Vob. 7 , No. 5, May 1968
DISSOCIATION OF THE
I n order to estimate theoretically the magnitude of the Davydov splitting and the intensity enhancement for the direction parallel to the c axis, we carried out the calculation of the exciton-exciton type of interaction for the pyridine molecules in the crystal form. The actual calculation was made by the SCFMO method which was adopted by Tanaka and Tanaka21 for the calculation of anthracene, longrange interaction (50 A- w ) being taken into account following the approximate method developed by Rice, et a1.22 The result shows that the splitting is larger for the direction parallel to the b axis than for the direction parallel to the c axis. Further, in consistency with the theoretical consideration, the absorption band appears a t lower frequencies for the former direction than for the latter. The calculated oscillator strengths depend strongly on the model used for the estimation of the intermolecular Coulomb integralz3 This prevents us from discussing quantitatively the intensity change due to the excitonexciton type of interaction. However, from the qual(21) M.Tanaka and J. Tanaka, private communication, (22) R . Silbey, J. Jortner, and S. A. Rice, J . Chem. P h y s . , 48, 1515 (1965).
AQUOPENTAAMMINECOBALT(III) ION 897
itative point of view, the calculation shows that the intensity of the b-parallel band considerably decreases as the result of exciton-exciton type of interaction and that this absorption has comparable intensity with the weak c-parallel band.24 From the above discussion, we consider that the two bands a t 4.84 eV (ql) and 4.65 eV (bii) may both be atrributed to the local excitation within pyridine. Acknowledgment.-The authors wish to express their sincere thanks t o Dr. Ichiro Hanazaki of the Institute of Physical and Chemical Research for his kind advice given them in doing the theoretical calculations. (23) I n the present calculation, interatomic Coulomb integrals for distances within 50 k were estimated by use of two models. I n one of them, the point charge approximation was adopted, and in the other, interatomic Coulomb integrals were represented by e2e-Ri20/R ( R is the interatomic distance). In the latter, the screening effect of the other electrons was considered. The calculated oscillator strengths sometimes differ by the order of 10 by changing the model from one to the other. Moreover, i t was found t h a t the long-range interaction over 50 k of interatomic distances gives great effect on the oscillator strengths. Taking the latter model and considering the long-range effect, the band under consideration turns out t o have comparable intensities in the directions parallel to the b and c axes. (24) As already mentioned above, as f a r as the plane of pyridine molecule tilts from the yz plane by only -loo, the intensity of the c-parallel band is small.
CONTRIBUTION FROM THE DEPARTMENT OF CHEMISTRY, UNIVERSITY OF MINNESOTA, MINNEAPOLIS, MINNESOTA55455
The Solvent Isotope Effect on the Dissociation of the Aquopentaamminecobalt(II1) Ion1 BY ROGER C. SPLINTER,? SIMON J. HARRIS,S AND R. STUART TOBIAS
Received August 28, 1967 Potentiometric and spectrophotometric techniques were used to determine the equilibrium constants for three reactions: (1) C O ( N H ~ ) ~ O H ~HzO ~ + = Co(NHa)60H2+ HaO’; (2) Co(NH3)60Dz3+ DzO = Co(NH3)50D2+ D30’; (3) CO(ND3)50DzSf DzO = Co(NDa)50D2+ D 3 0 + a t 25” in a medium with [C104-] = 0.3000 M. Values of log *K1= - 6.22, -6.75 (89y0 DzO), and -6.70 (99% DzO), respectively, were obtained. Each value of the equilibrium constant was refined by least squares. The partially exchanged species C O ( N H ~ ) ~ O Dwas Z ~studied + using a flow system. Contrary t o an earlier report, the aquopentaamminecobalt(II1) ion exhibits a rather normal isotope effect, log ( K H / K D = ) 0.48 i 0.01 Z ~ +that of C O ( N D ~ ) ~ (error a t the 99% confidence limit). A comparison of the dissociation constant of C O ( N H ~ ) ~ O Dwith ODza+, log K I = - 6.81 and - 6.70 (valid for 100 mol % DzO), respectively, indicates the size of any secondary isotope effect which arises from the exchange of the 15 ammine hydrogens.
