Abstract
Report at the XII Physicochemical Conference, June 1–5, 1935, in Dnipropetrovsk.
Full Text
Absorption Spectra of Electrolyte Solutions*
A. N. Terenin, Leningrad
1. The study of the visible and ultraviolet absorption spectra of solutions, and in general of substances in the liquid phase, is usually made difficult by the fact that, owing to the strong interaction of the electron shell of the absorbing center with neighboring molecules, the spectrum consists not of separate lines but of broad continuous bands, overlapping one another and often creating a region of continuous absorption that increases rapidly toward shorter wavelengths. To analyze such a resultant curve, i.e., to resolve it into its component maxima, is very difficult if the positions of some of them are not known in advance. Added to this is the complication associated with the presence of impurities, which, even in minimal quantities, give additional absorption maxima and make interpretation of the observations more difficult. Therefore, despite the large number of earlier investigations, it has only quite recently become possible to obtain sufficiently reliable experimental material permitting more confident interpretations.
The first question that arises when considering the spectra of solvated ions concerns the nature of the elementary process caused by light. A considerable part of the attention in the present review will be devoted to this question. Physical chemists usually turn to the absorption spectra of electrolyte solutions only in order to elucidate the character of the interaction of dissolved ions with one another. As is known, there are the following two views on the nature of ion association at high concentrations:
1) ions of opposite signs form pairs or “swarms,” unstable in time and not satisfying any stoichiometric ratios (ionic or electrovalent bond);
2) ions form stable stoichiometric complexes or even molecules (homeopolar or covalent bond).
* Report at the XII Physicochemical Conference, June 1–5, 1935, in Dnepropetrovsk.
In the first case the closed electron shells of the ions do not undergo any significant changes, apart from the usual electrostatic polarization deformations of the ions; in the second case the electron shells of the interacting ions undergo a far-reaching deformation connected with the formation of an entirely new system.
Such different behavior of the ions must also affect the form of the spectrum. In the first case, even at high concentrations, the absorption spectrum will consist of bands belonging to individual hydrated ions, with some changes in the position and form of the maxima being possible, caused by the increasing electrostatic interaction of the ions. In the second case, the appearance of a new electronic system belonging not to the individual ions but to their compound must cause a fundamental change in the spectrum, no longer directly derivable from the spectra of the original ions. Simultaneously with the creation of a common electron shell and a stable configuration of the nuclei, quite definite vibrational molecular frequencies also appear in the infrared and Raman spectra.
In exactly the same way as the ionic and homeopolar types of bonding in molecules represent limiting expressions of a general law of interaction, so here the two types of association of ions in concentrated solutions cited are limiting cases. Thus, depending on the properties of the initial ions, the character of their association in solutions will approach the first or the second type as limiting cases. However, in associated complexes consisting of many ions, both kinds of bonding may be present simultaneously, occurring between different components of the system.
Correspondingly, the absorption spectrum of the solution will also change, showing a greater or lesser similarity to the spectrum of the individual ions; moreover, from the magnitude of the shifts of the bands belonging to the latter one may judge the degree of stability and the kind of bonding of the complexes formed.
The very first quantitative characteristic of an absorption spectrum consists in determining the positions, i.e. the wavelengths and frequencies \((\lambda_{\max}, \nu_{\max})\), of the individual maxima observed for the given solution. The difficulties encountered in such a determination are connected chiefly with the circumstance that the absorption spectra of solutions very rarely reveal sufficiently narrow, isolated absorption maxima. In the ultraviolet region there is usually observed only a general continuous absorption background, extending toward shorter wavelengths and caused by the overlapping of a number of individual broad bands. To distinguish the maxima hidden in the general background of continuous absorption, careful photometric measurements are required. The most widespread photographic method of photometry is least suitable for this purpose, since it is not very sensitive to small changes in the intensity of the transmitted ...
light. More reliable results are obtained by photoelectric photometry, which is gradually beginning to displace photographic methods in such investigations.*
In obtaining the spectra of solutions it is necessary to work with extremely pure substances, since foreign impurities even in minimal amounts are capable of giving additional absorption maxima that complicate the interpretation of the spectrum. Thus, for example, in the very careful investigations of Fromherz \(^{9,10}\), which will be discussed below, it was incidentally shown that the weak absorption bands in the region \(\lambda > 250\,m\mu\), observed by various authors in aqueous solutions of halide salts of the alkali and alkaline-earth metals, are caused by contamination with organic substances (Vaseline!) at a concentration of \(0.001—0.01\%\). One can get rid of such a negligible concentration of impurity only if its nature is known; otherwise even very careful purification by ordinary methods will miss the mark. Therefore, in most cases such weak bands in the long-wavelength region, with an absorption coefficient 100,000 times smaller than that of the principal maxima, may be neglected.
Besides its position, an individual band of the absorption spectrum can be characterized numerically by the value of the absorption coefficient at the maximum, and also by its width. For considerations connected with ease of calculation, instead of the absorption coefficient it is customary in investigations to use the extinction coefficient (Extinktionskoeffizient), defined by the following relation:
\[ \frac{I}{I_0}=10^{-kcd}, \]
where \(c\) is the concentration of the solution in moles per liter,
\(d\) is the thickness of the layer in centimeters,
\(I_0\) and \(I\) are the intensities of the incident and transmitted light of the given wavelength.
In view of the enormous difference in the absorption coefficients of different bands (reaching \(100\,000:1\)), it is customary to use the values \(\lg k\). Plotting the latter as a function of wavelength (usually expressed in \(m\mu\)) gives a graphical representation of the absorption spectrum of the solution.
* The technique of photographic spectrophotometry of solutions and the analysis of the curves obtained is described in great detail in the papers of Fromherz \(^{7—15}\), who succeeded in measuring the position of narrow isolated maxima and the absorption coefficient with the limiting accuracy for this method, namely:
\[ \delta\lambda_{\max}=\pm 0.2\,m\mu,\qquad \delta k:k=1—2\%. \]
The sensitivity of the method was such that, for strongly absorbing ions \((\lg k \simeq 4)\), it was possible to observe distinctly concentrations of the order of \(10^{-6}\) mole/liter. The photoelectric method is described, for example, in the papers of Gal’ban \(^{2}\).
