PHYSICAL CHEMISTRY

A. I. Rivkind

NUCLEAR RELAXATION IN SOLUTIONS OF VANADYL SALTS. FORMATION OF HYDROGEN COMPLEXES $\mathrm{VO}\cdot\mathrm{H}^{3+}$

(Presented by Academician A. E. Arbuzov, July 24, 1961)

In our work ($^{1}$), for aqueous solutions of $\mathrm{VOSO}_{4}$ we obtained a value of the ratio of the “longitudinal” ($T_{1}$) to the “transverse” ($T_{2}$) relaxation time of the protons of the solvent (water) equal to $\sim 16.5$. However, later other authors ($^{2}$) found, for aqueous solutions of this same salt, $T_{1}/T_{2}$ equal to only 2.2. Comparison of the results led to the supposition that the cause of the discrepancy might be the different acidity of the solutions studied ($^{2}$)*. Subsequent measurements ($^{3}$) confirmed the existence of a strong influence of acidity on proton relaxation in solutions of vanadyl salts. In detail, however, this somewhat unexpected effect has not been studied by anyone, and its nature has remained unexplained.

The aim of the present work was a further, more complete investigation of the influence of acidity on nuclear relaxation in solutions of vanadyl salts. The measurements were carried out by the nuclear spin-echo method, at an oscillating magnetic-field frequency of 18.1 MHz and at room temperature. The values of the relaxation times $T_{2}$ were obtained by means of a $90—180^{\circ}$ sequence of radio-frequency pulses ($^{4}$); the opposite, $180—90^{\circ}$ pulse sequence was used to determine the relaxation times $T_{1}$ (the “null” method ($^{5}$)). The principal measurement results are presented in Fig. 1, which shows the dependence on acidity of the proton relaxation times $T_{1}$, $T_{2}$ and of their ratio $T_{1}/T_{2}$ for 0.02 M solutions of $\mathrm{VOSO}_{4}$. The acidity of the solutions was varied over wide limits by addition of up to 10 N $\mathrm{HNO}_{3}$ (Fig. 1A), up to 5.5 N $\mathrm{HClO}_{4}$ (Fig. 1Б), up to 35.2 N $\mathrm{H}_{2}\mathrm{SO}_{4}$ (Fig. 1В), and 0.7 mole of $\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}$ (Fig. 1Д). Without yet considering the region of high $\mathrm{H}_{2}\mathrm{SO}_{4}$ concentrations, one may conclude that, from the qualitative point of view, the action of all the acids used is approximately the same: with a comparatively small change in the time $T_{1}$, the time $T_{2}$ is sharply shortened, as a result of which the ratio $T_{1}/T_{2}$ increases strongly, reaching, for example, for a solution in 10 N $\mathrm{HNO}_{3}$ the unusually high value $T_{1}/T_{2}=81.5$, whereas without addition of acid this ratio is only $\sim 2.5$ (Fig. 1). It is true that, in contrast to the other acids, oxalic acid causes not a shortening but a lengthening of $T_{1}$ (Fig. 1), but this is unambiguously explained by the additional process occurring in this case—the formation of vanadyl complexes with $\mathrm{C}_{2}\mathrm{O}_{4}^{2-}$ ions ($^{6-8}$).

The sharp increase in the ratio $T_{1}/T_{2}$ indicates that, with increasing acid content, the time of the electronic paramagnetic relaxation of $\mathrm{VO}^{2+}$ ions is lengthened. The connection between the relaxation of electron and nuclear spins in paramagnetic solutions, as a result of which, for sufficiently long electronic paramagnetic relaxation times $\tau_{s}$ ($\gtrsim 10^{-8} \div 10^{-9}$ sec), the ratio of nuclear relaxation times ($T_{1}/T_{2}$) proves to be much greater than unity, was established in work ($^{1}$). At present, the existence of such a connection is generally recognized (see, for example, ($^{9}$)).

* To prevent hydrolysis we worked with acidic solutions.