+
+
+
+
+
Introduction Both theory and measurement of acid dissociation constants in protium and deuterium oxides have indicated a correlation between the magnitude of the dissociation constant and the magnitude of the solvent isotope effect. This equilibrium isotope effect is conveniently described in terms of log (KH/’KD)where KII and K D are the acid dissociation constants in HzO and
D20 solution, respectively.* In general, this quantity increases as the acid strength decreases. Early measurements suggested an approximately linear relation between log ( K H / K D ) and ~ K H The . same conclusion was anticipated4 on the basis of a very simple model; however, more recent s t u d i e ~ have ~,~ shown that this result is not necessarily true if the acids are of different structural types. One class of acid which has appeared to behave very
(1) Research sponsored by AFOSR(SRC)-OAR, USAF Grant No. AFAFOSR-691-65 and -67; portions of this report are based on a dissertation submitted by R. C. S. to the Graduate School of the University of Minnesota in partial fulfillment of the requirements for the Ph.D. degree, 1967. (2) Du Pont Fellow, 1964-1965. (3) Research Fellow in Chemistry.
(4) See R. P. Bell, “The Proton in Chemistry,” Cornel1 University Press, Ithaca, N. Y.,1959, Chapter 11, and R. W. Gurney, “Ionic Processes in Solution,” McGraw-Hill Book Co., Inc., New York, N. Y., 1953, p 150, for discussions of this effect. (5) R. P. Bell and A. T. Kuhn, Trans. Faraday Soc., 69, 1789 (1963). (6) A. 0.McDougall and F. H. Long, J . Phys. Chem., 6 6 , 429 (1962).
898 R. C. SPLINTER, S.J. HARRIS,AND R. S. TOBIAS irregularly is the aquo acid, that is, an acid where the proton is transferred from water molecules in the first coodination sphere of a metal ion. Huldis and Dodson reported that the first dissociation of the hexaaquoiron(111) ion ( p * K 1 = 2.92, 21”) p = 0.55) exhibited no measurable isotope effect7 and a similar result was reporteds for the first dissociation of the aquothallium(II1) ion (p*& = 1.16, 25O, p = 3.0). Taube has reportedg that the aquopentaamminecobalt(II1) ion showed an unusually small isotope effect: log ( K H / K D ) = 0.18, p*K1 = 6.16, 30°, p 0.25.1° I n contrast, measurementsll on the aquo cation (CzHg)3Sn+ indicated a normal isotope effect: log (KH/ K D ) = 0.69, p*K1 = 6.81, 25”, p = 3.0. The first dissociation of the hexaamniineplatinum(1V) cation12 also shows a rather typical isotope effect: log ( K K / K D ) = 0.62, pK1 = 7.16, 25”. Simple ammine complexes might be expected to show discrepancies analogous to those exhibited by aquo complexes. A better understanding of the structure and solvation of aquo acids and the nature of their protontransfer processes may be gained from a study of the apparent anomalies which they sometimes exhibit in the isotope effect. It has been suggested” that a possible cause of small isotope effects with aquo and ammine complexes could be large secondary isotope effects. Not only is the ionizing proton changed to a deuteron in the study of an ion like Fe(OH2)e3+ but 11 other hydrogens are also exchanged. The studies of the aquopentaamminecobalt(II1) ion were conducted on the species Co (NH3);OHz3+and C O ( N D ~ ) ~ O where D ~ ~ +16 hydrogens other than the one ionizing are isotopically substituted. Since the charge on the acid is reduced in going to the conjugate base, the hydrogens should become less satisfactory donors in forming hydrogen bonds to the solvent molecules. This has been reported to lead to a strengthening of the N-H bonds within the first coordination sphere of ammine complexes.13 This change in bond character going from reactant to product could give rise to a secondary isotope effect which would either oppose or, conceivably, completely compensate for the primary effect. Indeed the reaction Co(NH3)jOHs3+
+ C1-
=
Co(n’H3)jCI2+
+ HsO
where no primary effect is involved, has been reported8 to exhibit an “inverse” isotope effect: log ( K H / K D )= -0.167. A significant secondary isotope effect has been observed14 with formic and deuterioformic acids, DCOzH, in HzO. The exchange of the single hydrogen leads to a change in ~ K ofH0.035 i: 0.002unit. ( 7 ) J. Huldis and R. W.Dodqon. J . A m . Chem. Soc., 78, 94 (1956). ( 8 ) T. E. Rogers and G. M. Waind, Tvans. Pavaday Soc., 61, 1360 (1961). (9) H. Taube, J. A m . Chem. S o r . , 82, 624 (1960). (10) J. Bjerrum, ‘‘Metal Ammine Formation in Aqueous Solution,” Thesis, Copenhagen, 1841; reprinted by P. Haase and Son, Copenhagen, 1957, p 280. (11) R. S. Tobias and M. Yasuda, J . P h y s . Chem., 68, 1820 (1964). (12) R. G. Pearson, N. C. Stellwagen, and F. Basolo, J . A m . Chenz. Soc., 82, 1077 (1960). (13) See ref 11 for a discussion of the evidence for this. (14) R. P. Bell and W. B. T. Miller, Tvans. F a r a d a y SOC..69, 1147 (1963).
