1868
K. L. Craighead, P. Jones, and R. G. Bryant
Nuclear Magnetic Resonance Investigation of Cobalt (111) Outer-Sphere Complexes in Aqueous Solutions K. L. Cralghead, P. Jones, and R. G. Bryant* Department of Chemistry, University of Minnesota, Mlnneapolis, Minnesota 55455 (Received October 3 1, 1974; Revised Manuscript Received May 15, 1975) Publication costs assisted by the National Institutes of Health
Nuclear magnetic resonance relaxation time measurements are reported for nuclei participating in weak outer-sphere complexes of cobalt(II1) complex ions. The data are analyzed in terms of outer-sphere association constants and line broadening parameters. Analysis of the relaxation times in the outer-sphere complexes is made with the aid of measurements on model systems to evaluate some of the several contributions to the relaxation rates. It is concluded that the solvent-solute interaction of halide ions in outersphere association with tris(diamine) chelates of cobalt(II1) is significantly perturbed. Within experimental errors, both optical and NMR methods gave the same values for equilibrium constants.
Introduction The existence of ion pairs or outer-sphere metal complexes is often postulated to explain data from a variety of experiments ranging from thermodynamic measurements1 on electrolyte solutions to kinetic measurements on inorganic2 reactions. Nevertheless relatively little detailed in,formation has been presented concerning ion pair structure or other physical properties in aqueous solutions, Experimental difficulties in the study of outer-sphere complexes are accute in aqueous solutions. Reports of outer-sphere association constants between simple inorganic anions and complex cations have differed significantly if different measuring techniques are used in the same or different lab~ r a t o r i e s For . ~ example, the suggestion based on NMR experiments that hydrophobic substituents such as alkyl groups on one ion will promote ion association4 is not supported by conductance or spectrophotometric result^.^ It might be suggested that these discrepancies are associated with the selective detection of different ion pair structures by different physical techniques. However, assuming that equilibrium thermodynamics may be applied, Orgel and Mulliken6 have shown that even if a large number of structurally different 1:l ion pairs are formed, analysis of the data from any experiment should yield the same value for the apparent 1:l association constant. The observed equilibrium constant will be the sum of equilibrium constants for the formation of each structural type. According to this analysis each physical technique should yield the same equilibrium constant even if some structural types of 1:1 complex have a negligible extinction coefficient or its equivalent for a particular measurement. On the other hand, if the equilibrium under study is complicated by additional weak associations due to presumably passive electrolyte ions, such as perchlorate ion, Johansson6 has pointed out that different types of measurement may lead to different results depending on the experimental details. The present investigation was undertaken to examine the equilibrium constants and structural properties of the outer-sphere complexes of various cobalt(II1) amine complexes in water using both broad line NMR and optical methods. The Journal of Physical Chemistry, Voi. 79, No. 17?1975
Experimental Section Spectrophotometric equilibrium measurements were made on a Cary 14 spectrophotometer using a short pathlength cell so that the same metal complex concentrations could be used in NMR measurements. The cell was calibrated a t 545 nm using potassium permanganate in 1 M sulfuric acid by comparison with a standard 1.00-cm cell and by comparison with Lingane and Collat's' value for the extinction coefficient of 2.31 A4-l cm-l. Temperature was controlled at 25.0 or 30.0°. NMR spectra were recorded on a Varian DP-60 NMR spectrometer employing methods described previously.8 Samples were contained in 15-mm 0.d. test tubes. For bromine measurements temperature was controlled with a Varian variable temperature controller because 81Br line widths are very sensitive to small changes in temperature. ' In all experiments the radiofrequency power was adjusted to be below saturation. For the broadest bromine lines where derivative spectra were obtained, the modulation amplitude was adjusted to obtain negligible modulation broadening. Line widths were measured as the full-width at half-height of the absorption mode signal. For the derivative signals line widths were measured between extrema and corrected to the absorption mode width by multiplying by 1.732. In all cases the magnetic field was calibrated from side band separations. 59C0 chemical shift measurements were made using 16-mm sample tubes with standard 5-mm thin walled NMR tubes containing the reference solution placed coaxially inside. 35Clmeasurements of 2'1, were made using the adiabatic half passage experiment^.^ The field was swept off resonance with a 100 to 200 mA current placed on the probe helmholtz coils on top of the audiomodulation. The transient signal taken from the PAR Model 121 lock-in detector was accumulated on a Varian C-1024 CAT or recorded directly on a Midwestern Instruments LCRII oscillographic recorder. T I , values were extrapolated to zero Hi. The response of this configuration was measured to be 0.05 sec for a modulation frequency of 500 Hz and was not determined by the lock-in amplifier time constant.
