NMROF ''0
AND
2689
W 1 IN AQUEOUSHC1 SOLUTIONS OF Co(I1)
Nuclear Magnetic Resonance of Oxygen-17 and Chlorine-35 in
Aqueous Hydrochloric Acid Solutions of Cobalt(11).
11.
Relaxation and Chemical Exchange1 by A. H. Zeltmann, N. A. Matwiyofl, and L. 0. Morgan2 University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87644
(Received January 10, 1969)
Aqueous solutions of cobalt(I1) in hydrochloric acid have been found to contain the species Co(H20)~?+, CoC1(Ha0)6+,COCI~(H~O)~, CoCla(Hs0)-, and CoClP. Relative concentrations of these species as functions of temperature and hydrochloric acid concentration were reported previously on the basis of analysis of oxygen17 and chlorine-35 shifts. In this article the species distributions were modified to take advantage of improved treatment of water and hydrochloric acid activities at elevated temperatures. Using those species concentrations nuclear resonance line broadening results were interpreted in terms of chemical exchange rate parameters and transverse nuclear relaxation rates in the complex ions or molecules. Four-coordinated, presumably tetrahedral complexes exchange both C1- and HZO with bulk solution at rates too rapid to be measured by these techniques, but measurable rates were observed for six-coordinated, octahedral species. Pseudo-firstorder rate constants (corrected for water activity) for H20,per ligand, are 2.6 X lo6 and 1.7 X lo' sec-l at 300'K for Co(Hz0)o2+and CoCl(Ht0)6+, respectively. For C1- in CoCl(H20)6+,the equivalent rate constant is 6.8 x lo6 sec-l. In all cases it was assumed that the exchange process is bimolecular, involving an incoming HzO molecule. Nuclear transverse relaxation was found to occur for oxygen-17 principally through modulation of the isotropic hyperfine interaction and for chlorine-35 through modulation of the quadrupole interaction. In the first instance, the correlation time is the very short electronic relaxation time for cobalt(I1) and, in the second, the characteristic time for reorientation of the complex or "tumbling."
Introduction Estimated relative abundances of complex species in cobalt(I1)-hydrochloric acid solutions were reported in an earlier article3 (part I). Those values were obtained by analysis of chemical shifts for oxygen-17 (in HzO) and chlorine-35 (as C1-) over a wide range of temperature and HC1 concentrations. With some modifications, to be discussed in detail in a later section, those estimated abundances were used in this work to correlate line broadening results for the two nuclear species in similar solutions. The correlation permits identification of contributing line broadening mechanisms and, for octahedral species, chemical exchange rate parameters. Analysis of the broadening data is based on the nuclear relaxation rate equations given by Swift and Connick4 for application t o oxygen-17 relaxation in relatively dilute paramagnetic ion solutions. In that work they brought together and discussed the various possible contributions to line broadening.6-1Q They applied their interpretation to experimental results on a number of aquated transition metal ions in aqueous solution, among which was C O ( H ~ O ) ~ ~ + . Recently, Chmelnick and Fiat20 reinvestigated the chemical shifts and line broadening of oxygen-17 in aqueous cobalt(I1) perchlorate solutions. As it was necessary to obtain accurate parameters for the hexaaquocobalt(I1) species in aqueous solution to provide a basis for interpretation of our results in hydrochloric
acid solutions, a similar investigation was carried out in this laboratory. A report of the chemical shift results (1) Work performed under the auspices of the U. S. Atomic Energy Commission. (2) Department of Chemistry, The University of Texas, Austin, Texas 78712. (3) A. H.Zeltmann, N. A. Matwiyoff, and L. 0. Morgan, J . Phys.
Chem., 72, 121 (1968). (4) T. J. Swift and R. E. Connick, J . Chem. Phys., 37, 307 (1962); 41, 25553 (1964). (5) N. Bloembergen, E. 679 (1948).
M. Purcell, and R. V. Pound, Phys. Rev., 73,
(6) I. Solomon, ibid., 99, 559 (1955) (7)
(8)
I. Solomon and N. Bloembergen, J . Chem. Phys., 25, 261 (1956). H.M. McConnell and 5. B. Berger, ibid.,27, 230 (1957).
(9) N. Bloembergen, ibid., 27, 572, 596 (1957). (10) H. M. McConnell, ibid., 28, 430 (1958). (11) R. S. Codrington and N. Bloembergen, ibid., 29, 600 (1958). (12) R. E. Connick and R. E. Poulson, ibid., 30, 759 (1959). (13) R. Hausser and G. Laultien, 2.Phys., 153, 394 (1959). (14) R. A. Bernheim, T. H. Brown, H. 8. Gutowsky, and D. E. Woessner, J. Chem. P h m , 30, 950 (1969). (15) Lo0. Morgan and A. W. Nolle, ibid., 31, 365 (1959). (16) P. F. Cox and L. 0.Morgan, J. Amer. Chem. Soc., 81, 6409 (1959). (17) R. G. Pearson, J. Palmer, M. M. Anderson, and A. L. Allred, 2. Elektrochem., 64, 110 (1960). (18) N. Bloembergen and L. 0 . Morgan, J . Chem. Phys., 34, 842 (1961). (19) R. E. Connick and E. D. Stover, J . Phys. Chem., 65, 2075 (1961). (20) A. M. Chmelnick and D. Fiat, J . Chem. Phys., 47, 3986 (1967).