Inorganic Chemistry I n order to determine whether appreciable secondary isotope effects occur with aquo and ammine complexes, we have measured the equilibrium constants at 25’ in a constant ionic medium with [C104-] = 0.3000 M for reactions 1-3 using precise spectrophoCo(h’H3)jOHz3+ 4 Hn0 = Co(NH3)jOH2++ H30+ (1) Co(XHa)jODn3+ 4- D%O= Co(ISH3)sODZt + D30+ (2)
+
C O ( S D ~ ) ~ O D ~Dz0 ~ + = Co(ND3)aOD” f DyO+
(3)
tometric and potentiometric techniques. The aquopentaamminecobalt(II1) cation is probably the most extensively studied aquo ion, and its equilibrium constant is of a convenient magnitude for precise determination. Since effects such as those outlined above could occur in the formation of the transition state of a reaction involving aquo or ammine complex cations, large secondary kinetic isotope effects might also occur with these cations. For reactions proceeding by a conjugatebase mechanism, a knowledge of the equilibrium isotope effect is also necessary for an interpretation of the observed kinetic effect. The change of solvent from HzO to DzO affects both the magnitude of the equilibrium constant for the proton-transfer process as well as the rate constant of the slow step. Some of these aspects have been discussed by Pearson, et a1.12 Experimental Section Preparation of Solutions.-Aquopentaamminecobalt( 111) perchlorate was prepared from carbonatopentaamminecobalt( 111) nitrate which was synthesized by standard methods.15 Carbonatopentaamminecobalt( 111) nitrate (70 g) was dissolved in 4500 ml OF water at room temperature. Perchloric acid (390 ml, 2 X) was added, and the solution a t p H 2 was evaporated to 1100 ml, filtered, and cooled overnight in an ice bath. The crystals were separated by filtration, washed with 20 ml of ice water, recrystallized three times from 2 A!f HClOl and once From water, and finally air dried at 50” for 4 hr. The compound was analyzed for cobalt by destroying the complex with sodium hydroxide, reducing the oxide with sulfur dioxide, and titrating the cobalt (11) with EDTA.lB The other analyses were carried out commercially .I7 Anal. Calcd for [Co(NH3)sOH2](C104)3: Co, 12.8; S,15.2; H, 3.72; C1, 23.1. Found: Co, 12.9; IT,15.6; H, 3.79; C1, 23.2. Anhydrous NaC104 and stock solutions of DClO4 and NaOD were prepared as described earlier .I1 Solutions containing Co(NH3)50Ha3+were prepared by adding weighed amounts of [Co( NH3)sOH2]( C 1 0 4 ) 3 to standard HClOl or DC104 and protium or deuterium oxide. The perchlorate ion concentration was adjusted t o 0.3000 &’by adding either anhydrous liac104 to the deuterium-containing solutions or weighed portions of a standard solution of the salt in HnO for the protium oxide solutions. The near-infrared spectrum of solutions of the aquopentaamminecobalt(II1) in DaO was scanned, and the intensities of the band at 5988 cm-’ ( V I ra(HD0)) and the band at 6452 cm-’ of the ammine complex were measured as a function of time. Exchange wits found to be almost complete in 1 . 5 hr a t the pH of the stock solution, and it was only necessary to let the solutions stand a t 25” For 24 hr to ensure complete exchange. All ammine hydrogens behave as if they were equivalent, and a pseudo-first-order rate constant for their exchange was calculated
+
( 1 5 ) A. B. Lamb and K. J. N y s e l s , J . A m . Chem. Sor., 61, 468 (1845); Inoip. Syn., 4. 171 (1953). (16) F. J. Welcher, “The Analytical Uses of Ethylenediaminetetraacetic Acid,” D. Van Nostrand Co., Inc., Kew York, iX.Y . , 195X. p 230. (17) Schwarzkopf Microanalytical Laboratories, Woodside, N. Y .