In intense absorption maxima lying in the ultraviolet region, \(\lg k_{\max}\) is equal to 3–4 (\(k\) ranging from 1000 to 10 000), varying within comparatively narrow limits. On recalculation to a single absorbing center, we obtain for such an elementary absorption coefficient* a value of the order of \(10^{-17}\).
The width of a symmetrical absorption band (more precisely, the half-width) is taken to be that segment of the wavelength scale at whose boundaries \(k\) has the value \(\frac{1}{2}k_{\max}\) (\(\lg k = \lg k_{\max} - \lg 2\)). The width of bands varies approximately within the limits from 10 to 100 \(m\mu\).
The significance of these data, derived from the absorption spectrum, becomes clear if one recalls that the shift and broadening of bands may serve as a measure of the interaction of the absorbing center, i.e. the hydrated ion, with the surrounding other ions and solvent molecules.
The area of the curve of a symmetrical absorption band, or the integral \(\int k d\nu\), approximately equal to \(k_{\max}\Delta\nu\) (\(\Delta\nu\) is the half-width in frequencies), after division by the frequency of the middle of the band \(\nu_{\max}\), gives the quantity
\[ F=\frac{k_{\max}\Delta\nu}{\nu_{\max}}, \]
which characterizes the probability of absorption of light by an individual center. Calculation shows that this probability has the same order of magnitude as for the first absorption lines of gaseous atoms and ions. Thus, the probabilities of electronic transitions undergo no substantial changes upon formation of hydrated or complex ions of a solution. Similar constancy is not exhibited, however, by the positions of the energy levels, which for ions in solutions are considerably shifted in comparison with gaseous ions. The next paragraph is devoted to consideration of these shifts.
Absorption of hydrated cations
2. The absorption bands of ions and their complexes in solutions lie for the most part in the ultraviolet region at wavelengths shorter than \(\lambda = 250\,m\mu\). The increasing opacity of the solvent and of the walls of the absorption vessel sets a limit to investigations at \(\lambda = 180\,m\mu\); moreover, for work in this extreme ultraviolet region one must use very thin (0.1–0.001 mm) layers of liquid and eliminate air from the path of the light (Table 1 and Fig. 1).
The absorption spectrum of strong electrolytes, for example, aqueous and alcoholic solutions of halide salts of alkali and alkaline-earth metals, contains characteristic bands belonging only to the halide anions. Absorption bands of the cations of these metals are not detected at all, which is in agreement with refrac-
* Determined by the formula
\[ I:I_0=e^{-knd}, \]
where \(n\) is the number of absorbing centers in \(\mathrm{cm}^3\).
TABLE 1
Limits of transparency of solvents in the ultraviolet region37
| Solvent | Layer thickness in mm | Transparency at λ (in mμ): good | Transparency at λ (in mμ): still noticeable |
|---|---|---|---|
| Water H₂O | 0.07 | 179 | 176 |
| Alcohol C₂H₅OH | 0.1 | 185 | 179 |
| Acetonitrile | 0.1 | 194 | 185 |
| Quartz (crystalline) | 0.76 | 155 | 152 |
| Quartz (fused) | 1.12 | 160 | 155 |
| Lithium fluoride (single crystal) | 1.57 | 159 | 150 |
tometric data, according to which they should lie in the region of wavelengths below λ = 100 mμ, an area inaccessible to investigation.
Fig. 1. Absorption spectra of water and ethanol22
In the absorption spectrum of medium and weak electrolytes, such as, for example, the halide salts of heavy metals Ag, Cu, Cd, Hg, Tl, Pb, absorption maxima are observed at low concentrations that belong both to the halide anions and to the metal cations. The latter thus fall within the accessible-to-investigation limited portion of the ultraviolet spectrum*.
* Forbes and Elkins3 calculate from the molecular dispersion of solutions \(R\), with the aid of the simplified formula
\[ R=\frac{C}{\nu_i^2-\nu^2} \]
the natural frequencies \(\nu_i\) or absorption maxima \(\lambda_i\) of the dissolved ions. The numerical values they obtained for \(\lambda_i\) (in mμ), which represent a very rough approximation, are as follows:
\[ \begin{array}{ccccccccccc} \mathrm{Ag}^{+} & \mathrm{Hg}^{++} & \mathrm{Hg}_2^{++} & \mathrm{Tl}^{+} & \mathrm{Pb}^{++} & \mathrm{J}^{-} & \mathrm{Br}^{-} & \mathrm{Cl}^{-} & \mathrm{NO}_3^{-} & \mathrm{ClO}_3^{-} & \mathrm{BrO}_3^{-} & \mathrm{JO}_3^{-} \\ 207 & 216 & 252 & 163 & 182 & 217 & 193 & 153 & 195 & 133 & 192 & 198 \end{array} \]
\[ \begin{array}{cccc} \mathrm{SO}_4^{-} & \mathrm{SeO}_4^{-} & \mathrm{SO}_3^{-} & \mathrm{S}_2\mathrm{O}_3^{-} \\ 106 & 140 & 145 & 172 \end{array} \]
The absorption bands characteristic of the named cations are found in pure form in solutions of perchlorates of the indicated metals, for example \( \mathrm{AgClO_4} \), \( \mathrm{TlClO_4} \), \( \mathrm{Pb(ClO_4)_2} \), since the anion \( \mathrm{ClO_4} \) has no noticeable absorption in the spectral region under consideration (Fig. 2). Nitrates are unsuitable for this purpose because of the presence of intense absorption maxima at 302 and 194 \(m\mu\).
In Table 2, the column \(\lambda_{\mathrm{aq}}\) gives the wavelengths of the absorption maxima found in aqueous solutions of perchlorates and ascribed to the corresponding cations. The works in which they were obtained are given in the last column. In addition, the column \(\nu_{\mathrm{aq}}\) gives the values of the frequencies of these maxima, expressed in electron-volts. The subsequent columns refer to the gaseous state of the ions.