Volume 73, Number 8 August 1060
2690
A. H. ZELTMANN, K. A. MATWIYOFF, AND L. 0. MORGAN
was given in part I, and those for line broadening are included here. They are in substantial agreement with the results obtained by Chmelnick and Fiat, but some details of interpretation are different. Those are pointed o u t in the discussion to follow. At low hydrochloric acid concentrations, cobalt(I1) solutions are pink, changing to deep blue at higher concentrations. If chloride ions are present, the pink solutions also change to blue a t high temperatures and the temperature at which the change takes place decreases with increasixg hydrochloric acid concentration. I n the intermediate concentration range the purplish color of the solutions may be converted into pink by lowering the temperature to 0" and below. Those qualitative observations are borne out by the quantitative species abundances, if the pink to blue color change is associated with the transition from octahedral to tetrahedral species, which apparently occurs at the dichloro complex, CoC12(H20)2. I n the absence of chloride ions, as in aqueous cobalt(I1) perchlorate solutions, the pink color becomes more intense with increasing temperature. Spectra of solutions at temperatures as high as 150" do not show any indication of the characteristic tetrahedral spectral components, but do reveal increased absorbance at the position of the octahedral doublet (ca. 20,000 cm-l) and a shift of the band to lower energy. Those changes probably do not indicate appearance of a new species, but reflect thermal excitation to higher levels in the electronic ground state. Chemical shift data give no indication of lower coordination number at elevated temperatures in those solutions. Results reported here confirm the absence of exchangeable water in the highest chloro complexes and substantiate the species distributions determined by chemical shift mea~urements.~Dependence of both chlorine-35 and oxygen-17 relaxation on the rate of chemical exchange of chloride and water between the complex octahedral species over a considerable range of both concentration and temperature permits evaluation and comparison of the exchange rate parameters for such species.
Experimental Section Cobalt(I1) perchlorate (G. Frederick Smith Co.) was recrystallized twice from perchloric acid solution. The resulting crystals contained a small amount of free perchloric acid. Solutions prepared by dissolving the recrystallized cobalt(I1) perchlorate in water containing enriched H2Ol7were analyzed for cobalt(I1) by titration with ethylenediaminetetraacetic acid. Total cation equivalence of the solutions was determined by displacement of hydrogen from a cation-exchange resin and titration of the acid solution. Upon subtraction of the cobalt(I1) equivalence, a value of the hydrogen ion concentration in the crystals was obtained. The difference between the weight of crystals used in preparation of the solution and the known amounts of cobalt(I1) The Journal
of
Physical Chemistry
perchorate and perchloric acid was assumed to be water. That value was then used to correct the enrichment factor for oxygen-17 in the solutions used in magnetic resonance measurements. Cobalt(I1) chloride solutions were prepared, as described previously,a by mixing weighed amounts of analyzed stock solutions. Cobalt(I1) concentrations ranged from 0.10 to 0.30 m. Oxygen-17 contents were in the range 2.0-3.2%. Nuclear measurements were made as before,21except that a proton magnetometer was employed for calibration of spectra.
Results Solution compositions and line broadening for both oxygen-17 (8.000 MHz) and chlorine-35 (5.000 MHz) a t 300°K are given in Table I (see Figure 1). Relative species abundances, a,,,,listed there differ from those given in part I, as small errors were introduced in the original analysis by using incorrect solute activities in a few cases. The activities listed in the previous tabulation were correctly entered, however. While making the necessary corrections, i t was decided to include temperature-corrected solute and water activities in order to obtain more realistic enthalpies and entropies of reaction. The method by which those corrections were made is given in the Appendix. The indices m = 0 , 1, 2, 3, 4 refer to C O ( H , O ) ~ ~CoC1(HzO)s+, +, CoC12(H20)2, -, I n Tables CoC13(H20)-, and C O C I ~ ~respectively. I1 and 111, revised values are listed for the reaction parameters and other derived quantities. Those values
t
\
L
I d I!