Vol. 7 , No. 5, M a y 1968
DISSOCIATION OF THE
AQUOPENTAAMMINECOBALT(III) I O N 899 N2
THERMOSTAT
MOTOR DRlVENf BURETTES
110 m M C1Ag AgC1,290 m M C104300 m M Na+
I
H m M H30+( D 3 0 ) + I 300 m X CAIm M Co(NH&OH3+'Glass NaC104 (Co(ND3)60Dz3+) elec300-3Cnr - H m M N a + trode I300 m M ClOs-
REFERENCE ELECTRODE
Figure 1.-Flow
(18) F. Basolo, J. W. Palmer, and R. G. Pearson, J . A m . Chem. Soc., 83, 1073 (1960).
(19) J. W. Palmer and F. Basolo, J . Inovg. Nucl. Chem., 16, 279 (1960). ( 2 0 ) C. E. Freidline and R. S.Tobias, Inorg. Chem., 0 , 354 (1966). (21) W. Forsling, S. Hietanen, and L. G. SillCn, Acta Chem. Scand.,6, 901 (1952). (22) V. Gold and B. M. Lowe, J . Chem. SOC., A ,936 (1967). (23) P. K. Glascoe, J . Phys. Chem.. 69, 4416 (1965). (24) D. Bunn, F. S. Dainton, and S. Dickworth, Trans. Faraday Sac.,57, 1131 (1961). ( 2 5 ) N. C. Li, P. Lang, and R. illathur, J . Phys. Chem., 66, 1074 (1961). (26) K. Mikkelson and S. 0. Nielsen, ibid., 64, 632 (1960).
system for the titration of C O ( N H ~ ) ~ O D in ~ ~ + DzO.
ferent degrees of neutralization were obtained. For example, 45 ml of D20 was streamed with 5.130 ml of a solution 50.03 m M in CO(NH&OHS~+.During this time, 1.224 ml of 0.1035 M NaOD was added. T h e degree of neutralization, which within the experimental error is equal to E , was then 0.494 a t the mixing chamber. The complex was titrated with OD- within 10 sec after it was streamed with DzO. Each run was of 3-min duration, a sufficient period for the electrode to attain a constant potential. Since the diluted amine complex solution was still slightly acidic, exchange was negligible during this period. The hydrogen isotopic composition of the final solution was calculated from the initial volumes of protium and deuterium oxide. It was 89 mol yodeuterium. Spectrophotometric Measurements.-Absorbance data were obtained at 25.00 + 0.05' using a Cary Model 14recording spectrophotometer equipped with a thermostated cell compartment. The solutions were matched against blanks containing 0.300 M NaC104 in either HzO or 99.9 mol yo DzO, and 1-cm quartz cells were used throughout. All solutions containing deuterium were prepared under dry nitrogen gas to prevent isotopic dilution, and the solutions were filtered under the same gas prior to the absorbance measurements. The absorbance values were varied as a function of pH by mixing a solution of [Co(NH&OHZ](ClO& with standard HC104 or NaOH and adjusting [Clod-] to 0.300 M . The DsO solutions were prepared in a similar way. Molar absorptivities of [Co( NH3)sOHzl (C10& and [eo(XD3)40D2](c104)awere obtained from measurements on solutions with pH 3. The values for [Co(N H Z ) ~ O H ] ( C ~ Oand ~ ) Z[Co(ND&OD]( C104)L were obtained with solutions adjusted to pH 11. Experiments a t pH 12.6 showed that the absorbance, particularly in the ultraviolet region, increased appreciably in the time needed for the measurements probably because of base hydrolysis of the complex. No such drift was observed a t pH 11. The absorbance values for the acid and conjugate base represent the average of nine independent measurements each. The remaining absorbance values were measured in triplicate. Mass spectrometric determination of the isotopic distribution of the aquopentaamminecobalt(111) solutions indicated that they still contained more than 99 mol yodeuterium.
Results Calculation of the Equilibrium Constants from Emf Data.-The emf data were subjected to least-squares