TABLE 2
Absorption maxima of cations in the hydrated \((\lambda_{\mathrm{aq}})\) and free \((\lambda_{\mathrm{gas}})\) states
| Cation | Structure of the outer electron shell | \(\lambda_{\mathrm{aq}}\) (\(m\mu\)) | \(\nu_{\mathrm{aq}}\) (eV) | \(\lambda_{\mathrm{gas}}\) (\(m\mu\)) | \(\nu_{\mathrm{gas}}\) (eV) | Ionization potential (eV) | References |
|---|---|---|---|---|---|---|---|
| \(\mathrm{Cu}^+\) | \(3d^{10}\) | (235) | (5.26) | \(1^{\circ}0.6\) | 8.20 | 20.5 | 5 |
| \(\mathrm{Ag}^+\) | \(4d^{10}\) | 210.5 | 5.86 | 124.7 | 9.90 | 22.5 | 5, 6, 8 |
| \(\mathrm{Ag}^+\) | \(4d^{10}\) | 193 | 6.40 | ||||
| \(\mathrm{Cd}^{++}\) | \(4d^{10}\) | \<180 | >6.86 | 74.7 | 16.5 | 35 | 15 |
| \(\mathrm{Hg}^{++}\) | \(5d^{10}\) | 180 | 6.86 | \(84.6^{23}\) | \(14.7^{23}\) | (36) | 5, 14 |
| \(\mathrm{Tl}^+\) | \(5d^{10}6s^2\) | 214 | 5.77 | 190.9 | 6.46 | 20 | 5, 11 |
| \(\mathrm{Pb}^{++}\) | \(5d^{10}6s^2\) | 208.5 | 5.92 | 155.3 | \(7.97^{\circ}\) | 32 | 5, 11 |
The data presented exhaust almost all reliable material* on the absorption spectra of cations with a closed outer electron shell. Much weaker bands lying in the region of longer wavelengths, observed in older investigations and ascribed to cations of alkali or alkaline-earth metals, undoubtedly belong to impurities.
Cations that do not possess a closed structure of the electron shell, such as, for example, \(\mathrm{V}^{+++}(3d^2)\), \(\mathrm{Cr}^{+++}(3d^3)\), \(\mathrm{Mn}^{++}(3d^5)\), \(\mathrm{Cu}^{++}(3d^9)\), \(\mathrm{Fe}^{++}(3d^6)\), \(\mathrm{Fe}^{+++}(3d^5)\), \(\mathrm{Co}^{++}(3d^7)\), \(\mathrm{Co}^{+++}(3d^6)\), \(\mathrm{Ni}^{++}(3d^8)\), in the hydrated state give the well-known absorption bands located in the visible region of the spectrum**.
* In the works of Kato\(^{5}\), many other absorption maxima were also observed which, however, are absent in the more careful investigations (Fromherz). The question of their origin thus remains open. See also, in this connection, the work of Folbert\(^{6}\).
** \(\mathrm{Cu}^{++}\) also has, besides the absorption maximum at \(\lambda = 820\,m\mu\), an absorption band with a maximum at \(\lambda < 225\,m\mu\).\(^{15}\) (Fig. 6, curve 12). Ultraviolet bands are also found in the remaining ions listed.
However, the value of the maximum absorption coefficient for these bands, \(k_{\max}\), is several thousand times smaller than for bands lying in the ultraviolet region. In addition, these bands are considerably broader than the ultraviolet ones. Most of these bands must be attributed to complex ions consisting of a multivalent metal cation combined with a greater or smaller number of anions of the salts that were taken for the solution. Such complexes will be discussed further below.
However, in some cases, with sufficient dilution, such bands located in the long-wavelength region of the spectrum must be attributed to the hydrated cations themselves, since their position does not depend on the nature of the anion. These include the band with a maximum at \(517\,m\mu\), characteristic of \(\mathrm{Co}^{++}\), the band at \(820\,m\mu\) of the \(\mathrm{Cu}^{++}\) ion, and the bands at \(405\), \(690\), and \(1210\,m\mu\) of the \(\mathrm{Ni}^{++}\) ion.
- For understanding the nature of the electronic transition caused in a hydrated ion by absorption of light, the experiments of Reichardt and Bonhoeffer\({}^{16}\) are very valuable; using the mercury atom as an example, they established the changes undergone by an atomic absorption line when its carrier is dissolved in an indifferent solvent. In Fig. 3, taken from the work of these authors, there is shown the form of the band obtained instead of the absorption line \(2537\,\text{\AA}\) of mercury when the latter is dissolved in water, methyl alcohol, and hexane.
Fig. 2. Absorption maximum of the hydrated \(\mathrm{Tl}^{+}\) ion
In Fig. 4, for greater clarity, only the positions of the absorption maxima are marked, as well as their displacement when the density of the solvent is decreased, which was achieved by raising the temperature. The greatest shift toward the red from the initial position of the line upon dissolution in water, for one of the maxima, is about \(60\,\text{\AA}\), which corresponds on the energy scale to a shift of approximately \(0.1\,\mathrm{eV}\). The width \(\Delta\lambda\) of each of the two overlapping maxima may be estimated at \(100\,\text{\AA}\), or \(0.2\,\mathrm{eV}\).
In its normal state the mercury atom possesses a closed
by the electronic shell \(6s^2\,{}^1S\), which has no free valences, resembling to some extent an atom of a heavy rare gas. Such an electronic configuration is hardly subject to any significant influence from the surrounding molecules of the solvent.
Fig. 3. Absorption spectra of a dissolved mercury atom
The situation is different with the excited state of the mercury atom \(6s6p\,{}^3P\), which differs from the normal state not only
with high energy, but also by an open electron shell, more subject to external influences, on the one hand, because of the presence of two free valences, and, on the other, because of the character of the distribution of charge density (a \(p\)-electron). Therefore the broadening, shift, and splitting experienced by the 2537 Å line upon dissolution must undoubtedly be attributed chiefly to a distortion of the upper energy state.