0
1
1
2
3
I 4
I
I
5
6
HCL
1
I
I
I
7
8
9
IO
I II
I 12
I 13
I4
14
MOLALITY
Figure 1. Dependence of oxygen-17 and chlorine-35 line broadening on HC1 molal concentration. Solid lines were calculated using eq 5, species abundances from Table I, and parameters listed in Tables 111 and IV: 0 , oxygen-17 at 8.0000 MHz; 0, chlorine-35 4t 5.0000 MHz (all a t 300'K). (21) A. H. Zeltmann and L. 0,' Morgan, (1966).
J. P h y s . Chem., 70, 2807
NMROF
170
AND
Wl
IN
2691
AQUEOUS HC1 SOLUTIONS OF Co(I1)
Table I : Oxygen-17a and Chlorine-35b Line Broadening in Aqueous HC1 Solutions a t 27 COCll
0,424 0.932 1.99 3.41 3.89
0.109 0.117 0.123 0.122 0.115
5.79 6.66 7.88 8.21 8.97
0.139 0.123 0.133 0.139 0.157
9.70 10.20 11.00 12.01 12.38 12.96 13.12 13.81 14.43 15.36
144 145 125 109 104
151 144 127 101 92.2
a1
a2
a8
U4
0.973 0.951 0.898 0.815 0.798
0.916 0.843 0.674 0.439 0.373
0.084 0.156 0.324 0.549 0.610
0.000 0.000 0.002 0.011 0 017
0.000
0.000 0.000 0.000 0.001
0.000 0.000 0.000 0.000 0.000
18.8 27.6 45.0 51.1 71.6
0.672 0.615 0.541 0.521 0.468
0.148 0.088 0.035 0.026 0.009
0.750 0.712 0.530 0.458 0.253
0.091 0.166 0.296 0 325 0.347
0,009 0.027 0.088 0.114 0.191
0.002 0.008 0.050 0.076 0.200
67.0 53.7 31.6 28.4 18.0
63.1 52.6 37.3 32.7 20.0
102 132 245 287 378
99.5 125 221 255 364
0.138 0.168 0.136 0.152 0.147
94.2 113 151 213 240
0 426 0.396 0.355 0.307 0.291
0.003 0.001 0.000 0.000 0.000
0.122 0.064 0.021 0.005 0.003
0.292 0.231 0.140 0.065 0.048
0.232 0.238 0.215 0.163 0.143
0.351 0.466 0.624 0.767 0.806
11.1 7.6 3.3 1.4
11.5 7.3 3.6 1.6
484 512 606 642 664
459 518 589 650 667
0.159 0.173 0.141 0.209 0.151
289 302 370 443 567
0.268 0.261 0.238 0.215 0.189
0.000 0.000 0.000 0.000
0.001 0.001 0.000
0.030 0.026 0.015 0,009 0.004
0.116 0.109 0.085 0.066 0.046
0.853 0.863 0,900 0.925 0.949
714 745 745 705 771
689 695 717 735 758
0.49 0.97 2.39 5.63 7.21
I
5.0000 MHa.
Equilibrium oonstant (300’K)
0.000
0.000 0.000
‘ Mean ion activity of
A8,b
AH,^
entropy units
kcal/mol
(0.18 f 0.03) (2.0 dz 0.2) X 10-8 (3.6 5 0 . 4 ) X 10-8 (6.8 f 0 . 5 ) X
3 . 6 Z!= 1 . 0 5,5fl.l 10.6 f 1 . 2 6.6&0.4
I
I
8 . 7 i3 . 6 6.0 f 3.8 24.0 i= 4 . 2 12.1 f 1 . 5
’
( A ~ n / u ) = (1/3)S(S
(Aw/o)
Nucleus
Symmetry
Cla5 Clas
Octahedral Tetrahedral Octahedral Tetrahedral
x
104
36.3 f 6 . 4 115.9 3~ 0 . 6 169.5 i 1 . 1 354.0 f 10.2
+ 1)(A/kT)g85iP/fi~~(1)
Reduction of line width data to normalized relaxation rates was doqe as in previous work.21 The quantity ( T2p’)includes correction for total cobalt(I1) concentration through =
moles of cobalt(II)/moles of HzO (or C1-)
(2)
but does not contain the coordination number n for exchanging ligands, or fractional abundance am, of specific complexes. The complete factor for a particular species is
Table 111: Coupling Constants for Oxygen-17 and Chlorine-35 in Cobalt(I1) Complexes (A/h) 10-7, radian
5.6 10.7 23.9 46.1 53.7
The value given in Table I11 for the coupling constant of oxygen-17 in octahedral coordination, ( A / h ) = 1.35 X lo7 Hz,is to be compared with the value 1.70 X lo7 Hz reported by Chmelnick and Fiat.*O The line shifts on which both constants are based are essentially equivalent. We can only conclude that their value was calculated using the free electron g value, whereas ours was obtained with peff = 5.00 [for octahedral cobalt(11) ] in
p’
x
5.3 11.4 18.0 40.9 48.1
HC1.