NMR Investigation of
Co(lll)Outer Sphere Complexes
1869
Data were fit to assumed equilibrium models both manTABLE I: 35CC1and 81BrNMR Line Broadening in Aqueous Bromide and Chloride Solutions ually and using a least-squares fitting program described of Co(II1) Complexes by Bevington.lo In some cases the data were not of sufficient precision to permit establishment of a unique mini*'Br broad- 35Clbroad- Ligand mum on the least-squares surface so that equilibrium data Complex , ening,aHz ening,bHz concn, 114 are reported to only one figure. [ C O ( N H ~ ) ~ ][ C ~ O ~( N , ~H~~ ) ~ C ~ [Co(NH3)5BrjBr~,~~ ]C~~,'~ C o (NH,) 63+ 1.5 0.50 [ C O ( N H ~ ) ~ ~ H Z I ( C [CO(NH~)~(OHZ)~I(C~~~)~,~~ ~~~)~,~~ 50 C [Co(en)3]C13,l6and [Co(pn)3]C13l7were synthesized accordCo(NH,),Br2+ 30 C ing to standard procedures. Butylenediamine (bn) was pre3 0.50 C 0 ("315 (HzO)~+ pared as described by Cooley, Liu, and Bailar.ls 90 0.60 [Co(bn)3]C13was prepared by diluting 14 ml of the bn pre5 0.6 Co(NHJ,(H,0),3+ pared above (-0.1 mol) with 15 ml water and partly neuC o (en) 18 0.5 tralizing with 4 ml of concentrated HC1 (0.047 mol) in 15 500 0.45 ml of water. This mixture was poured into a solution of 3.6 38 0.6 C~(pn),~+ g of CoClz.6Hz0 (0.015 mol) in 11 ml of water and air was 1230 0.45 rapidly bubbled through the solution for 3 hr. The dark, Co (bn)33+ 72 0.6 red-brown colored solution was evaporated on a steam bath Line width increase over 450 Hz of 0.6 M NaslBr at 25". b Line until a crust formed over the surface and was then cooled width increase over 12 Hz of 0.5 M Na3W1 at ambient temperature in an ice bath. Concentrated HCl (3 ml) and 70 ml of absoof 27 f 2". Saturated solution' of t h e complex bromide salt, no lute ethanol were added to precipitate the salt, which was other salts present. filtered and washed with absolute ethanol. The product was recrystallized three times from a small amount of warm TABLE 11: 59C0NMR Line Widths and Chemical Shifts water with cold absolute ethanol and dried under vacuum of Aqueous [Co(en)a]Ls Solutions a t room temperature. Perchlorate and bromide salts of the complexes were Total metal 59C0line 5yC0 prepared by dissolving the chloride salts in a minimum Complex concn, 11.1 width, Hz shift, ppm amount of warm water, adding concentrated HC104 or HBr while cooling in an ice bath, filtering, and washing with ab120 O = refer[Co (en),] (C IO4), 0.2 0 solute ethanol. Three recrystallizations were performed ence using the same procedure. 120 +5 [Co(en),lC1, 0.20 0.20 110 -27 [Co(en)31Br3 Results and Discussion Saturated 130 -8 [C0(en)~11~ Table I summarizes the effects of a series of cobalt(II1) 120 +12 [Co(en),I~l, 0.20 + 0.1 M complexes on 35Cl and 81Br line widths in aqueous chloride phosphate at and bromide solutions. Table I1 shows changes in the 59Co PH 6 resonance line width and chemical shift for C0(en)3~+in [co(en),l~l, 0.20 + 0.1 M 180 1-43 the presence of various anions. phosphate at There may be a number of reasons for the decrease in pH 10.5 35Cl and 81Br relaxation times caused by Co(II1) complexes. These include quadrupole relaxation due to viscosiTABLE 111: Outer-Sphere Association Constants for t y changes affecting the correlation times characterizing Co(II1) Complexes with Chloride and Phosphate Ions the solution, relaxation mechanisms other than quadrupole from 35Cl and 59Co Line Width and Chemical relaxation, and quadrupole relaxation caused by innerShift Measurements sphere substitution and outer-sphere complex formation. Aw,,, Nucleus Direct measurements made on the solutions used in obComplex K,, A V , ~ Hz , ppm obsd taining the data for Table I11 indicate that over the range of concentrations used, the viscosity changes are approxi35~1 [ ~ o ( e n ) , ] ~~+ ,1 1 200 mately 5-10% and therefore cannot account for the effects [ ~ o ( p n ) ~ ]C1' ~+, 1 400 35~1 shown in Table I. Viscosity corrections were applied before [Co (bn),I3+, Cl1 1000 95~1 calculating association constants. 260 122 59cO [Co(en),I3+, Pod3- 30 For 35Cl and 81Br, the nuclear electric quadrupole mo89 53c~ [ ~ o ( p n ) , ] ~P+O,.,,20' ment dominates the nuclear spin relaxation. Often a most efficient relaxation mechanism is the interaction of the nua Derived for [trans-A-C0((-)pn)3]~+ and [truns-A-Co((+)clear magnetic moment with electron magnetic moments. pn)3I3+. However, the cobalt(111) complexes studied are diamagnetic and therefore this relaxation mechanism is not imporspecies. However, the line width for a halogen in the first tant. The absence of paramagnetic effects is supported by coordination sphere of a cobalt complex will be several ormeasurements of the water proton relaxation rate in these ders of magnitude larger than that observed for the uncoorsolutions. dinated species, and would not be observed employing the Some of the cobalt(II1) complexes studied undergo subconditions used here to observe the free ion. stitution reactions with chloride and bromide ions. Half59C0 chemical shifts have been previously related to lives for these reactions are on the order of several hours to outer-sphere complex formation.29 The present study supdays.19 Since these reactions are so slow, separate NMR ports this conclusion and will indicate that the 59C0 line signals should be observed for each substituted product width monitors the same chemical interactions.