900
R. C. SPLINTER, S.J. HARRIS,AND R.
S.TOBIAS
refinements usingZ7 the FORTRAN-60 program GAUSS z and the University of Minnesota CDC-1604 computer. This program minimizes the quantity 2;wi (ai,obad ?&,c&d)* where wiis a weighting factor. The input data for this calculation are the total aquopentaammine concentration, the measured pH, and experimental n values. For reasons discussed earlierz0 equal weights were employed in the refinement. The pH (or pD) value a t fi = 0.5 was used as the input value of the equilibrium constant. (The refined values are listed in Table 111, and the observed and calculated n values from the last cycle of the least-squares refinement are given in Table IV.) Calculation of the Equilibrium Constants from the Spectrophotometric Data.--A modification of the GACSS method program described above was written in order to carry out a least-squares refinement af the spectrophotometric data. In this program, GAUSS AB, the quantity minimized is 2 p i (A i,obsd - A i, c a l c d ) where A is the solution absorbance.z8 The input data for these calculations are the independently measured absorptivities of the acid and conjugate base, the observed absorbance of the solution, and the pH of the solution. The pH values of these solutions mere calculated using the equilibrium constants obtained from the standard emf measurements. Experimental determination of the pH of some of the solutions used in the spectrophotometric measurements, using the cell described above for standard emf measurements, gave values equal within the anticipated experimental error to those calculated. The values of the constants obtained from the emf measurements mere used as input values for the least-squares refinement. I n these calculations, wi was set equal to unity, since an examination of the effect of errors in the ammine concentration, the value of [ H f ] , the measured absorbance, and the two molar absorptivities indicated that the weights would not be greatly different for the different points. The moIar absorptivities are listed in Table I for the different wavelengths studied. A comparison with data obtained by other workers using the same cation (though not necessarily the same anion) is given in Table 11. The agreement is generally reasonable, although errors are difficult to estimate. The refined values of the equilibrium constants are given in Table 111, and the observed and calculated absorbances from the last cycle of the least-squares refinement are listed in Table IV. Discussion The results from the spectrophotometric and potentiometric measurements are not strictly independent of one another. The quantity fi can be expressed in terms of the master variable a = *K1[H+]-l, = a / (1 a ) , Similarly, the equilibrium concentration of the hydroxopentaamminecobalt(II1) ion is given by [MI = CnI(1 a ) - l where CnI is the total cobalt ammine concentration. Since the aquopentaammineco-
+
Inorganic Chemistry TABLE I MOLAR ABSORPTIVITIES( c M - ~ & - I ) AT DIFFERENT WAVELENGTHS A,
[Co-
[Co-
[Co-
(Co-
(NHa)sOHz](ClO4)a
(SDa)aOD2](Cl04)s
(NDz)jOD](ClO4)r
20.3 26.9 33.65 39.3 43.7 46.45 47.3 8.2 10.3 16.7 26.65 36.8
18.2 24.6 31.36 37.3 42.1 45.0 46.2 6.9 8.7 14.5 23.7 34.0
(NHa)sOH](ClO4)a 38.7 47.1 55.3 62.4 66.6 67.0 63.4 38.4 51.6 60.4 63.1 60.8
5500 5400 5300 5200 5100 5000 4900 4000 3900 3800 8700 3600
TABLE I1 MOLARABSORPTIVITIES (cni-1 AI-1) SELECTED WAVELENGTHS A,
AL
Co(SHdaOHz3'
36.2 44.6 53.2 60.6 66.0 67.5 64.5 35.1 48.9 59.55 63.35 61.75
AT
Co(NDa)s0Dz3+ C O ( N H E ) S O H ~Co(XDs)aODz'+
5500 2 0 , 3,c 21.0" 18.2,c 19.2a 5000 46.45,c 47.OU 45.0," 45.3" 67.0,O 66.8a 67.4,c69. Z a 5040d 67.P 5020d 67. 6c 4910d 47.3; 47. Eib 4890d 46.2,C46.2b 3700d 63. 4c 3680d 63. BC 3450d 44. 44, 3430d 43. 2,c 43. 2h a A. 1 %'. Adamson and F. Basolo, Acta Chem. Scnnd., 9, 1261 (1955). Reference 9. c This work. d Band maxima.
TABLE Irr REFINEDVALUESOF THE EQUILIBRIUM CONSTANTS AND THEIR STASDARD E R R O R S ~ Method
Log KH
Log KD
Standard emf ( K Din 99 mol % D20)
-6.217 10.004 (242, 1 0 . 0 2 2 ) -6.216 =to.002
-6.702 10.002 ( 5 2 , &0.006) -6.702 10.002
Spectrophotometric ( K Din 99 mol yo DzO )
Log (KH/Ku)
0.485 10.005 0.486 10.003
(108, rk0.008) (96, i-0.01) -6.184 -6.78 0.59 10.003 10.01 10.01 (20, =k0.008) (23, 1 0 . 0 1 ) Flow system (KD -6.223 -6.748 0.525 in 89 mol yoDzO) 1 0 . 004 rk0.001 10.004 (4, rk0.004) (5, 1 0 . 0 0 2 ) The number of experimental points used in calculating t h e constants and the standard error t o the fit are given in parentheses. Fast titration (Koin 89 mol % DsO)
balt(II1) ion is a weak acid, FZ in the range of interest is essentially equal to the degree of neutralization of the complex and can be calculated from the solution stoichiometry. Experimental measurement of [H+] than permits the calculation of *K1. The absorbance of the solutions also can be expressed as a function of a , the path length I , the molar absorptivities of the aquo acid and of the conjugate base Ebb, and the total cobalt ammine concentration C J ~ . Thus
+
(27) 12. S. Tobias and M. Yasuda, Inoig. Chem., 2, 1307 (1963). ( 2 8 ) Deck listings of all of the least-squares programs may be obtained b y writing to K . S. T.