The tetravalent vanadium ion is in the \(^{2}D\) ground state. In a cubic electric field the lower orbital level is a triplet. As shown by Van Vleck’s calculations \((^{10})\), carried out for salts of trivalent titanium, whose ions have the same system of energy levels as \(V^{4+}\), the time of electron paramagnetic relaxation \(\tau_s\) in the case under consideration is proportional to the sixth power of the splitting of the orbital triplet \((\tau_s \sim \Delta^6)\).* But a cubic field cannot remove the orbital degeneracy of the lower level; fields of lower symmetry are required for this. In the \(VO^{2+}\) ion, a field of low (axial) symmetry

Fig. 1. Change in the relaxation parameters of protons of \(0.02\,M\) aqueous \(VOSO_4\) solutions as a result of the introduction of acids: A—nitric and \(0.7\) mol oxalic; Б—hydrochloric; В—sulfuric. \(1\)—\(T_1\); \(2\)—\(T_2\); \(3\)—\(T_1/T_2\); \(a\)—\(T_1\), \(б\)—\(T_2\), \(в\)—\(T_1/T_2\) for a solution containing oxalic acid, \(T_1, T_2\) (msec.).

is created by the bonding electrons with the oxygen atoms. Therefore the electron paramagnetic relaxation time of vanadium, \(\tau_s\), should be a sensitive indicator of changes in the character of the \(V=O\) bond. There is every reason to suppose that the increase in the ratio \(T_1/T_2\) and in \(\tau_s\) discussed here is the result precisely of such changes. Apparently, with increasing proton concentration, the process of formation of hydrogen complexes of vanadyl becomes significant:

\[ VO^{2+} + H^{+} \rightleftarrows VO\cdot H^{3+}. \tag{1} \]

Capture of a proton by the oxygen of vanadyl should lead to partial dissociation of the \(V=O\) bond and, probably, as often occurs when bond order is lowered \((^{12})\), to an increase in the degree of its covalency. As a result, the bonding electrons, being shifted toward the vanadium atom, will cause an increase in the splitting of the lower triplet \((\Delta)\), and consequently an increase in \(\tau_s\) and in the ratio \(T_1/T_2\).

The foregoing is well confirmed by the measurement results. We shall proceed from the \(T_1/T_2\) curves as directly characterizing the course of the protolytic process of equation (1). Assuming additivity of the reciprocal relaxation times of protons produced by the paramagnetic ions \(VO^{2+}\) and \(VO\cdot H^{3+}\), from the measured \(T_1/T_2\) data it is not difficult to estimate the instability constants \((K)\) of the \(VO\cdot H^{3+}\) complexes:

\[ K=\frac{[VO^{2+}][H^{+}]}{[VO\cdot H^{3+}]} . \tag{2} \]

The method of calculation has been discussed for a large number of examples in works \((^{7,8})\). It turned out that the instability constants of the hydrogen complexes \(VO\cdot H^{3+}\)

* Although the theory \((^{10})\) pertains directly to solid layers, here, as in \((^{11})\), it is used for a qualitative interpretation of the results of measurements in solutions.

depend strongly on the acid chosen as the source of protons. The following series of approximate values was obtained:

\[ \begin{gathered} \mathrm{H_2C_2O_4} > \mathrm{H_2SO_4} > \mathrm{HNO_3} > \mathrm{HClO_4}.\\ \sim 0.4 \qquad \sim 3 \qquad \sim 4 \qquad \sim 8 \end{gathered} \tag{3} \]

The numbers under the acid formulas are the estimated approximate values of the instability constants of the complexes \(\mathrm{VO}\cdot\mathrm{H}^{3+}\). The most stable hydrogen complexes are formed upon addition of oxalic acid to aqueous vanadyl solutions (\(K \sim 0.4\)), and the least stable upon addition of perchloric acid (\(K \sim 8\)); i.e., the basic properties (affinity for the proton) of \(\mathrm{VO}^{2+}\) ions decrease as the strength of the added acids increases. The reason is obvious. In the process of formation of \(\mathrm{VO}\cdot\mathrm{H}^{3+}\) complexes, solvation of \(\mathrm{VO}^{2+}\) ions by acid anions must play an important role, lowering the effective positive charge of the vanadyl ions and thereby facilitating proton addition. This influence of solvation will be stronger the higher its stability. The above series of approximate values of instability constants (equation 3) precisely reflects this circumstance: oxalic acid is the most effective, since its anions form stable chelates with \(\mathrm{VO}^{2+}\) ions, whereas the anions of the most weakly acting perchloric acid, at the concentrations used (Fig. 1Б), are unlikely to have any appreciable probability of entering the coordination sphere of vanadium.

