Xov., 1961
RATEOF ELIXINATION OF WATER
hfoLECULES FROM CATIONS
2075
RATE OF ELI&IINATION OF WATER MOLECULES FROM THE FIRST COORDTll'hTION SPHERE OF PA4RAA3XAGNETIC CATIONS AS DETECTED BY NUCLEAR MSGSETIC RESONANCE MEASUREMENTS OF 0 1 7 1 BY ROBERT E. CONNICK AXD E. DIANESTOVER Department of Chemistry and the Radiation Laboratory, University of California, Berkeley, Calif. Received June 19, 1961
Earlier nuclear magnetic resonance measurements on the rates of exchange of water molecules between bulk water and the first coordination sphere of cations have been amplified and refined using water enriched in 0 ' 7 . Limits for the rates of these processes were calculated from the transverse relaxation time. h sideband technique was used in making the measurements. The following lower limits for the first-order rate constants for the exchange of a particular water molecule in the first coordination sphere were found: &In2+,2.2 X lo7 sec.-l; Cu2+, 3.3 X lo6 sec.-l; Co2+, 3.1 X lo5 sec.-l; X 2 + , 3.2 x lo4sec.-l and Fe3+, 2.4 X lo4set.-'.
In a previous paper2 preliminary results were reported on the effect of paramagnetic ions on the width of the nuclear magnetic resonance signal of 0 1 7 in water. The corresponding Tz values were interpreted in terms of an exchange between bulk mater molc~culesand the water in the first coordination sphere of the metal ions, and from the data a lower limit for the rate of this exchange could be calculated. In the present work the measurements have been repeated with greater precision by using mater enriched in 0 1 7 , and the linear dependence of the line width on the concentration of the paramagnetic ion has been established. During the course of the work the longitudinal relaxation time, T,, was measured for 0l7existing in the form of water. Also, the acidity dependence of the transverse relaxation was determined. Experimental A sideband technique3-5 was used with a Varian Associates model V-4200 wide-line nuclear magnetic resonance (variable frequency) spectrometer. The frequency was 5.77 Mc., corresponding to a ca. 10 kgauss field, for all but the final cobalt experiments where it was 5.44 Mc. The sweep frequency was 400 c.p.s. and the sweep amplitude ca. 0.9 gauss. The T , measurements were all taken a t the same rf power setting of ca. 0.06 gauss, where no saturation was occurring. For the 2'1 measurements the radiofrequency was increased from the non-saturating value of ca. 0.05 to 0.25 gauss. The phasing of the audio-amplified voltage delivered to the synchroverter phase detector was tuned so that the zeroeth harmonic was eliminated; the first sideband \vas detected as an absorption signal. The time constant of the integrating filter was 0 64 sec., and the polarizing magnetic field was scanned at a sweep speed of 1.3 gauss per min. Samples of 4-ml. volume were contained in 15 X 125 mm. Pyrex tubes fitted with ground glass jointed caps. The enriched viater, obtained from the Weizmann Institute of Science, had 0.7 atom % 0': and ca. 10 atom yc deuterium.6 The solutions of paramagnetic ions contained 0.10 M HCIO, in addition to the salt, except for the chromic perchlorate solutions. The water was recovered by distillation. Perchlorate salts were employed in an attempt to minimize complex formation. In early measurements the samples were degassed on a vacuum line and the sample tube refilled with nitrogen in (1) Presented a t the September 1960 meeting of the American Chemical Society, Xew York. (2) R. E. Connick and R . E. Poulson. J . Chem. Phus., 30, 759 (1959). (3) K. V. Wadimirski, Doklady Akad. .Vauk, S.S.S.R., 58, 1625 (1947). (4) €I. Prim:ts, H e h . Phiis. Acta, 31, 17 (1958). ( 5 ) J. V. Bcrivos. Lawwenee Radiation Laboratory Report UCRL 9649, 1961, University of California, Berkeley, California. (6) The deuterium was measured by comparing the n.m.r. signal of deuterium witl-. that. of n diluted D20 solution.
order to prevent dissolved O2 in the water from broadening the resonance. It was found that this effect was not measurable, and the degassing technique was dropped for later samples The spectra were taken a t a temperature of ca. 26'.