Measurement of the solution absorbance a t different wavelengths and different stoichiometries gives only values of the master variable 01. Once again, in order
VoZ. 7, No. 5, May 1968
DISSOCIATION OF THE AQUOPENTAAMMINECOBALT(III) ION 901 TABLE IV CALCULATED AND OBSERVEDfi AND ABSORBANCE VALUES~
PROTIUM O X I D E 8.2.6 8.223 8.219 8.206
3.014
$.I92 8.179 8.166
4.261 4.699 4.929
0.152 8.139
3.101
-.a10 -.010
3.207
-.a00
3.328
-.OOL
3.5117 3.831
-e002
.001 .DO1 .a01 .001 002
.OOL .at1
e028
.a29
.OS0
0.126 8.113 8.100
S.114
-072
5.240 5.339
.,I6
.a49 .a73 .a95 .,I7
8.086 8.073 8.047 a.022 7.996 7.971 7,945 7.920 7.895
3.617
a136
.137
5.494 5.622
.I60
.!S9
-205
5.745 Si.827
a249
.LO2 -252
Si.917 6.005 6.064 6.144 6.210 e.297 6.379 6.454
a330
7.773 7.7.8 7.72s 7.701 7.689 7.677
6.5441
,692 e756
?ab65
7.050
7.6%
?.la3 7.2.3 7.376
7.870 7.846 7.811
7.797
7.612 7.630
7.619 7.607
7.S96
,094
6.632 6.734 6.846
-592 ,633 -678
.azs
6.909
6.9'16
7.523 7.772
.e47 e869 .e98 ~911 e936 .95a .980 1.000
1.00o
8.296 8.930 9.410 9.711 9.966
.?E2 a767 .SI0 .a31
-851
.a72 .a94 .91.
.93s .953
5.872 5.963
-318 e362
7.913
6.041
a106
4.883 4.873
6.302 6.376
5.625
6174
.20b
.Eta a263
.240
..a Es 6& 1
6.457
5.736 5.837
5.924 6.005
,307
6.076
a.40 6396
4.817
.LO*
.338 ,300 ..EO 472 .513
.529
.561
5.000
,573
e601 -648 e692
.e990
L.554 4.645
..69
.9s
.a91
4.537 4.529
,517
,51S
4.¶>1
.S38
,480
...
,351
.?*?
-714
4.4.54
.772
..$56
6.875 7.061
.a27 .E83 ,938 a971
,769 .e20 .a75 .92l .952 ~982 .002
4..I+
-003
4.404 4.682
9 4 2 5 1.015
*.,96
3.491
4.587 ..570 4 s 562
3.876 e.594 5.043 ¶.e91 5.459
8.207
8.194 8.181 (1.16'1 8.154 8.141 8. 127 8.114 8.101 8.085
10.492 2.206
1.002 -e000
1.000 .On0 .000
2.324 2.420
-000
8.eI3 8.179
2.481
.a01
.DO0 .000 .000
3.645
,013
.a03
a.!66 8.152 0.146 8.139 8.132
4.083
.ole
.007
4.563 4.739 b.860
-033
.a22
.a43 e054
.a32
4.953
e064
8.119
5.113
.0?3 ~ 0 8 6 .os2
8.106
5.241
,107
e042
.010
4.905
.a30
5.1OL
.m2
,026 -046 .a72
5.216
.07.
~091
5.322 5.413
a096 ,118
.I13
S.964 6.046 6.126 6.203 6.279 6.3LI8 6.429 6.517
.*62 ,207 .2-1 ,296
.226 .270 -315
e340
-350
.38. .a28 6473
.403
6.603
6.?05
6.819 6.9L1
,783 .a27
,800 ,842
7.690 7.679 7.667 7.655 7.6.4
7.005 7.086
.*eo
7.632 7.620
7.634
,549 . 8 ' 2 .89. ~916 .938 .960
8.033
.9a2
, . S O 8.637 3.055
A055
.755
4.133 6.125 4.417
...