The considerable magnitude of the splitting observed in water, and its decrease on going to methanol and hexane, i.e. a certain parallelism between the splitting and the magnitude of the dipole moment, compels one to seek its cause in the Stark effect, produced by the extremely strong molecular fields of the solvent. The authors of this work estimate, by an approximate calculation on the basis of the observed splitting, the magnitude of the internal electric field of the solvent to be \(33 \cdot 10^{6}\ \mathrm{V/cm}\). In doing so they proceed from the assumption that the field is constant in time and homogeneous in space, which is clearly not the case for the intermolecular fields of moving molecules \(^{17}\). The presence of splitting even in the case of a solvent consisting of symmetrical nonpolar molecules, such as, for example, hexane, for which the cited order of magnitude of the intermolecular field is hardly applicable, indicates that the cause of the shift and splitting of the electron term should rather be seen in the formation of a temporary, weakly bound compound between the excited atom Hg and a molecule (or molecules) of the solvent \(^{18}\). It is known that an excited mercury atom reacts with a water molecule in the gaseous state according to the equation \(\mathrm{Hg}^{*} + \mathrm{H}_{2}\mathrm{O} \to \mathrm{HgH} + \mathrm{OH}\) \(^{25}\). The possibility of formation of the compound \(\mathrm{Hg}^{*}—\mathrm{H}_{2}\mathrm{O}\) in solution is thus very probable. The presence of axial symmetry in such a compound also explains well the appearance of two excited molecular states arising from one atomic state, just as occurs for an Hg atom placed in an electric field. The shift of absorption toward the red becomes understandable if one makes use of a diagram representing the changes in potential energy upon interaction of the mercury atom in its various states with solvent molecules (Fig. 5a).
Fig. 4. Position of the absorption maxima of the dissolved mercury atom in various solvents and at various temperatures.
The construction of this diagram is based on only one assumption, namely, that the mercury atom in the excited state
interacts with water molecules more strongly than when it is in the normal state, i.e., the heat of hydration \(H^{*} > H\). For the exact construction of this diagram, information is needed on
Fig. 5. Displacement of electronic energy levels upon dissolution. 1—characteristic absorption band; 2—\(U\) band; 3—\(F\) band; 4—bottom of the characteristic band; 5—absorption band of colloidal particles (blue coloration)
Fig. 6. Absorption maxima of sodium and potassium atoms dissolved in molten halide salts of the same metals (\(R\)—position of the absorption lines of gaseous Na and K atoms; \(F\)—position of the absorption maxima of Na and K atoms in the crystal lattices of the corresponding salts, the so-called Farbzentren)
...the heats of hydration of \(H^*\)- and \(H\)-atoms in various states of their electron shell, which are still unknown.
Another example of the absorption spectrum of an atom in solution is provided by the broad absorption bands of the alkali metals Na and K dissolved in molten halide salts of the same metals (Fig. 6). For Na in all salts a band is obtained with a maximum at \(790\,m\mu\), and for K a band with a maximum at \(980\,m\mu\) \(^{19}\). Undoubtedly these bands arose from the first absorption lines of atoms having wavelengths, in round numbers, \(590\,m\mu\) for Na and \(770\,m\mu\) for K. The magnitude of the shift of the center of the absorption band is, in energy units, \(0.3\)—\(0.5\) eV, and the amount of broadening is about 1 eV.
The shift and broadening are several times (3—5 times) greater than in the case of the dissolved Hg atom, which is naturally explained by the stronger perturbing influence of strongly polar and ionized liquids, such as molten salts, and, moreover, by the higher temperature of the solution. The absence of splitting of the energy levels of the alkali-metal atoms apparently indicates the spherical symmetry of the perturbing field in this case. In other words, in contrast to the mercury atom there is no reason to assume the formation of stable molecules from Na, K atoms and molecules or ions of the molten salt.*
- Analogous relations will hold for electronic transitions of dissolved hydrated cations, with the difference that, owing to the presence of electric charge and small volume, these ions interact considerably more strongly with the molecules even of an indifferent solvent. For cations with a closed electron configuration in the normal state of the shell, listed in Table 2, it may be assumed, as in the case of Hg, that the upper energy level undergoes the greatest distortion. The relative magnitude of the shift of the upper and lower levels may be judged from the difference between the wavelengths of the absorption line of the gaseous ion \((\lambda_{\mathrm{gas}})\) and the absorption band of the same ion in solution \((\lambda_{\mathrm{aq}})\), which are given in Table 2 together with the values of the corresponding frequencies \(\nu_{\mathrm{gas}}\) and \(\nu_{\mathrm{aq}}\) in electron-volts. The first absorption bands of hydrated cations are displaced by an amount of the order of \(1\)—\(10\) eV toward lower frequencies from the first absorption lines of free gaseous ions.
Table 3 gives, for the cations under consideration, the frequency differences \(\nu_{\mathrm{gas}}-\nu_{\mathrm{aq}}\), expressed in electron-volts, as well as the hydration energies of the cations in the normal state of the electron shell. Such a large magnitude of the shift indicates a very strong bond between the water molecules belonging to the hydration shell and the excited ion, exceeding in its magni-
* When alkali metals are dissolved in ammonia and amines, strongly colored solutions are formed, the absorption of which must be attributed to the solvated electron, since it remains unchanged for different atoms \(^{20}\).
chine, the bonding of the same molecules with the normal ion, or the heat of hydration \(H\) (Fig. 5a).
TABLE 3
Shift of the cation spectrum upon hydration and heat of hydration
| Cation | \(\nu_{\mathrm{gas}}-\nu_{\mathrm{aq}}\) (eV) | Heat of hydration \(H^{24}\) (eV) | Heat of hydration \(H^{24}\) (kg cal) |
|---|---|---|---|
| \(\mathrm{Cu}^+\) | 2.9 | — | — |
| \(\mathrm{Ag}^+\) | 4.1 | 7.05 | 162 |
| \(\mathrm{Cd}^{++}\) | 9.6 | 20.1 | 462 |
| \(\mathrm{Hg}^{++}\) | 7.8 | 20.9 | 480 |
| \(\mathrm{Tl}^+\) | 0.7 | 4.65 | 107 |
| \(\mathrm{Pb}^{++}\) | 2.1 | — | — |
The circumstance that for \(\mathrm{Cu}^+\), \(\mathrm{Ag}^+\), and, apparently, other cations listed in the table, one observes not a single, but several maxima situated comparatively close to one another, recalling the splitting of the absorption band of the dissolved mercury atom, may be attributed to the same cause, i.e., to the formation between the excited ion and the solvent molecules bound to it of a certain temporary compound, stronger than for the ion in the normal state. Such a stronger bond is probably due to the appearance, alongside the electrostatic interaction of the cation with the surrounding shell of water molecules, also of forces of a valence, i.e. homopolar, character, arising as a result of excitation of the closed shell of the ion.
For a more reliable comparison of the absorption bands of hydrated ions with a definite electronic transition in gaseous ions, it would be highly desirable to establish the position not only of the first absorption bands, but also of the subsequent ones. The increasing opacity of the solvent, however, sets a limit to such an extension of observation. It should be noted in passing that for many multiply charged cations observed in solutions, their spectrum in the gaseous state has not been established.