Results and Discussion The line widths (Le., half widths a t half height) and transverse relaxation times, Tz, for the various solutions are given in Table I. The dependence of line-width on concentration of paramagnetic ion is shown in Fig. 1. The absorption curves of some of the more concentrated solutions were broadened considerably, making accurate measurement of line width difficult. This accounts at least in part for the scatter. If it is assumed that the spin of an OI7 nucleus can undergo transverse relaxation by two independent, first-order processes, ie., relaxation in the bulk water and relaxation caused by paramagnetic ions, one can write
where ( T ~ ) Drefers to the relaxation time in the diamagnetic bulk water and (T& refers to the relaxation time arising from the presence of the paramagnetic ions. According to this equation the line width, which is inversely proportional to T2 at a given frequency, should be linearly dependent on the concentration of paramagnetic ion. This was found to be the case in Fig. 1. As shown earlier2 (T& can be related to a lower limit for the rate of exchange of mater molecules between the first coordination sphere of the metal ion and the bulk ~ v a t e r . ~The values of the firstorder rate constant for the loss of a particular water molecule from the first coordination sphere
+ H2O +bf(HzO)+" + HzO* h-l
M(H20*)+"
(2)
are given in Table 11,as calculated from the data of Table I. It was assumed that erery m d a l ion had a coordination number of 6. In the last column of Table I1 are reported for comparison the values obtained earlier. When allowance is made for the large experimental uncertainty in the previous measurements, the results for A h + + . S i + + and Co++ compare favor(7) From the chromic ion results, where such an exchange is known to be very slow (J. P. Hunt and H. Taube, J . Chsm. Phge., 19, 802 (1951)) i t is inferred t h a t the much more rapid relaxation observed nith the other ions must be occurring in the first conrdination sphere.
ROBERT E. CONNICK AND E. DIANE STOVER
2076
Vol. 65
TABLE I1 CALCULATED LOWERLIMITSFOR FIRSFORDER RATECONSTANTS FOR WATEREXCHANGE (EQUATION 2) Solution=
ci,
Lower limit for kl, see. -1
Lower limit for kl, sec.-1 from Connick and Poulsona
3 . 3 x 108 6 x 106 CU(C104)2 2 . 4 x 104 1 . 1 x 106 Fe( Clod 8 2 . 2 x 107 I x 107 Mn( C1O4)Z 4 x 104 xi(C104)s 3 . 2 x 104 2 x 106 CO(ClO4)2 3 . 1 X 106 =Since the relaxation is not occurring in the first coordination sphere for Cr3+, no value for kl can be calculated.
14.0
P,
v
S I 4 12.0 .e
2 a 10.0 'e 0
i-1
Eigen8 has compared the rates of formation of inner sulfate complexes of metal ions with the 8.O lower limit for the rates of exchange of water molecules measured previously.2 It is of interest to 6.0 repeat the comparison with the newer data. In Table I11 is given in the second column the firstorder rate constant for the conversion of an outer sphere sulfate complex to an inner sphere complex.* 0 2 4 6 8 1 0 1 2 1 4 In the 3rd column are listed the lower limits for the Metal ion concn. x 10" (moles/l.). Fig. 1.-Variation of line width with concentration. water exchange found here. Except for Cu++, Concentrations of metal perchlorate solutions are muhi- the relative orders and absolute values are remarkplied by 10"where n is: 4 for Cu*+, 1 for Cr3+,2 for Fe3+, ably similar, as might be expected if the primary 5 for Mnz+, 2 for W+,and 3 for C O ~ + . impediment to the formation of the activated complexes is the partial removal of a water molecule TABLE I from the first coordination ~ p h e r e . ~Although .~ LINEWIDTHSAND TRANSVEFSE RELAXATION TIMESOF 0 1 7 the water exchange data are only lower limits, this IN SOLUTIONS OF PARAMAGNETIC IONSAT ROOM rather striking comparison supports the idea that TEMPERATURE the rate of exchange is actually being measured. 0.10 M HClOd present except in Cr (ClO4)r experiments. Solution
Molar concn.