‘See ref 3 for representations of the K , which apply to formation of species n and are semithermodynamic. K , = ocnaHzo/ oc,-la, except for K I = oc~a~zo8/ala*. AH and A S apply to temperature dependence of the K , values as written and are not truly thermodynamic. AS, especially, should be interpreted with caution, as the ratio of species activity coefficients is not included in the K,.
017
10-4
Calod
ao
a*c
Table I1 : Equilibrium Parameters for Cobalt(I1) Species in Aqueous Hydrochloric Acid Solutionsa
017
x
Exptl
aaao
8.0000 MHx.
KI Kz Ka Kc
1’ (Tap’017)-1
-Molalitv--HCl
a
Z!=
( ~ / h ) X 10-6,
sec -1
HZ
1.31 4.34 8.44 18.4
2.06 6.91 13.5 29.3
were used in obtaining species abundances for interpretation of line-broadening data.
p = p’a,n (3) Temperature dependences of chlorine-35 and oxygen17 line broadening are shown in Figures 2 and 3 and discussed in the following section. Data were also obtained at 1.99 and 7.88 m HC1 for chlorine-35 and a t 2.14 and 7.80 m for oxygen-17, which were included in the statistical analysis of results. As they reveal no features not represented in the figures, they were omitted in order to simplify the graphical presentations. Volume 73, Number 8 August 1969
2692
A. H. ZELTMANN, N. A. MATWIYOFF, AND L. 0. MORGAN
(T2&di
factors governing variations in line broadening with temperature and HCl concentration, appear to be relative species abundances and coordination number. For chlorine-35 a reasonable fit to experimental data over the entire range of HCl concentrations at room temperature (300°K) may be obtained with a two-parameter equation
SEC-'
(TzP'ci)-' =
IO4
26
2.7
28
29
30
31
32
l/T x 1 0 '
53
3.4
3.5
W
37
3R
a9
40
*K1
Figure 2. Temperature dependence of chlorine-35 line broadening. Solid lines were calculated using eq 5 and parameters listed in Tables 11, 111, and IV: 0,13.77 m HC1 at 5.0000 MHz; 9 , 5.79 m HC1 at 5.0000 MHz; Or 5.79 m HCl at 3.0000 MHz.
Cia1
Figure 3. Temperature dependence of oxygen-17 line broadening. Solid lines were calculated using eq 5 and parameters listed in Tables 11, 111, and IV: 0,Co(ClO4)a in 0.2 m HClOl solution; 0 , 5.73 m HCl; 0 , 8.74 m HC1 (all at 8.0000 MHz).
One set of data for chlorine-35 broadening in 5.79 m HCI solution was taken a t 3.0000 MHz for comparison with 5.0000 MHz results and is also presented in Figure 2. Oxygen-17 broadening was measured in 0.100 m cobalt(I1) perchlorate solution (300°K) at 5.0000, 3.0000, and 2.0000 MHz to obtain values for (Tzp')-' of 7.8 X lo5, 3.0 X 106, and 1.6 X lo5 sec-l, respectively. The corresponding value at 8.0000 MHz is 1.55 X lo6 sec-'.
Discussion For both chlorine-35 and oxygen-17, the dominant The Journal of Physical Chemistry
~ )(4)
but the contributions to C1 and Cz must be resolved by analysis of temperature dependence data, and a better fit results from consideration of concentration effects on relaxation parameters. There appears to be a marked difference in the behavior of octahedral and tetrahedral species, the latter producing more effective relaxation. Similarly, for oxygen-17 broadening at 300"K, the data are fitted well by an expression involving only octahedral species
(TzP'o)-l
1
+ Cz(2az + 3 ~ +~ 34
= C3ao
+
clal
However, a small residual broadening at higher HC1 concentrations suggests some contribution from tetrahedral aquochloro complexes. The general expression for transverse relaxation of exchanging ligand nuclei in dilute paramagnetic solutions, according to Swift and C ~ n n i c kis, ~
in which T2, is the intrinsic relaxation time for ligand nuclei L in the complex species m, T. is the residence time in the complex, and Aw, is the chemical shift relative to nuclei in the bulk diamagnetic environment. The assuinptions are made that all enhancement of the nuclear relaxation rate occurs in the first coordination sphere of the complex species, that the fraction of complexed nuclei is small, that is, p > Tarn;
(TzPL'),-~
nam7m--l
(54
This result is obtained regardless of the value of Awm. (b) I n the limit of fast exchange 7, (< Tzm; (T2pL')m-l = namTzrn-l(l
+
T2m7mAwmZ)((1
+ T ~ ' A w ~ ' ) - ~(5b)
In this instance, the result clearly depends on the
NMROF ‘’0 AND W1 IN AQUEOUS HC1 SOLUTIONS OF Co(I1) relationships among T,, T2,, and Aw,,,, as in the following cases. (c) If Aw, is very large T2mTmAOm2, Tm2AOm2
>> 1 ;
( T B ~ L ’= ) ~n (-l l n~T m - l
(5C)
=
(5d)
as in (sa). (d) If T~ is very short T2m~mA0m~j
> T . , ~ A O , ~ ; (T2pL’)m-1
=
+
(5e)
n(~mT~rn-~(lT2rn~mA~rn~)
>> 1 >> r m 2 A w m 2 ;
T 2 m ~ m A ~ m ~
(TzpL’),-l
= ~ C X ~ T , A(5f) O ~ ~