If a gaseous ion has several excited electronic states differing little in their chemical properties, being, for example, components of a single multiplet group of terms, then one may expect a parallel course of the potential curves depicting the perturbation experienced by these terms upon dissolution. If this picture is not complicated by splitting of the atomic terms analogous to that observed for mercury,
then one may expect in the absorption spectrum of the dissolved ion a group of maxima, the components of which are separated by approximately the magnitude of the intervals of the electronic terms of the multiplet of the gaseous ion. The presence of such a coincidence would serve as good confirmation of the correctness of the interpretation of the spectrum of the solution. An attempt at such a comparison of the spectra of the dissolved and gaseous ions was made by Cato ^5, who observed a large number of absorption maxima for a series of ions and extended her observations into the Schumann region. However, apart from the fact that many of the bands observed by her were not found by other, more careful investigators, the numerical coincidence of the intervals between maxima with the differences of terms of gaseous ions is partly accidental in character, as was shown for the ion Ag+ by Föhlberg ^6, and partly is based on an arbitrary choice of the most suitable term, without taking into account the presence of a whole series of other terms located in the same region. The origin of the maxima observed by Cato thus remains open. Below is given a table taken from her work, with the introduction of some corrections in the values of the terms of the gaseous ions.
It should be noted that Cato’s article abounds in erroneous notions concerning the position of levels in ions, the electronic transitions between them, and the lifetime of excited states.
The agreement of the values of the differences of terms $\Delta \nu$ of gaseous ions with the frequency differences of the absorption maxima of hydrated ions is most convincing in the case of Tl+ and Pb++.
In comparing the first ultraviolet absorption bands of the hydrated ion with the first absorption lines of the gaseous ion, we do not take into account the existence, in the latter series, of lower levels, transitions to which from the normal state of the ion are forbidden on the basis of the usual selection rules. For example, in the Ag+ ion, in addition to the cited absorption line 124.7 m$\mu$ ($^1S \rightarrow {}^3P$), there exists the possibility of optically forbidden transitions from the normal level $^1S$ to a series of levels $D$ ($4d^9 5s$), lower than $^3P$ ($4d^9 5p$), and of the corresponding lines with wavelengths, in round numbers, of 256, 246, 223 ($^1S \rightarrow {}^3D$) and 217 m$\mu$ ($^1S \rightarrow {}^1D$). It might be supposed that, under the influence of intermolecular fields of tens of millions of volts per centimeter, which occur in solutions, the prohibition rules valid for free gaseous ions lose their force and that the absorption bands observed in solutions may correspond also to the forbidden transitions of the gaseous atom or ion.
This supposition is contradicted, however, by the absence of forbidden absorption lines in the spectrum of the dissolved Hg atom. Moreover, upon hydration one should, as a rule, expect a displacement, and a considerable one, of the ion spectrum toward the red, whereas the absorption band of hydrated Ag+ ($\lambda = 210.5$ m$\mu$) lies on the short-wavelength side of the indicated
TABLE 4
Absorption maxima of certain cations according to Kato5
| Ion | Dissolved in H₂O λ (mμ) | Dissolved in H₂O ν (cm⁻¹) | Dissolved in H₂O Δν | Gaseous λ (mμ) | Gaseous ν (cm⁻¹) | Gaseous Δν | Symbol | Ionization potential, ΔeV |
|---|---|---|---|---|---|---|---|---|
| Cu⁺ | 287 | 34 843 | 1521 | 150,6 | 66 415 | 1498 | $3d^{10}\,{}^{1}S_{0}\longrightarrow 3d^{9}\,4p\,{}^{3}P_{2}$ | 20 |
| Cu⁺ | 275 | 36 364 | 6189 | 147,2 | 67 913 | 5680 | $3d^{10}\,{}^{1}S_{0}\longrightarrow 3d^{9}\,4p\,{}^{3}P_{1}$ | 20 |
| Cu⁺ | 235 | 42 553 | 6189 | (73 098) | 5680 | $3d^{10}\,{}^{1}S_{0}\longrightarrow 3d^{9}\,4p\,{}^{3}P_{0}$ | 20 | |
| Cu⁺ | 135,9 | 73 592 | $3d^{10}\,{}^{1}S_{0}\longrightarrow 3d^{9}\,4p\,{}^{1}P_{1}$ | 20 | ||||
| Ag⁺ | 225,5 | 44 346 | 3501 | 124,7 | 80 172 | 3449 | $4d^{10}\,{}^{1}S_{0}\longrightarrow 4d^{9}\,5p\,{}^{3}P_{2}$ | 21,9 |
| Ag⁺ | 209 | 47 847 | 2404 | 119,6 | 83 621 | 2517 | $4d^{10}\,{}^{1}S_{0}\longrightarrow 4d^{9}\,5p\,{}^{3}P_{1}$ | 21,9 |
| Ag⁺ | 199 | 50 251 | 116,1 | 86 138 | $4d^{10}\,{}^{1}S_{0}\longrightarrow 4d^{9}\,5p\,{}^{3}P_{0}$ | 21,9 | ||
| Hg⁺ | 240 | 41 667 | 5062 | 194,2 | 51 485 | 9123 | $5d^{10}\,6s\,{}^{2}S_{\frac{1}{2}}\longrightarrow 5d^{10}\,6p\,{}^{2}P_{\frac{1}{2}}$ | 18,7 |
| Hg⁺ | 214 | 46 729 | 165,0 | 60 608 | $5d^{10}\,6s\,{}^{2}S_{\frac{1}{2}}\longrightarrow 5d^{10}\,6p\,{}^{2}P_{\frac{3}{2}}$ | 18,7 | ||
| Tl⁺ | 223 | 44 843 | 2777 | 202,2 | 49 452 | 2941 | $6s^{2}\,{}^{1}S_{0}\longrightarrow 6s\,6p\,{}^{3}P_{0}$ | 20,5 |
| Tl⁺ | 210 | 47 620 | 10860 | 190,9 | 52 393 | 9333 | $6s^{2}\,{}^{1}S_{0}\longrightarrow 6s\,6p\,{}^{3}P_{1}$ | 20,5 |
| Tl⁺ | 171 | 58 480 | 162,0 | 61 726 | $6s^{2}\,{}^{1}S_{0}\longrightarrow 6s\,6p\,{}^{3}P_{2}$ | 20,5 | ||
| Pb⁺⁺ | 224 | 44 643 | 3901 | 165,6 | 60 395 | 3993 | $6s^{2}\,{}^{1}S_{0}\longrightarrow 6s\,6p\,{}^{3}P_{0}$ | 30,6 |
| Pb⁺⁺ | 206 | 48 544 | 15150 | 155,3 | 64 388 | 14595 | $6s^{2}\,{}^{1}S_{0}\longrightarrow 6s\,6p\,{}^{3}P_{1}$ | 30,6 |
| Pb⁺⁺ | 157 | 63 694 | 126,6 | 78 983 | $6s^{2}\,{}^{1}S_{0}\longrightarrow 6s\,6p\,{}^{3}P_{2}$ | 30,6 |
higher forbidden transitions ($S—D$) of the gaseous ion. In the case of Cu⁺, the forbidden transitions ($3d^{10}\,{}^{1}S \longrightarrow 3d^{9}4s\,{}^{3}D,{}^{1}D$) correspond to the lines 456, 438, 417 and 381 mμ, which in no way can be correlated with the ultraviolet absorption maxima of the hydrated Cu⁺ ion lying at $\lambda < 290$ mμ.