G. B. Bokii et al. \({}^{(13)}\), using X-ray structural analysis and taking ruthenium complexes as an example, established that when a hydroxyl group is present in the structure of complexes, the multiple bond \(\mathrm{Me}\)—addend tends to become a single bond. If this is also true for the multiple bond \(\mathrm{V}=\mathrm{O}\), then, in accordance with what was stated above, in vanadyl solutions a sharp increase in the ratio \(T_1/T_2\) (shortening of \(T_2\)) should be accompanied not only by formation of \(\mathrm{VO}\cdot\mathrm{H}^{3+}\) complexes (equation (1)), but also by formation of hydroxo complexes. The latter indeed occurs experimentally: upon careful increase of the pH of a \(0.02\,M\) aqueous solution of \(\mathrm{VOSO_4}\) to \(\mathrm{pH}_{\max} \sim 3.6\)*, a two- to threefold shortening of the time \(T_2\) is observed.

In work \({}^{(15)}\), for vanadyl solutions an acid-induced shift of the optical absorption bands toward shorter wavelengths by several hundred reciprocal centimeters was found. Naturally, no conclusions about changes in the first coordination sphere could be drawn on the basis of this fact alone. Probably, the indicated shift should be attributed, at least in part, to an increase in the splitting of the lower orbital triplet \((\Delta)\) as a result of formation of \(\mathrm{VO}\cdot\mathrm{H}^{3+}\) complexes.

As shown in Fig. 1 and noted in the text, the full range of changes in the ratio \(T_1/T_2\) is very large. Does this occur as a result of only a change in the electron paramagnetic relaxation time \(\tau_s\)? According to the approximate theory \({}^{(9)}\), a contribution to the ratio \(T_1/T_2\) can also be made by a change in the hyperfine coupling constant \((A)\) in the scalar \(\vec{A}\vec{I}\cdot\vec{S}\) interaction of the nuclear and electron spins. However, no reasons are apparent why the latter circumstance could become the principal one. Therefore, within the framework of this brief discussion, we have not taken it into account.

At high concentrations of sulfuric acid the curve of \(T_1\) values passes through a minimum, and the ratio \(T_1/T_2\) tends to unity (Fig. 1В). This special course of the relaxation curves is due to the chemical combination of water with sulfuric acid. The minimum on the \(T_1\) curve corresponds practically exactly to the stoichiometric ratio \(\mathrm{H_2O}:\mathrm{H_2SO_4}=1:1\) (vertical \(I—I\) in Fig. 1В), i.e., it corresponds to the formation of the monohydrate \(\mathrm{H_2SO_4}\cdot\mathrm{H_2O}\) \({}^{(16)}\).**

* Further increase of pH is impossible because of the appearance of turbidity (precipitate). At \(\sim \mathrm{pH}\ 3.6\), the concentration of hydroxo complexes is less than 10% of the total vanadyl concentration \({}^{(14)}\).

** The reason for the influence on relaxation of the chemical combination of solvent components (\(\mathrm{H_2O}\) and \(\mathrm{H_2SO_4}\)) requires additional clarification.

The observed affinity of $\mathrm{VO}^{2+}$ ions for the proton indicates that the $\mathrm{V}=\mathrm{O}$ bond is polar to a considerable degree and that the valence capabilities of oxygen are not exhausted entirely by this bond. As is known, the functions of vanadyl in its double salts with mineral acids have not yet been established ($^{17}$). On the basis of the results of the present work, it is possible that these salts are built according to the type of oxonium compounds. For example, “acid vanadyl sulfate,” $2\mathrm{VOSO}_4 \cdot \mathrm{H}_2\mathrm{SO}_4$, very probably has the structure $(\mathrm{BH}^{+})_2\mathrm{SO}_4^{2-}$, where $\mathrm{B}=\mathrm{VOSO}_4$.

Physico-Technical Institute
of the Kazan Branch
of the Academy of Sciences of the USSR

Received
24 VII 1961

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