,O(aq) values are decreased by 1.3-1.9 J K-'mol-' (case 1) and increased by 3.5-5.9 J K-I mol-' (case 2); AHaSo(aq)values are changed within -0.2 kJ mol-' (case 1) and within the range -0.1 to 0.6 kJ mol-' (case 2). Although the values of K A are sensitively changed with the assumed values of A"([CO(NH,),]~+X-/~),the relative order in the magnitude of KA, the apparent features for the temperature dependence of log K A in Figure 1, and the relative relationship between AGaSo(aq)and AGhyo(X-) in Figure 4 are not changed. The changes in the values of tminand AH,'(aq) are not significant and do not affect the discussion in the present study, although the plots in Figures 2 and 3 are slightly and systematically shifted. Although the changes in the values of ASaso(aq) are relatively large, the deviations at 25 "C from those given in Table VI1 are similar between the salts: -1.7, -1.6, -1.6, -1.6, and -1.5 J K-l mol-' (case 1) and 5.0, 4.7, 4.5, 4.5, and 4.0 J K-' mol-l (case 2) for the chloride, bromide, iodide, nitrate, and perchlorate, respectively. This leads only to a shift of the plots given in Figures 2 and 3 and to a change of the values of the sums of pSh:(M3+X-) and ASaso(gas), which are equal to the sums of ASaso(aq), hshy"(M3+),and AShyo(X-),by the above deviations in ASmo(aq). However, the other values derived from the relative comparisons by use of ASaso(aq)are not changed. This indicates that all the contents in the discussion are not essentially changed. Registry NO. [CO(NHJ)~]CI~, 10534-89-1; [ C O ( N H ~ ) ~ ] B10534T~, 85-7; [CO(NH&]I,, 13841-85-5; [CO(NH3)6](NO3)3, 10534-86-8; [CO(NH3)6](ClOd)3, 13820-83-2. (38) Hanna, E.M.; Pethybridge, A. D.; Prue, J . E. J . Phys. Chem. 1971, 75, 29 1. (39) Kubota, E.;Yokoi, M. Bull. Chem. Soc. Jpn. 1977, 50, 1425. (40) Fuoss, R. M.; Edelson, D. J . Am. Chem. SOC.1951, 73, 269.
