95Mo and 97Mo magnetic resonance in aqueous molybdate solutions

JOURNAL

OF MAGNE’l3.C

RESONANCE

19,365-371

(1975)

95Moand 97MoMagnetic Resonancein AqueousMolybdate Solutions R. R.

VOLD

R. L.

AND

VOLD

Department of Chemistry, University of California, San Diego, La Jolla, California 92037 Received March 19,1975

ysMo and g7Mo relaxation times have been measured for aqueous solutions of sodium molybdate in the pH range 7-12. From the relaxation times at high pH where exchange effects are negligible the quadrupole moment ratio 97Q/95Q = 11.4 zt 0.4 was obtained. This large ratio allows a particularly simple determination of kinetic parameters of interest, such as the protonation rate constant and the relaxation time of the protonated anion.

INTRODUCTION

Recent work in our laboratory has been concerned with magnetic resonance studies of the chemical kinetics in aqueous solutions of sodium molybdate, and some features of the I”0 NMR spectra of the Moo,-2 anion have been reported (I). The very narrow 170 lines allowed the observation of the g5Mo satellites in this system, from which information about the molybdenum relaxation rate was obtained. In this paper we describe some characteristics of the g5Mo and g7Mo magnetic resonances of molybdate solutions. Naturally occurring molybdenum contains significant amounts of isotopes with atomic weights 92,94,95,96,97,98 and 100. Of these gsMo (15.72 %) and g7M~ (9.46 %) both have spin 512. Reports of direct observation of the magnetic resonance of g5Mo and g7Mo are scarce. To the best of our knowledge only five papers (2-5) have appeared, all of which deal with the determination of physical parameters rather than chemical applications. Proctor and Yu (2) first observed the g5Mo and g7Mo resonances and determined values for the magnetic dipole moments. The observation of negative magnetic moments in combination with predictions from the nuclear shell model (6) strongly suggested I = 5/2 for both isotopes. This value for the spin was subsequently unambiguously confirmed by Owen and Ward (7) from the ESR hyperfine coupling patterns. The second report (3) on molybdenum NMR dealt with Knight shift measurements in the free metal. Relaxation time studies were first performed by Kaufmann (4), who obtained an electric quadrupole moment ratio, g7Q/g5Q = 9.2 + 0.8 from the comparison of linewidths of the g5Mo and g7Mo resonances in viscous solutions of potassium molybdate and sucrose in water. This ratio was used by Narath and Alderman (5) to determine absolute values of g7Q = (1.1 L- 0.2) and 95Q = (0.12 + 0.03) x 1O-24 cm2 from the interactions between the quadrupole moments and the conduction electrons in molybdenum metal. Such a large difference between the quadrupole Copyright 0 la75 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

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moments of two isotopes of one element with identical spin is exceptional and arises from the fact that g5Mo has an outer half-filled d5,2 neutron shell, which has no permanent electric quadrupole moment. The addition of two neutrons to this shell therefore results in a relatively large change in Q. The large quadrupole moments presumably explain the apparent lack of interest in the NMR of molybdenum, since very wide lines are expected for all but the most symmetric environments. However, the large difference in quadrupole coupling constants has promising implications for the study of exchange phenomena, since a range of conditions may exist for which relationships between g5Mo and g7Mo relaxation times on the one hand, and chemical exchange rates on the other, allow unique determination of kinetic parameters of interest. We have utilized this property of the molybdenum isotopes for a particularly simple determination of the rate of protonation of the molybdate anion. EXPERIMENTAL