,,+
(I
The Journal of Physical Chemistry, Vol. 79, No. 17, 1975
1870
K. L. Craighead, P. Jones, and R. 0. Bryant
Assuming then that these relaxation time and chemical shift changes can be attributed to outer-sphere complex formation, it is possible to determine outer-sphere association constants from these effects. The equilibrium constant, KO,,for the association of a cation M and an anion L to form an outer-sphere complex (or ion pair), X, can be measured from the concentration dependence of a physical property of either the cation or the anion. Exchange of either partner between free sites and ion pair sites is expected to be diffusion controlled20and therefore very fast compared with NMR shifts or line widths. In this case the observed NMR line width and chemical shift for a nucleus exchanging rapidly between free and ion pair sites will be a weighted average of the values for each site in If a property of the metal complex is measured, the line width, chemical shift, or optical density, represented by Wobsd, is given by
?I 20
m
oi
0'5
IO 1'5 [Cl-I M
2'0
Figure 1. 35CI NMR line width vs. chloride ion concentration for 0.15 M [Co(pn)3]CIS at ambient temperature.
where wf and Wb are the observables for the free and bound sites, respectively, [XI is the ion pair concentration, and (M) is the total metal concentration. By combining eq 1 with the expression for KO,
KO, = [Xl/[MI[Ll
(2)
the following equation is obtained: 05 Kos(M)wobsd2
Ob
-
Wf}wobsd
-
{Kos(M)(wb
+
{K~~[Llwb(wb
wf) -
K,(wb wf)
WbWf
- of)
+ KOS(M')WbWf
+
- Of2} = 0
(3)
[ci-l,
10
M
15
Figure 2. Absorbance at 281 nm and 25.0' for 0.10 M [Co(~n)~]-
(C104)3vS. [cl-].
If changes in [L] are negligible during the experiment, the concentration dependence of the observable becomes
Similarly, if a property of the anion is measured, eq 3 is replaced by
where q, and vf are the values of the observable for the anion in the outer-sphere complex and free in solution, respectively. This may be reduced to
if outer-sphere complex concentration is small compared with total ligand concentration. For many of the cases shown in Tables I and I1 it was not possible to determine ion pair association constants, either because the complex solubility is too low or because the effects are too small to observe changes outside experimental error as a function of ligand concentration. Formation constants that were determined by fitting the concentration dependence of NMR and optical data to one of the eq 1-6 are shown in Table 111. Examples of the data and calculated curves are shown in Figures 1-3. For the chloride ion pairs the approximate expression yields the same results as the more exact equations; however, for the phosphate experiments eq 3 is necessary. The Journal of Physical Chemistty, Vol. 79, No. 17, 1975
"B
501
1
I
02
Flgure 3. 5eCo chemical shift and line width for 0.10 M [Co(en)s]Cl3 vs. phosphate concentration at pH 13.5 and ambient temperature. Shift reference is saturated [C0(en)~](ClO~)3.
Although the error in measuring NMR line widths in these experiments is 5% or less, the concentration range available for the study of the equilibria involved is small. The precision and accuracy of the derived equilibrium constants is therefore limited. The optical methods did in general give slightly different values for the equilibrium constants. However, large values of the reduced x2 statistic for the NMR data make it impossible to conclude that the NMR results for outer-sphere complex association constants disagree with the somewhat more precise optical experiments.
1871
NMR Investigation of Co(lll)Outer Sphere Complexes
Outer-sphere complex formation constants are known to be a function of ionic strength. They become quite large in dilute solutions, but the dependence on ionic strength is weaker in concentrated electrolytes.2 In many cases ionic activity is controlled by maintaining a supporting electrolyte concentration an order of magnitude higher than the concentration of the species studied. In the present study it is difficult to use this method because extremely high salt concentrations are required which cause additional difficulties such as precipitation of the metal complexes being studied. Some authors choose to maintain total electrolyte concentration constant. The solution composition changes using this procedure, however, and activities of individual ions may vary significantly even though the total ionic strength remains constant. An attempt was made to assess the effects of ionic strength on the association constants measured here. Ionic strength was controlled for the chloride system by adding sodium perchlorate to maintain the total ionic strength a t 2.8 M . Differences in the 35Cl NMR data between experiments in which ionic strength is controlled and when it is not are within the experimental uncertainties. On the other hand, in analyzing the data from the optical experiments performed in the presence of perchlorate ion a weak interaction between the perchlorate ion and the metal complex was required to fit the data. In this case the equation for the observed extinction coefficient becomes Ef