Because the temperature dependence of T, is often much greater than that of T2, or Ao,, it may be possible to see relaxation behavior as a function of temperature in which each limiting case obtains. Starting at low temperatures where rm is long, with increasing temperature (5a) 4 (5b) + (5d), and (5b) might appear as (5e) or (5f). Equation 5 contains parameters essentially constant at a single temperature for a given solution species, except that T , may vary with solution composition if there is a dependence of chemical exchange rate on composition. Changes in T , as a function of solution composition are expected to be (a) small, if exchange is controlled by unimolecular decomposition, (b) larger if the process is bimolecular and involves attack by solvent water molecules, and (c) very much larger if attack by C1- is the dominant process. The absence of strong medium effects in this instance suggests that a and/or b is responsible for exchange in cobalt(I1) complexes, or that relaxation is in the limit 5d. To a good approximation, T2, is expected to be independent of HC1 and H20 activities but may vary with viscosity and density, if relaxation is through the quadrupole interaction modulated by tumbling of the complex. I n Figure 1 the normalized relaxation rates for oxygen-17 and chlorine-35 are shown as functions of HCl molal concentration. Variation of relaxation rate with temperature is given in Figure 3 for oxygen-17 and in Figure 2 for chlorine-35. I n each case the data presented illustrate relaxation behavior at HCl concentrations chosen to represent the regimes in which the various contributions to relaxation are best evaluated. We find that present results for both oxygen-17 and chlorine-35 relaxation require that the complete eq 5 be used for each octahedral species and that the limit 5d is attained by tetrahedral species. We have made the further assumption that T2, is essentially the same for a given nucleus in any tetrahedral species on the basis of the linear dependence of chlorine-35 broadening on
2693
tetrahedrally complexed chloride. Contributions of tetrahedrally coordinated oxygen-17 to over-all broadening are so small that a similar assumption there should lead to negligible error. All rate and relaxation processes were taken to have exponential dependences on temperature, characterized in each case by a 300°K value and an apparent activation energy, E,. For chemical exchange, rate expressions were written to include terms for the activity of water. However, the experimental data used for evaluation of rates involving a given complex species cover such a limited range of water activities in HCl solutions that the inclusion of such a term is not an absolute necessity. As the results were slightly more consistent with the term present, it was retained, but the conclusions reached are not significantly affected by it. Each was of the form T,
= (k’aH,o)-l
(6)
aHIO equated t o unity at infinite dilution and 25”. A nonlinear least-squares program22 for the CDC6600 was adapted to analysis of broadening data a t all
with
temperatures and concentrations, using species concentrations given in Table I, based on parameters in Table IT and reIative shifts listed in Table 111. The several relaxation and rate constants, together with their temperature dependences, were treated as variables in the statistical analysis. A simultaneous solution using all available data was found to be impractical, and the following procedure was adopted. (1) Relaxation and exchange rate parameters for oxygen-17 in C O ( H ~ O )were ~ ~ +determined in the absence of chloride. (2) Temperature dependence of electronic relaxation, which is important in determining the temperature variation of Tz, for electron-nuclear spin exchange, was taken to be that observed for protons14 in C O ( H ~ O ) ~ ~ + , -1.5 kcal/mol (for both octahedral species). (3) Parameters for chlorine-35 in tetrahedral species were evaluated separately, using data obtained at 13.77 rn HCI where concentrations of octahedral species are negligible (over 90% of cobalt(I1) is present as CoC142at 300°K). (4) All data were then processed to determine the remaining parameters. (5) As a check on the assumptions, tetrahedral compIex parameters were fixed for oxygen-17, and the program was used to evaluate all octahedral parameters, including those for C O ( H ~ O ) ~ ~ + + . The results were the same within the specified error. I n analysis of chlorine-35 data in 13.77 m HCI solutions, T2m-l was separated into two terms, one for contact relaxationg (T2m-1)s=
assuming
re=
T~
(2/3)S(S
+ 1)(A/fi)2~e
(7) = T I , = T2,, because of the expected
(22) R. H . Moore and R. K. Zeigler, Los Alamos Scientific Labor& tory Report LA-2367, Los Alamos, N. M., Oct 1959, available from the Office of Technical Services, U. S. Department of Commerce, Washington, D. C.