1 M molybdate samples (2 ml) were prepared from Na,Mo04*2Hz0 (Mallincrodt) and triply distilled water. The ionic strength was held at 6 M by addition of NaCl, and pH was adjusted by addition of small amounts of concentrated HCl and NaOH. The virtual absence (< lo-’ M) of paramagnetic impurities was ascertained by ESR measurements at 77 K. g5Mo and g7Mo relaxation times were measured at 29 + 1°C on a homebuilt, variable frequency pulsed NMR spectrometer at 3.910 and 3.993 MHz, respectively. Fieldfrequency stabilization of our Varian 12” high resolution magnet is achieved by an external fluorine lock system, which utilizes a V4311 rf unit modified (8) for time share operation (9) at 8 kHz derived from a PAR Model 122 lock-in amplifier. A Schomandl ND 1OOM frequency synthesizer and F & H Instruments rf gates drive an EN1 320 L linear amplifier and a James Millen No. 90881 transmitter, which gives200 W (rms) pulse power at 4 MHz. This power is sufficient for 14 psec 90” pulses at this frequency in a Q-switched, 10 mm single coil probe equipped with sample spinner and constructed following a design by Clark (IO). Signal amplification and demodulation is accomplished with a broad band (I-150 MHz) preamplifier with active damping of rf pulses (II), a 2-500 MHz if strip consisting of Avantek amplifier modules (three GPD 461 and 2 GPD 462) and an F & H Instruments l-30 MHz phase detector. At 4 MHz the probe and amplifier chain has an overall dead time of 10-l 5 psec after the rf pulse. Digitization and data treatment is performed by a Nicolet Instruments 1082 Fourier transform system. The overall response time is in practice determined by the choice of the ADC input filter, usually set to match the sampling rate for optimum signal-to-noise ratio. Molybdate spectra obtained under typical conditions are illustrated in Fig. 1. g5Mo spin lattice relaxation times as a function of pH were measured by the usual 180”~r-90”~FT sequence (12). Relaxation times for g7Mo were obtained from the linewidth (- 50-90 Hz) after it was ascertained that Tl = T2 at pH 7.5 and 12. Inhomogeneity broadening was in general less than 0.5 Hz. Significant savings in time during time averaging was achieved for g7Mo by digitizing less than 1 Kpoints in the time domain, using accumulation times of N 5 T2. A simple connection of pins C and H on the Nicolet SW-80 sweep plug-in allows data accumulation to be performed into any desired number of channels by setting of the address selector switches. Typical pulse

NMB IN MOLYBDATE SOLUTIONS

367

repetition times for g7Mo were 50-60 msec at sampling rates of 10 or 20 kHz. After accumulation a correction for any dc offset is made, and the time domain zero-filled to 4K before Fourier transformation in order to obtain adequate digital resolution for accu.rate linewidth measurements.

~200

Hz--+

Fm. 1. g5Mo and w MO Fourier transform NMR spectra of 2 ml 1 MNazMo04, 3 MNaCl at pH 12. For g5M~ 32 transients were accumulated in 17 set; for 97Mo 2048 transients in 1.8 min were required. Line broadening from exponential multiplication of the free induction decays are 2.4 and 7.8 Hz for “MO and “MO, respectively. RESULTS

AND

DISCUSSION

Typical spectra of g5M00;2 and g7M00;2 with adequate SINfor accurate relaxation time measurements could be obtained in a couple of minutes and are shown in Fig. 1. Between pH 9 and 12 the molybdenum relaxation times are independent of hydrogen ion concentration. For aqueous solutions of 1 M sodium molybdate and 3 M NaCl we find in this region T1e5Mo) = 840 _+20 msec and T1(g7M~) = 6.5 _+0.2 msec. The value obtained for g5Mo agrees within experimental error with that previously obtained (I) from the (less accurate) measurement of the difference between 170 satellite linewidths. From the relaxation times we derive a value for the ratio of quadrupole moments, g7Q/g”Q = 11.4 t- 0.4. This value is larger than the value, 9.2 + 0.8 obtained by Kaufmann (4), who measured linewidths as a function of viscosity in molybdate solutions containing different amounts of sucrose. Molybdenum(V1) is known to bind to polyhydroxy compounds (13) and in view of the results reported below it is likely that this binding contributed to the g5Mo linewidths in Kaufmann’s solutions. Hence we regard the value of 11.4 as more accurate.’ Using this ratio with the data of Narath and Alderman (5) and following their procedure, we obtain a slightly lower value for the g5Mo quadrupole moment, (0.10 _+0.02) x 1O-24 cm2. The accuracy of this value still depends on theoretical calculations of the d-band electron densities (14) and the assumption of negligible i By private communication we recently learned that Kaufmann “Q/g’;y*; 11.4 + 0.3 by methods similar to ours.