4.40, 09 1.391 1.000 L.990 4.980 a.970 4.960 4.950
e881 e902 -922
.94S e963 .985
1.004
.P9*
-.a35
.a01
ACbL
4.488
4.480 4.471 a e . 6 . e620 4e.56 ~ 6 6 6 4.448 .709 4.440
e535 .575
7.726 7,702
7.290
4.513 4.505 4.496
..a7 a492
7.774 7.750
7.183
4.417
4.554 ..s.5 4.536 4.529 ..s2,
.IS8 .I01
e141
4.b48 4.440 4.433 4.425
e.579
,136
.SI? ,561 ,606 e650 -601 .739
..6X
ACbL -LOG W
9.5
.Otl
7.609
.09b
.sa2
4.639
s.786 5.880
7.798
..so5 4.513
.555
-e007
..ZOO
5.492 5.561 5.682
8.075 8.049 .973 8.023 .992 7.998 a998 7.972 ~ 9 9 9 7.9*7 1.000 7.922 1.000 7.897 1.000 7.872
8.520
LOBS
-163
6.740
,.em
-LOG H
.ita
.457 .e36
.0.2 .086 .,10
6.614
7.847
8.440
~ 0 0 6 .a35
5.364 5.508
7.731 7.701
7.607
6.LSO
..775 S.129
.473 ,484
7.517 7.950 1.001 3.461 -e017 3.742 -.a15
5.898 s.99, 6.071
4.912 4.902 4.892
4.570
e661
7.302
5.016
*e931 Il.PP1
4.562
6.502
7.671 7.642 7.625
4.941
4.590 ..879
7.791 7.760
6.361
.a02 .a00
..00
.15B
e605 ..a8 ~ 6 2 5 4.480 -6SS 1.472
1.000
.wo
-.027
.620
1.000
-000
.001 .001
6.103
1.002
2.240
4.600
3.338 3.385 4.119
6.*39
10..02
10.159
3.179
4.615 4.601
.Ell -269 -31 1
7.809
IO.28i!
7.550 7.538
e462
4.624
-177
7.82,
7.s27 7.516 ?.SOL 8.630 0.593
7.561
e140
-130
.539 -561 .sa4 -606
1.000 1.001 1.001 1.001 1.001 1.002
7.584 7.572
6.10s 6.143 6.164 6.183 6.202 6.213 6.283 6.313
7.833
.SO0 .Sa6
-781
7.983 7.958
7.870 7.858 7.811
..s0
9648
8.009
.I29 .273
7.889 7.883
-415
.359 .SO3
,!as
7.895
.334 .380
,471 e515
.I41
5.549 5.670 S.783
7.91L 7.901
~ 3 0 0 .ZB9
,382 ,426
5.392
8.060
8.03s
*
,001 -006
8.086
-LOG U
bbBS
6.168 6 . 2 . 0 6.32. 6e.00 6.482 6.S69 6.662 6.77b 6.895 7.036 7.224 0.148 7.518
2.641
,617 .662
$075
,294
~ 7 0 6 .736 .750 e703
,795 .a39 .081 a928 ~971 -.025 -a003 ,027
,008 ,068 6112
e526 .a68
e910 .9S2 e908 ,999 .000
4.845 4.836 4.826 ..798 ..?e9 4.980
4.970 1.960 4.950 ..9*1 a.931 as921 ..912 0.902 4.892 4.883
.002
4.873
.on5
4.. I 88 5.64
.a23
-063 e106 .I49
..8.5
a. e36
6.225
6.336 6.625
6.723 6.885 6.9.9 7.290 7.603 4.300 ..939 S.234 5.42B S.576 5.696 5.802 5.894 5.983 6.066 6.139 6.216 *.e92 6.369 6.447 6.328
6.621 6.711
4.826
8.502
6.820 6.936 *.a08 7.087 4.798 7.297 .285 .998 e.662 a328 -996 s.018 .383 .99. 5.2*9 .*I0 ~462 .992 5.426 .990 5.562 .so4 ,988 5.673 .5.7 e986 5.768 .590 .Pa4 5.861 -632 .9az 5.943 -676 .9a0 6.022 -71T .970 6.093 ,760 .9?6 6.159 ,802 a975 6.230 ,802 1973 6.300 .a82 6.372 .9?1 -962 e 922 n 969 644. -967 6.514 .995
4.268
.011
-96s
6.583
*.gas
.os5 .IO2 -145
.e63 .961 ,960
6.657 6 . 7 . 1 6.837
e192 -237
e956
.l$6
5.602
.ZOO
* 195
B.726
.P19 .289
.E.4
1.818
5.906 6.01"
6.074 6.151 6.224 6.299 6.376 6.4S2 6.536 6.620
.33* .378
. . e 3 ,467
6.717
6.521) 6.942 7.089 7.619 7.289
5.271 S*&47 9.593
5.709
ACAL
-LOG H
4.817
.=a
bCbL
CAST TlTRbTION HZ0
6.WI 7.073
-LOG H
4-S
*CbL
DCUTERI W O X I D C LAMBD1
LAMBDb
=
AWS
-LOG W
LbWDb
-LOG
H
100s
bCAL
-LOG Y
Lb4Dl 5.991
5400 A
-
*
LAYBOA
I
3900 A
=
3700 1
-306
~302
5100 b
LIWDb 5000 A
bCAL
5200 1
.