Further, by analogy with the dissolved mercury atom16, one may expect that the higher electronic transitions of cations will not retain their discrete character upon hydration, but will give a continuous absorption region corresponding to photoionization of the cation in the hydrated state, as is the case for anions (the affinity spectrum9).
Thus, the considerable difference in the regions of the spectrum in which absorption of light by cations occurs in the free and hydrated-
...in ionic states (Table 2), cannot be ascribed to the simple perturbing action of water molecules on the electron shell of the cation, which in this case remains, in its essential features, unchanged. Such an assumption is contradicted, moreover, by the low polarizability of these cations. Evidently, a cation that strongly deforms forms, together with water molecules, a new electronic system with its own energy levels, sharply different from the energy levels of the unperturbed cation. Only in the case of the large ion Tl\(^+\) can one, with some approximation, admit merely a deformation of its energy levels not connected with a general restructuring of the electronic system. The formation of a new, comparatively uniformly constructed electronic system is indicated by the fact of the surprisingly small variation in the positions of the maxima for hydrated cations, localized in a relatively narrow energy interval about 1 eV wide (5.8–6.9), whereas the absorption lines of free cations and their ionization potentials vary over a wide range of the order of 10 eV, and the structure of their electron shell also changes substantially (Table 2).
- For cations whose outer electron shell is not closed, such as, for example, Cu\(^{++}\), Fe\(^{++}\), Fe\(^{+++}\), Co\(^{++}\), Co\(^{+++}\), Ni\(^{++}\), etc., interaction with the surrounding water molecules will be determined not only by electrostatic forces, but also by forces of valence origin.
As a result these cations enter into so close a union with the solvent molecules that coordinatively bound complexes of the type (Cu, 4H\(_2\)O)\(^{++}\), (Cu, 4NH\(_3\))\(^{++}\), (Cr, 6H\(_2\)O)\(^{+++}\), (Co, 6NH\(_3\))\(^{+++}\), (Ni, 6NH\(_3\))\(^{++}\) are formed.
Indeed, the indicated cations usually exhibit the same spectrum as in solution also in the solid state, namely in salts crystallizing with a definite stoichiometric content of water molecules (mostly 6H\(_2\)O). Upon removal of the water of crystallization, however, the salt loses the color characteristic of the given cation. For example, as is known, anhydrous CuSO\(_4\) is colorless, whereas its hydrate has a blue color like the aqueous solution. Similarly, cupric ammine has a dark-blue color, attributed to the complex ion (Cu, 4NH\(_3\))\(^{++}\) \(^{26}\).
Thus the absorption bands in the visible region, characteristic of the cations under consideration, belong not to the cations themselves, but to their compounds with a definite number of solvent molecules (H\(_2\)O, NH\(_3\)). These complexes represent entirely new electronic systems with new energy levels and, consequently, with a new absorption spectrum different from the absorption spectrum of the free cation.
The considerable shift of the absorption spectrum toward the red, as compared with the absorption spectrum of the free ion, shows that in these cases not only does the lower (normal) level of the latter undergo a strong distortion upon hydration, but that...
and the upper level is displaced still more, i.e. in the excited state such cations bind still more strongly to the surrounding solvent molecules that enter into the complex.
However, it may turn out that the magnitude of the distortion of both levels will be approximately the same. This, undoubtedly, will occur when the normal and excited levels of the free cation are components of one multiplet, i.e. belong to the same electron configuration, differing only in the direction of the electron spin relative to the orbital angular momentum \(l\). In these cases one may expect that the absorption bands of the hydrated cation will be close to the absorption lines of this cation in the gaseous state (Fig. 5b). Indeed, in a number of cases good coincidence or close correspondence has been established between the spectrum of the free cation and the spectrum of the same ion in solution \(^{27,2}\). To explain such cases there is no need, as is usually done, to assume a very weak bond of the cations with water molecules, only slightly changing the position of the levels of the free cation \(^{26,28}\). It is sufficient to assume that the hydration energy of the cation in the excited state has approximately the same magnitude as in the normal state of the cation.
Such behavior in solution is exhibited, for example, by \(\mathrm{Cr}^{+++}\), whose absorption maxima (for \(\mathrm{CrCl}_3\)) in aqueous solutions, lying at 669 \((15\,000\ \mathrm{cm}^{-1})\) and 527 \(m\mu\) \((19\,000\ \mathrm{cm}^{-1})\), agree well with the first transitions \({}^{4}F \to {}^{2}G\) \((15\,014\ \mathrm{cm}^{-1})\) and \({}^{4}F \to {}^{2}H\) \((21\,027\ \mathrm{cm}^{-1})\) of the free ion, known from the spectrum of CrIV. The electron configuration in the excited states \({}^{2}G\) and \({}^{2}H\) remains the same as in the normal state, differing only by a change in the spin direction of one of the electrons \(^{27}\). An analogous correspondence is also observed for the ions \(\mathrm{Cr}^{++}\) and \(\mathrm{Cr}^{+}\), and also for other cations of elements of the transition group V, Mn, Fe, Co, Ni, J and Pd \(^{26,28}\).