Volume 78,Number 8 August 1969
A. H. ZELTMANN, N. A. MATWIYOFF, AND L. 0. MORGAN
2694
~-
Table IV: Relaxation and Chemical Exchange Rate Parameters for Cobalt(I1) Species in Aqueous HCl Solutions
Complex species
Activation energies, kcal/mol Chemical exchange, H P O
-----
CO(HIO)E~ +
This work
11.9 =!= 0 . 7
Ref 14
CoCI(Hz0) 6 +
10.4 ( A H * ) = 5 . 3 eu)
CoClz(Ha0)I, CoCla(H10) -, CoClrI-
13.8 & 0 . 7
(A#*
Chemical exchange, (a6C1)Spin-exchange (contact) relaxation Rate constants, chemical exchange, 300"K, sec-l H2"O (k' x 10-6) ("C1)- ( k ' x 10-8) Relaxation constants, 300"K, sec-l (T2m-l)afor oxygen-17 ( X 10-4) (Ttm-1)8for chlorine35 ( X 10-8) ( ! i " ~ ~ - 1 ) ~for chlorine-35b ( X 10-8) Electron relaxation times, ra ( = T I , = Tz,),sec-l Oxygen-17 data ( X lo1*) Chlorine-35 data ( X 10la)
13 -1.5" 3.6 & 0 . 2 1.6 5 0 . 8
9
f1 -1.5"
17 & 3 6 . 8 f 0.7
2.4 1.3
0 . 3 i0 . 5 >lo8
>5
x
107
2 . 3 & 0.8
4 . 2 -f 1.8 6 . 5 f1.0
5 . 3 f 0.7
6 . 8 & 0.3
13
4.6'
5d
13
' Fixed (ref 17). A single temperature dependence was assumed for all octahedral species. Similarly, a single value was assumed Determined by water viscosity at 300°K. (Tzm-l))r= (Tz,-l)QaOO. for all tetrahedral species, as determined from chlorine-35 data. Subject to large error because (7/T)/(7~~0/300). Using ( A / h ) = 1.35 X lo7 Hz, this value becomes 7.4 X 10-'8 sec (see Results). of the small contribution to over-all broadening. Errors in estimation of temperature coefficients are particularly significant.
short relaxation time for cobalt(I1) species, and a second term for quadrupolar relaxation2*
(Tzm-')e = (3/40) [ ( 2 1
+ 3)/1'(21 - I ) ] X
in which q is an asymmetry factor and is neglected here; (e2qQ) is the electric quadrupole coupling constant; 7c is the correlation time and is taken to be the tumbling time of the complex in solution. Temperature dependence of (T2m-1)ewas assumed to be that of q / T ( q = bulk viscosity). Estimation of q/T values is described in the Appendix. No evidence was found for quadrupolar relaxation of oxygen-17, and in that case (Tz,-l) = (T2m-1)8. Results of the complete data analysis are given in Table IV and the expected behavior of line broadenings as functions of HC1 concentration and temperature, calculated with those parameters, is plotted as solid lines in Figures 1, 2, and 3. Agreement appears to be satisfactory to within experimental error. The observed frequency dependence of oxygen-17 relaxation may be accounted for in terms of T2,-l, Aumn, and rm, using the listed parameters in Tables 111 and IV. Based on the observed value for (Tz~'oI,)-', 1.55 X lo6 sec-', a t 8.0000 MHz, those at 5.0000, 3.0000, and 2.0000MHz were calculated to be 6.6 X lo5, 3.0 x 106, and 1.9 X lo6sec-1. The corresponding observed values are 7.8 X lo6, 3.0 X lo5, snd 1.6 X lo5 see-', in reasonable agreement with expectation. Using the reported values for ( T2,-l) a for octahedral and tetrahedral chloride with eq 8 and estimating rc = 3 X lo-" sec, we find the values (e2q&/h)to be 6.8 and The Journal
of
Physical Chemistry
7.6 MHz, respectively. In the absence of measured values for comparison we can only say that those values are quite reasonable (see ref 23, p 348). I n any event, they depend on the chosen value of rc in each case and must be considered to be crude estimates at best. Values for (T2m-1)8 may be used to estimate T~ through eq 7 and ( A / & )from Table 111. Those results are also given in Table IV. Again, it can only be said that they are compatible with the expectation that cobalt(I1) species in solution have electronic relaxation times of the orde; of 10-15-10-12 sec. Without detailed information on the relaxation processes, no further deductions can be made. The discrepancy between the value of re = TI,obtained in this work and that of Chmelnick and Fiat14 is more apparent than real. It arises from the different assumptions for activation energy for the electronic relaxation. At high temperatures, where data are most reliable, the two are essentially equal. Ligand residence times, 7,, for C1- and HzO are related to individual ligand exchange rates, k', by CLIl>Ok'
=
7m-1
(9)
and to the over-all reaction rate constants k by
k
= nk' = n r m - l a H I O - l
( 10)
in which n is the number of equivalent exchanging species in the complex. Thus for HzO exchange between Co(H20)a2+and bulk solvent
R
= ~[CO(H~O)~~+]CLH~O (11)
(23) A. Abragam, "The Principles of Nuclear Magnetism," Oxford University Press, London, 1961, p 314.