LAMBDA
bms
5500 b
LbM80A
a
=
ACAL
s.991
=
3900 b
.!sa
.153
All aquopentaamminecobalt(II1) concentrations in millimoles per liter.
to calculate *K1, values of [H+] must be obtained exan examination of the data in Table IV indicates that perimentally. Consequently, there is one type of these are absent. error in the value of log *K1which would go undetected The agreement obtained between the standard potentiometric data and the spectrophotometric data is in this work. If all values of the solution pH were in error by a constant amount, e.g., if they were all 0.1 excellent: log K H = -6.217 f 0.010 and -6.216 f unit too large, the p*Kl value calculated by both the 0.005; log KD = -6.702 f 0.005 and -6.702 =t 0.005, respectively. In this discussion the errors are potentiometric and the spectrophotometric methods those a t the 99% confidence The values for would then be 0.1 unit too large. This follows from the H2O are in good agreement with those of earlier workrelation log (Y = p H - p"K1. ers: log *KH= -6.16, 0.25MNHdN08,3Oo;'O -6.55, While small errors might be made in the determination of the cell E" giving a constant error in log [H+], 1 M NaN03, 25°.30 The most likely source of error in (29) Tables of the "t" test of significance were used: see, for example. these should be randomized by the different sets of data. R. A. Fisher, "Statistical Methods for Research Workers," Hafner PublishErrors in the p H data other than one which is coni n-a c o ... N e w Y o r k . ~ . y . .1 9 5 4... ~ 1 7 4 . (30) G. E. Shaffer, quoted by L. G. Sillen and A. E. Martell, "Stability stant throughout give systematic deviations beConstants of Metal-Ion Complexes," Special Publication No. 17, The Chemitween the calculated and observed f i and A data, and cal Society, London, 1964. I
902 R. C. SPLINTER, S.J. HARRIS, AND K. S.TOBIAS the earlier spectrophotometric measurements lies in the molar absorbtivity of the conjugate base since this species is s l o d y hydrolyzed in strongly basic solution. The rate of exchange of the ammine hydrogen in similar complexes has been observed to vary inversely with the hydrogen ion c o n ~ e n t r a t i o n , ~and ~ > 1 Taube ~ has suggested that this is probably the case with the aquopentaamminecobalt(II1) Assuming this inverse first-order dependence obtains, the order of magnitude of the half-life for exchange of the ammine hydrogens of Co(NH3)5OHz3- in DzO a t ri = 0.5 and p D -6.7 is ca. 8 sec. With the flow system, no appreciable ammine hydrogen exchange will have occurred a t the time the [H+] is determined, but the exchange of the aquo protons is so rapid that these will have essentially the same composition as the solvent. The small number of points collected is a conscquencc of the large volumes of DzO which were consumed in the 3-min flow measurements. Because of the high rate of exchange, the data in the fast titrations span the entire period during which exchange was taking place. Values of the dissociation constant in HzO were determined by the fast titration and flow techniques to assess the systematic errors inherent in these measurements. As can be seen from the results listed in Table 111,the value from the flow measurements is in very good agreement with those from the standard emf and spectrophotometric procedures. The agreement of the fast titration value is poorer, probably a consequence of the short times allowed for the glass electrode to attain equilibrium. Using a linear extrapolation, the value of log K D for 100 mol % DzO is -6.81 from both the flow and rapid titration measurements. Considering the errors in the rapid titrations, the agreement is probably fortuitous. This gives log (I