et nl. also have obtained

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Sternheimer antishielding (5). For the exchange studies reported below knowledge of the absolute values of Q is fortunately not necessary. Below pH 9 both R1(g5M~) and R,(g7Mo) increase with increasing hydrogen ion concentration (activity) as shown in Fig. 2. To facilitate comparison of the relaxation rates of the two isotopes R1(g5Mo) has been multiplied by (g7Q/g5Q)2 = 129, and if quadrupole interactions were the only mechanism the curves in Fig. 2 would be superimposable. The observed pH dependences can be explained by considering effects of chemical exchange.

I

2

3

4

5

6

7

6

FIG . 2 . g5Mo and g7Mo relaxation ratesin 1 M NaaMo04, 3 M NaCl as a function of hydrogen ion concentration. The hexagonsrepresent the g7Mo relaxation rates obtained directly from linewidths (R, = R,), while the circlesare “normalized” g5MO spin lattice relaxation rates RI x (97Q/95Q)2. The solid lines representexact solutions to three-siteexchangemodified Bloch equations using valuesof zBAand T,, obtained from the two-site limit above pH 7.7 (dashedline) and tentative estimatesof the polymerization parametersat lower pH.

Extensive studies by a wide variety of techniques (1549) have shown that the following overall equilibria adequately describe basic and moderately acidic molybdate solutions : H+ + MoO;~ s 8H+ + 7M00i2

Kll

MoO,(OH)z

KS7

(hydrated)

Mo,0;,6 + 4H20

bl [lb1

The structure of the protonated monomer is not known, but expansion of the coordination shell by hydration is indicated by the relatively low protonation rate (18) and observ-

ations in our laboratory (I) of a fairly rapid, acid catalyzed l’0 exchange between molybdate and water. The mechanism of the polymerization reaction is not known. It is assumed to proceed via a series of rapid bimolecular reactions and despite con-

NMR

IN MOLYBDATE

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369

flitting reports in the early literature there is now strong evidence (15, 17-19) for the absence of any stable intermediate polymeric species. Equilibrium constants K,, and KS7 have been determined by several groups at a variety of concentrations, ionic strengths and temperatures, and values for logK,, range from 3.5 to 3.9 while values for log&, fall in the range 52-58. Critical reviews have been provided by Aveston, et al. (15) and Sasaki and Sillen (17). From the magnitude of K,, and KS7 and a semiquantitative evaluation of three-site exchange equations (see below) we can show that effects on the spin-lattice relaxation rates of either isotope from polymer formation are negligible at hydrogen ion concentrations below 2 x IO-* M. We can therefore treat the initial (linear) part of the curves in Fig. 2 by the usual two-site exchange formulas for R, (20). The use of modified Bloch equations to describe exchange of quadrupolar nuclei involves the assumption that changes in magnitude and orientation of the electric field gradient during exchange events produce only negligible effects. Marshall (21) has shown that such effects are unimportant if the exchange lifetimes are much longer than the reorientational correlation times. This turns out to be so for the molybdate solutions, and the use of Bloch equations appears to be safe. Si-riceNewton-Raphson iterative solutions of the mass action expressions for K,, and KS7 show that the concentration of protonated monomer never exceeds N lo-” M above pH 7.7 the approximate equation (20) &Cobs) = &A + PBU’IB + TBA) PI can be applied without loss of accuracy. Sites A and B refer to the MoO;~ and the protonated anion, respectively, rBA is the lifetime in site B with respect to return to A, and pB is the population of site B. In the limit of negligible concentrations of other species, we have pB rAB = pA zsa, and furthermore in this range pA = 1 -pB x 1. To a high degree of approximation pB = K,,[H+] (total molybdate concentration is 1 M) and it then follows that the initial slopes g5s and ls7.rof the observed relaxation rates of each isotope plotted vs [H+] are given by g5s = K11[T1B(g5Mo) + zJ1 g7s= K,,[T,,(g7Mo) + z,J1