NMROF
1 7 0 AND
35ClIN AQUEOUS HC1 SOLUTIONS OF Co(I1)
and n = 6, so that
2695
Conclusions
In this complex system, it is difficult to isolate specific regions of temperature or solution compositions where a single species or a small number of parameters dominate the analysis. However, a consistent analysis of Because a H I O is equated to unity at 25" and infinite dilution, the units of k are reciprocal seconds in all cases, both the chemical shift and line-broadening data for regardless of the molecularity of the rate-determining oxygen-17 and chlorine-35 require the following. step. The involvement of water in a bimolecular ex(1) Octahedral cobalt (11) complexes predominate a t change process for both C1- and HzO is not proved, as low HCl concentrations and low temperatures; tetrawas indicated earlier. However, treatment of the data hedral species are favored at higher HCI concentrations without the factor for water activity changes the resultand high temperatures. At the highest HCI concening rate constants by only a small factor, and relative trations studied, cobalt(I1) exists predominantly in the values are essentiallly unchanged. form of CoC142-. The transformation of complexes The specific ligand exchange rate for HzO is signififrom octahedral to tetrahedral forms occurs simultacantly increased by substitution of chloride in the octaneously with the addition of the second chloride ion. hedral coordination sphere, although the energy barrier (2) The exchange of HzO or C1- with octahedral for exchange is greater for the chloro complex. While species is substantially slower than exchange with tetrathis indicates a larger positive activation entropy hedral species. change for the latter process, it is hazardous to draw (3) The transverse relaxation of C1- in tetrahedral mechanistic conclusions in the absence of detailed species is due to quadrupolar and contact chemical shift understanding of the exchange reaction. It is entirely relaxation effects whereas the relaxation of HzO" in both possible that mechanisms in the two instances are acoctahedral and tetrahedral species is dominated by the tually different, if, for example, exchange in C o ( H ~ 0 ) 6 ~ + contact mechanism. is bimolecular and that in C O C I ( H ~ O )is~ + unimolecular, Appendix or if the two paths are competitive for each complex HCl activity data were obtained as a function of species. temperature from Harned and Owenz6below 4 m and I n a similar vein, chloride exchange in CoCl(Hz0)6+ from Akerlof and Teare2' above that concentration. has a rate constant 2.5 times less than that for water In each case the activity data were extrapolated above molecules, but the apparent activation energy is ap0-50" for which experimental data and below the range proximately the same. Again, a bimolecular step in4 m it was necessary to program were available. Below volving attack by water with elimination of chloride is equations to express constants tabulated by Harned and indicated but not substantially proved. Owen. Since Akerlof and Teare expressed the necesThese results may be compared with those of Luzz4 sary constants as analytical functions of temperature, for COCI(CH~OH)~+ in which proton shift and relaxathose equations were extrapolated. tion data were interpreted to obtain rate constants for Analysis of data for quadrupolar relaxation requires methanol exchange. Substitution of the chloride ion that values of viscosity for HCI solutions at all experiin the coordina,tion sphere of C O ( C H ~ ~ Hincreases )~~+ mental temperatures be known. I n the absence of prethe methanol exchange ratez5by a factor of ca. 300 (at cise measured values in all cases we have used the room 25", estimated from -63" results). I n that case, the temperature values for HC1-water solutions28 and the activation energy decreases from 15 to 12 kcal/mol. shape function for water over the range of temperaLua attributes the rapid exchange to ligands in equa tures.z6 Where values of HC1-water mixtures are torial positions in COCI(CH~OH)~+ and uses n = 4 to k n o ~ n , ~ they * ~ were ~ found to correspond satisfactorily obtain the rate constant. The constant we have listed with the calculated values. for CoCI(H,O)S+ is the mean value for all five positions, An equation was obtained by least-squares fit of data as there is no basis for evaluating separate equatorial for variation of relative viscosity of water as a function and axial rates from oxygen-17 line broadening data. Exchange rate constants for both chloride and water (24) 2. Luz, J. Chem. Phys., 41, 1756 (1964). are too large to be measured in any tetrahedral species, (26) 2. Luz and 