Line width, p.p.m.*
Ts X 108,sec.
C U ( C ~ O ~ ) : 1.10 ~ X IO-' 6.2 4.5 5.25 x 10-4 10.2 2.7 1.28 X lo-* 19.4 1.4 Cr(C104)8 0.088 5.1 5.5 .36 5 34 5.2 .67 6.4 4.3 Fe(C104)a 4.44 X lo-* 5.29 5.2 1.14 X 6.30 4.4 5.57 x 10-2 9 33 3.0 8.32 X 10-2 11.0 2.5 Mn(C104)2 6.24 X 8.74 3 2 1.43 X lo-' 14.3 1.9 Ni( C104)2 1.19 X 10-2 6.34 4.3 5.17 X loe2 9.89 2.8 9.44 X 14.4 2.1 Co(CIOJ8b 3.28 X 8.58 3.4 6.70 x 10-8 12.1 2.2 1.41 X loF2 19.0 1.5 HzOl' ......... 5 . 2 0 i 0.37 5 . 3 i 0.3" Field inhom0geneit.ywas less than 0.5 p.p.m. b Measured at 5.44 X IO6 C.P.S. All others measured at 5.77 X106C.P.S. Average of 8 different spectra.
TABLE 111 COMPARISON OF RATESOF FORMATION OF SULFATE COMPLEXES WITH LOWERLIMITSFOR RATESOF EXCHANGE OF WATERMOLECULES Ion
Mn2+ cuz+ co2+ NiZ+
Firsborder rate constant for formation of sulfate complex, sec. -1
4
x
106
4 0 4
2 1
x x
105 104
Lower limit for kl, Bec. -1
2.2 3.3 3.1 3.2
x x x
x
107 106 105 104
The new value for the exchange of waters bound to Fe3+can be compared with the rates of formation of FeC12+and FeSCN2+complexes. In each case a water molecule in the first coordination sphere is being replaced. .At 25' in 0.1 M HC104 and an ionic strength of 1.0 and 0.40 M , respectively, the apparent bimolecular rate constants for the formation of the complexes are 1.9 X 1OZ1Oand 3.3 X lo2 M-1 sec.-l,ll respectively, for FeC12+andFeSCN2+. The lower limit for the bimolecular rate constant for water exchange, where any of the six waters may be replaced, is from the present work 2.6 X ably. There is an appreciable discrepancy in the 103 M-' sec.-l. The values are much more nearly case of Cui+ and a large discrepancy between the the same than was thought previously2 and lend Fe3+ results. The source of these discrepancies is support to the idea that the rate in each case is unknown. In the latter case, a t least, instrumental primarily controlled by the elimination of the distortion of the absorption2 could scarcely ac- water m o l e ~ u l e . * ~ ~ count for the difference. Likewise the replacement (8) M. Eigen, Z.Elektrochem., 64, 115 (1960). of 2.0 and 4.0 X loe3 M Fe(N03)a2by Fe(C10*)3 (9) F. Basolo and R. G . Pearson, "Mechanisms of Inorganic seems unimportant. It should be emphasized Reactions," John Wiley and Sons, Inc., New York, N. Y., 1958,P. 163. (IO) R . E. Connick and C. P. Coppel, J . Am. Chem. Soc., 81, 6389 t'hat the present results for what is partially a DzO (1959). solvent would be expected to differ somewhat from 111) J. F. Below, Jr., R. E. Connick and C. P. Coppel, ibid., 80, 2961 those for HzO,but not greatly. (1958).
Nov., 1961.