Pal WI

In previous applications of formulae analogous to Eq. [2] it was necessary to rely on different temperature or magnetic field dependences of TIB and rBAto effect a separation of these two parameters. In the present case the availability of two isotopes with TIB values differing by a factor of 129 permits this separation to be made by measurements at a single temperature. The forward rate of reaction [I a] is first order with respect to hydrogen ion concentration and with respect to molybdate. Thus, the reciprocal lifetime l/r,, for this reaction is given by 1 Zns&,[H+]=~$ &i$. [41 A

BA

Here kH is the second order rate constant for the protonation. By combining Eqs. [3] and [4] with the known ratio R = TrB(g5M~)/T,B(g7M~) = (g7Q/g”Q)z = 129 we obtain k, = (R - 1)95sg7s(Rg5s- g7s)-1.

PI

370

VOLD AND VOLD

Eq. [5] and the data in Fig. 2 yield a value of 4.8 x lo9 1mole-l see-’ for kH, in excellent agreement with the value 5.0 x lo9 I mole-l set-’ determined by Honig and Kustin (18) using ultrasonic relaxation. The agreement may be fortuitious in view of the different experimental conditions employed and our value of k, is probably accurate only within a factor of N 2. Although the value of kH is independent of any assumed value for &,, it is clear from Eq. [3] and [4] that K,, must be known to obtain an accurate value for TiB. Using K,, = 6300 as obtained by Sasaki and Sillen (17) in solutions of ionic strength p = 3 M, we find T1B(95Mo) = 330 ,usec,and if we assume K,, = 3400 as found by Aveston, et al. (15) (p = 1 M), then T1B(g5Mo) = 180 psec. The former value is preferred since Sasaki and Sillen’s experimental conditions more closely approach those of the present study. At hydrogen ion concentrations higher than N 2 x lo-* M polymer formation becomes important and additional sites must be included in the analysis. Since the polymerization mechanism is not known, a complete analysis of the limited data in Fig. 2 is not possible. For [H+] 2 6 x lo-’ M the concentration of polymer greatly exceeds that of protonated monomer. If the exchange rates are much larger than any dz@rence between site relaxation rates, then the observed relaxation rate will be a weighted average which is insensitive to the exchange rates. Numerical solutions of Bloch equations modified to include exchange of MOO,= with Mo,0;,6 as well as MoO,(OH)-(H,O), indicate that this limiting condition is approximately obtained for 95Mo but not 97M~, but the data in Fig. 2 may be fit with more than one set of assumptions concerning polymerization kinetics. For the theoretical curves shown in Fig. 2 the specific rate of polymerization was assumed to be lo5 set-I, in reasonable agreement with values obtained by T-jump (19) and fast flow titrations (22). The relative magnitudes of the relaxation times for the molybdate anion, and the protonated monomer, reflect structural differences. TI of the molybdate anion is exceptionally long because the tetrahedral symmetry ensures a vanishingly small permanent electric field gradient at molybdenum. Certainly molybdenum is in a much more symmetric environment in MOO;’ (Tr = 840 msec) than in the protonated monomer (TI N 200-300 psec). The structure MoO(OH); has been suggested (Z8,22) for the protonated monomer, but it appears that the relatively short relaxation time for MO in this species is more consistent with a less symmetric structure MoO,(H,O)(OH); which contains a cis-dioxo moiety. Since cis-dioxo structures are very common in Mo(V1) complexes (23), this conclusion seems reasonable. Measurements at lower pH and lower total molybdenum concentration will allow more complete determination of the polymerization kinetics. Such measurements in combination with l’0 relaxation time studies are currently being undertaken in our laboratory. ACKNOWLEDGMENT Partial support of this research by the National Science Foundation (MPS 73-08575) and the Public Health Service (RR 00708-l) is gratefully acknowledged. We thank Dr. John Wright for help in design of the lock system for our spectrometer. REFERENCES 1. R. R. VOLD AND R. L. VOLD, J. Chem. Phys. 61,436O (1974). 2. W. G. PROCTOR AND F. C. Yu, Phys. Rev. 81,20 (1951).

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