8. Meiboom, ibid., 40, 2686 (1964). and no information other than lower limits for exchange (26) H. S. Harned and E. B. Owen, "The Physical Chemistry of rates is obtainable in the working temperature range. Electrolyte Solutions," 3rd ed, Reinhold Publishing Corp., New York, N. Y . , 1958, p 469. As the tetrahedral species are observed primarily a t (27) G. Akerliif and J. W. Teare, J . Amer. Chem. SOC.,59, 1855 very high HCl concentrations, attack by chloride in bi(1937). molecular processes may be significant for both chloride (28) "International Critical Tables," Vol. V, McGraw-Hill Book Co., Inc., New York, N. Y., 1929, pp 10, 12. and water exchange as well as that by water molecules. (29) M. A. Klochko, J. Gen. Chem. U S S R (Eng. Transl.), 26, 1149 Five-coordinated intermediate species should be readily (1956). formed, and we anticipate that associative mechanisms (30) M. A. Klochko and M. Sh. Kurbanov, Bull. Sector, Phys. Chem. are probably dominant for the higher chloro species. Anal. Akad. Sei. USSR, 24, 237 (1954). Volume 73, Number 8 August 1969
LAURINEL. GRAHAM AND RONALD E. DIEL
2696
of temperature. The relative viscosity of HzO was taken to be 1.OO at 20" and
&I = exp(16,262/T - 163.6976 + 0.64316T
- 0.00117107T2 + 8.0685 X
10-'T3)
where T = OK. Another equation representing the variation of viscosity of HC1 solutions at room temperature (25') as a function of molality was also fitted. The viscosity of F m HC1 solutions a t 25" relative to wa'cer at the same temperature is
7 =
+ 0.05603F - 7.493 X 10-6F2+ 9.865 X 10-5Fa- 2.535 X 10-6F4
1.004
The viscosity of any HCI solution at a given temperature was taken to be the product of the two functions. Acknowledgments. We are indebted to Dr. W. Burton Lewis and others for helpful comments during discussions of the work reported here. We also wish to thank Patricia Stein, who made many of the measurements, and Dr. B. B. McInteer and Mr. R. M. Potter of the Los Alamos Scientific Laboratory for supplying the enriched NO1'.
Nuclear Magnetic Resonance Studies of Internal Rotation in Aliphatic Tertiary Amides by Laurine L. Graham' and Ronald E. Diel Department of Chemistry, Northern Ill$mis University, DeKalb, Illinois 60116 (Received January 18, 1969)
The temperature dependence of the nmr line shapes of N-methyl-N-n-butyltrimethylacetamide, N-acetyl2-methylpiperidine, N,N-dimethylt,rimethylacetamide (TMA), and N,N-diethyltrimethylacetamideshow that the peaks due to the N-methyl protons are coalesced a t 35" but gradually separate into two nmr signals a t low temperatures. Therefore, a t 35", these highly substituted amides are rotating faster about the central C-N bond than simple amides such as dimethylacetamide. The activation energy for rotation of T M A in 10 mol yomethylene chloride solution was found to be 11.5 =!= 0.3 kcal/mol; log A , 12.3 0.3; and the standard free energy of activation, 12.2 kcal/mol. The method of total line shape analysis was used to calculate the activation parameters.
*
Introduction The cisltrans isomer ratios of eleven unsymmetrically N,N-disubstituted amides were determined at 35" using nuclear magnetic resonance (nmr) spectroscopy.2 The rotation about the C-N bond for most of the amides is slow enough a t 35" to observe two sets of N-alkyl proton peaks, one when the protons are cis and the other when trans to the carbonyl oxygen atom.
Ri
R2
\
C-N
/
/ / \
0
Rz
R1
\
+/ C=N
.t----f
R3
I
/
\
-0
R3
I1
However, only one set of N-alkyl proton peaks was observed for four highly substituted amides :2 N-methyl-N-e t hyltrimethylacet amide (111), N-met h yl-N-n-butyltrimethylacetamide (IV), N-methyl-N-t-butylacetThe Journal of Physical Chemistry
amide (V), and N-acetyl-2-methylpiperidine (VI). Two factors may cause the observation of only one set of N-alkyl resonance peaks at 35" : either very slow rotation about the C-N bond with one rotational isomer favored, or fast rotation about the C-N bond, resulting in both cis- and trans-N-alkyl protons experiencing the same magnetic environment. The first possibility was studied by preparing two new amides, N,N-dimethyltrimethylacetamide (VII) and N,N-die thy1trime thylacetamide (VIII). The nmr spectra of these pure amides at 35" also contain only one N-alkyl peak for each type of N-alkyl proton. If amides VI1 and VI11 were confined to the planar state 11, two N-alkyl resonance peaks would have been observed, one for the group cis to the carbonyl oxygen atom and one for the group trans. Thus, the rate of rotation cannot be slow (on the nmr (1) Author to whom inquiries should be addressed. LaPlanohe and M. T. Rogers, J . Amer. Chem. Soc., 85,3728 (1963). (2) L. A.