RATEOF ELIMINATION OF WATERMOLECULES FROM CATIONS
The value of 2.2 X lo7 set.-' for the lower limit of kl of Mn++ can be compared with that of 4 X lo7sec.-l found by Bernheim, et a1.,l2for the rate of replacement of protons in the first coordination sphere of Mn++ from measurements of the proton relaxation time in aqueous manganous solutions at 27O.I3 It has been pointed out by Pearson, et uZ.,'~ that the similarity in these two rates indicates the protons are entering and leaving the first coordination sphere by exchange of an entire water molecule. The difference could arise from: (a) the experimental accuracy of the two measurements, (b) the effect on the rate of the replacement of H 2 0 by D20, (e) a rate of relaxation of an 0'' in the first coordination sphere which is comparable to the rate of displacement of the oxygen, or (d) a proton replacement mechanism which is independent of water exchange and having about the same rate as the latter. Acidity Dependence of T , of 0 '' in Water.-In order to ascertain whether the acidity was at all critical, T? was determined in solutions of varying pH which contained the enriched water and amounts of perchloric acid or sodium hydroxide necessary to give the observed pH. The data are shown in Table IV. Since this work was completed Meiboom14 has published data on T z and T I of 0'' of water as a function of pH from pH 3.3 to 12.1. He sec. over most of this found Tz to be 4.4 X pH range as compared to an average value of 5.3 X 10-3 sec. in Table IV. The slightly smaller value obtained by Meiboom might have arisen from instrument broadening in the derivative method, as found in the work reported earlier.' The pronounced effect of pH on T z observed by Meiboom near the neutral region is absent from Table I1 because no measurements were made near pH 7. The only run where a significant derivation from constancy would be expected is that a t pH 8.0 where Meiboom's theoretical curve predicts a value of 3.2 X sec. The absence of such an effect in Table IV should not be construed as a (12) R. A. Bernheim. T. H. Brown, H. S. Gutowsky and D. E. Woessner, J . Chem. Phys., 30, 950 (1959). (13) Thsooinparison made earlier (R. G. Pearson. J. Palmer, hl. M. Anderson and A. L. Allred, Z. Elektrochem., 64, 110 (1960)) mistakenly quoted a sevenfold too high value from ref. 2. (14) S. Meiboom, J . Chem. Phys., 3 4 , 375 (1961).
2077
disagreement because of the uncertainty in both the Tz measurement and the pH determination. TABLEIV VARIATION OF T z OF OI7 IN WATERWITH pH PH
0.87 1.00 3.0 5.5 8.0 10.5 a From Table I.
Line-wid ,h, p.p.m.
TI X lo*, 8ec.
4.80 5 . 2 0 f 0.37 5 23 5.37 5.34 5.53
5.75 5 . 3 i 0.3" 5.25 5.14 5.17 4.98
T I of 0 1 7 in Water.-The saturation technique was used to measure TI in water enriched in O I 7 and containing 0.1 M HC104. I n the side band method the absorption is of the form5
where J1(p) is the first Bessel function, B = jy[ Hm/wm,(the subscript m refers to modulation), A rtl w = Aw f corn, and the other symbols have their usual significance. The effective field, HI, was found a t high power from the relation 6 = 2(wm'
- Y~HI')'/P
(4)
where 6 is the sideband separation; lower power values were read from the dial settings in terms of the high power value. Four separate saturation runs gave an average value of 0.178 gauss for HI at maximum peak sec. for amplitude and correspondingly 4.1 x T I . This value may agree with Tz within the experimental accuracy, as might be expected for a quadrupole relaxation mechanism. Divergent values have been reported by Shulman and W y l ~ d a ' ~ and Meib00m.l~ Our value agrees well with that of 4.4 X 10-3 sec. reported by the latter investigator. We wish to acknowledge our great indebtedness to Dr. J. V. hcrivos for making available to us the sideband method of detection on the wide line apparatus, and to thank Professor R. J. Myers for his helpful counsel. The research was supported by the United States Atomic Energy Commission. (1.5) R. G. Shulnian and B. J. Wyluda, J . Chelem. Phys., 30, 335 (1959).