For rare-earth ions, in which analogous electron transitions in the \(4f\) shell are shielded from the action of solvent molecules by the completed outer shell \(5s^{2}\ 5p^{6}\), one should expect narrower absorption bands and better coincidence of them with the electronic transitions of the gaseous ion \(^{27}\) (see Section 11).
If the absorption spectrum of a hydrated cation is shifted toward higher frequencies compared with the spectrum of the free ion, then this means that the excited ion is bound to the surrounding water molecules more weakly than the normal ion.*
* The supposition that, upon excitation of the cation, its bond with water molecules (orbital or of type \(l\)) is broken was made by Bose \(^{29}\) to explain the small increase, under the action of light, in the magnetic susceptibility of solutions containing paramagnetic cations of the kind considered here. This phenomenon was connected by him with a shift of the absorption bands to the violet side in comparison with the electronic transitions of the free ion \(^{26}\).
Absorption of Complex Halide Ions of Heavy Metals
- Halide salts of heavy metals (Ag, Cu, Tl, Pb, etc.) belong to the class of medium electrolytes. Dilute aqueous solutions of these salts exhibit absorption bands belonging to the hydrated cation and anion \(^{8,11,12}\). Increasing the concentration of halide anions, achieved by increasing the concentration of the dissolved salt*, causes the formation, from the strongly deforming cations of these metals and halide anions, of hydrated complex ions of the type \((\mathrm{MHal}_n)^{m-}\), the presence of which can sometimes be detected even by crude cryoscopic methods. A more convenient way of obtaining complex ions consists in dissolving salts of the indicated heavy metals (at concentrations of the order of \(10^{-4}\) mole/l) in saturated (\(1\)—\(4N\)) solutions of halide salts of alkali metals, which provide an excess of halide ions: the high concentration of halide anions in these mixed solutions favors the formation of such complexes. Such complexes form the more readily, the greater the polarizability of the anions; consequently, complex formation increases in the sequence \(\mathrm{Cl}^- , \mathrm{Br}^- , \mathrm{J}^-\). The stability of the complex also increases with decreasing size of the cation and increasing charge, i.e., it changes in parallel with the deforming action of the cation. Therefore such complexes are formed predominantly with cations of heavy metals**. Depending on the concentration of the anion in the given solution, complexes with different degrees of association \(n\) may form.
The formation of complexes \((\mathrm{MHal}_n)^{m-}\) is detected spectrally by the appearance in the ultraviolet region of very sharp absorption bands in the form of narrow maxima, shifted toward longer wavelengths from the background of continuous absorption lying in the region of shorter wavelengths and produced by the hydrated anion and cation, as well as by the solvent itself. With a gradual increase in the concentration of the added alkali-metal salt, these bands tend toward a certain limiting position and sharpness (Fig. 7). It should be noted here that no specific influence of the alkali-metal cation, also present in the solution, on the position and appearance of these bands is observed \(^{8,11-13}\). The composition of the complex, i.e., the number of halide ions bound to the metal cation, cannot always be established
* Saturation of an aqueous solution of these salts occurs at concentrations of the order of \(10^{-1}\)—\(10^{-4}\) mole/l.
** The composition of a saturated aqueous solution of \(\mathrm{PbCl}_2\) (\(0.04N\)), according to cryoscopic data, is as follows: \(\mathrm{Pb}^{++}\) (50 mol. %), \(\mathrm{PbCl}^{+}\) (44 mol. %), \(\mathrm{PbCl}_2\) (6 mol. %). In a mixed solution with KCl or HCl, \(\mathrm{PbCl}_4^{--}\) ions are formed. Analogously, \(\mathrm{PbBr}_2\) behaves, whereas \(\mathrm{PbJ}_2\) is completely dissociated into \(\mathrm{Pb}^{++}\) and \(\mathrm{J}^{-}\). A saturated aqueous solution of TlCl (\(0.01N\)) gives only 3% associated ions (not molecules); bromides and iodides of thallium are practically completely dissociated in solutions \(^{11}\).
unambiguously. For example, the composition of the complex giving the characteristic absorption band when TlCl is dissolved in a saturated (about \(4N\)) KCl solution may be either \(\mathrm{TlCl}_3^{--}\), or \(\mathrm{TlCl}_4^{---}\), or \(\mathrm{TlCl}_2^{-}\); in exactly the same way the mercury and cadmium complexes may have the formula either \(\mathrm{MHal}_4^{--}\) or \(\mathrm{MHal}_3^{-}\). If there are no additional data obtained by other methods, then the formula of the complex which appears the most probable is accepted.
Table 5 gives the positions of the maxima and the composition of those complexes to which they are assigned.
TABLE 5
Absorption maxima of complexes (in \(m\mu\)) \(^{8,11,12,14,15}\)
| Complex | Cl \(\lambda\) (\(m\mu\)) | Cl \(\nu\) (eV) | Br \(\lambda\) (\(m\mu\)) | Br \(\nu\) (eV) | J \(\lambda\) (\(m\mu\)) | J \(\nu\) (eV) |
|---|---|---|---|---|---|---|
| \(\mathrm{Cu}^{\mathrm{I}}\mathrm{Hal}_3^{--}\) | 272 | 4.54 | 276 | 4.48 | — | — |
| \(\mathrm{Cu}^{\mathrm{II}}\mathrm{Hal}_4^{--}\) | 259 | 4.77 | 293 | 4.22 | — | — |
| \(\mathrm{AgHal}_2^{-}\) | 216 | 5.72 | 227.5 | 5.44 | 252 | 4.9 |
| \(\mathrm{ZnHal}_4^{--}\) | — | — | — | — | 238 | 5.19 |
| \(\mathrm{CdHal}_4^{--}\) | 187.5 | 6.59 | 215.5 | 5.74 | 257 | 4.80 |
| \(\mathrm{HgHal}_4^{--}\) | 228.5 | 5.4 | 250 | 4.94 | 328 267 |
3.82 4.63 |
| \(\mathrm{TlHal}_3^{--}\) | 242 | 5.10 | 262.5 | 4.70 | 299.5 | 4.13 |
| \(\mathrm{PbHal}_4^{--}\) | 272 | 4.54 | 304 | 4.06 | 363.5 | 3.40 |
| \(\mathrm{PbHal}_4^{--}\) | 195 | 6.38 | 223.5 | 5.54 | 308 272 |
4.01 4.54 |
| \(\mathrm{PbHal}^{+}\) | 227 | 5.44 | 235 | 5.25 | 264 | 4.68 |
| \(\mathrm{PbHal}^{+}\) | 188 | 6.56 | 203 | 6.09 |
Analogous characteristic maxima, located approximately at the same places in the spectrum, are given by single crystals of alkali-halide salts into whose melt the cations of the indicated heavy metals have been introduced in negligible concentration*. In the following table the absorption maxima of mixed crystals and solutions are compared.
The omissions and doubtful places in the table are due to the difficulty of identifying individual maxima against the background of continuous absorption, especially with the photographic method of measurement (see Section 1). Nevertheless, in some cases it is possible to observe, in addition to the longest-wavelength maxima, also extremely intensive—
* To prepare such single crystals, several tenths of a molecular percent of the corresponding halide salt of the heavy metal are taken per 100 mol. % of the main substance; in this case actually only less than 1% of all the added salt goes into the formation of optically active centers.
TABLE 6¹³
Comparison of the characteristic bands of doped monocrystals of alkali-halide salts and the corresponding mixed solutions
| System | Crystal $\lambda_{\max}$ ($m\mu$) (width of the maximum in $m\mu$ in parentheses) |
Solution $\lambda_{\max}$ ($m\mu$) (width of the maximum in $m\mu$ in parentheses) |
|---|---|---|
| NaCl + AgCl | 210 (10) | 216.2 (18) |
| KCl + AgCl | 215.6 (20) | |
| NaBr + AgBr | 219 (10) | 227.5 (21.5) |
| KBr + AgBr | 226.5 (21) | |
| KJ + AgJ | 254 (double) | 252 (double) |
| KCl + CuCl | 269 (35) 205 (40) |
272 (28) |
| KBr + CuBr | 285 (30) | |
| KCl + PbCl$_2$ | 273 (12) 196 | 272 (12.9) ∞ 195 |
| KBr + PbBr$_2$ | 302 (15) 223 | 304 (17.6) 223.5 |
| KJ + PbJ$_3$ | — 304 ∞ 265 | 363.5 (24.4) ∞ 308 273 |
| KCl + KBr (1 : 1) + + PbCl$_2$ |
289 (21) | 291.7 (25.?) |
| KCl + TlCl | 247.5 (10.5) 196 (13.3) | 242 (19.3) Second band not determined. |
| KBr + TlBr | 261 (13) 210 | 262.5 (26.5) |
| KJ + TlJ | 287 (16) 236 218 | 299.5 (30) |
—i.e., ($\lg k = 4.1—4.9$) maxima located in the region of shorter wavelengths, whose height, estimated by the value of the absorption coefficient $k$, is 3–4 times greater than the height of the first maxima. It should be noted that such a considerable value of the absorption coefficient is observed only in the case of complex organic molecules.
The maxima of the solutions are always shifted on the average by 5–10 $m\mu$ to the red side from the maxima of the corresponding crystals and amount to 10–40 $m\mu$, increasing in the sequence Cl, Br, J. For example, for PbCl$_4^{--}$, $\Delta\lambda = 13\ m\mu$, for the bromide — 18 $m\mu$, and for the iodide — 24 $m\mu$. Even certain details of the band contours are identical in the crystal and in solution.
Such far-reaching similarity between the bands observed in crystals doped with heavy metals and in mixed solutions of the same composition compels one to ascribe them to the same centers, namely to complex ions $(\mathrm{MHal}_n)^{m-}$.
The absorption maxima of complex ions in solutions (Table 5) are shifted in the sequence Cl, Br, J farther and farther toward longer wavelengths; moreover, the magnitude of this shift, expressed in frequencies, is smaller on passing from Cl to Br than on passing from Br to J* (Fig. 9).
* The ratio of the shifts $\dfrac{(\mathrm{Cl}-\mathrm{Br})}{(\mathrm{Cl}-\mathrm{J})}$ has almost the same value for all Pb and Tl complexes (0.42 and 0.41); for Ag complexes this ratio is 0.35; for $\mathrm{PbHal}^{+}$, however, it is only 0.26.
Poorer complexes \(\mathrm{PbHal}^{+}\), containing only one halide anion, are obtained in a saturated solution of the salt \(\mathrm{PbHal}_{2}\),
Fig. 7. Shift of the absorption maximum of \(\mathrm{PbBr}^{+}\) into the absorption maximum of the complex ion \(\mathrm{PbBr}_{4}^{-}\) \((304\,m\mu)\) with increasing concentration of \(\mathrm{Br}^{-}\) ions in the mixed solution \(\mathrm{PbBr}_{2} + \mathrm{KBr}\).
where, as was indicated, they can also be detected cryoscopically. In an aqueous solution of \(\mathrm{PbHal}_{2}\), precisely the equili-
equilibrium \( \mathrm{Pb}^{++} + \mathrm{Hal}^{-} \rightleftharpoons \mathrm{PbHal}^{+} \); in a saturated solution the ions \( \mathrm{PbHal}^{+} \) predominate, and the spectrum contains an absorption band belonging to the latter; upon gradual dilution this band disappears, being replaced by the band belonging to the ion \( \mathrm{Pb}^{++} \). If the absorption coefficient of one complex \( \mathrm{PbHal}^{+} \) is measured, then the degree of association of the ions in the solution at its various concentrations can be determined optically.*
To obtain the spectrum of the ion \( \mathrm{PbHal}^{+} \) in pure form, Fromherz prepared a mixed solution \( \mathrm{PbHal}_{2} \) (0.001 mole) \(+\) \( \mathrm{Pb(ClO}_{4})_{2} \) (2 moles), in which the excess of \( \mathrm{Pb}^{++} \) ions [from \( \mathrm{Pb(ClO}_{4})_{2} \)] favors displacement of the equilibrium \( \mathrm{Pb}^{++} + \mathrm{PbHal}_{2} \rightleftharpoons 2\,\mathrm{PbHal}^{+} \) to the right. The positions of these maxima are given in Table 5. The same band, characteristic of \( \mathrm{PbHal}^{+} \), appears upon gradual dilution of concentrated solutions of alkali-halide salts containing a small amount of \( \mathrm{PbHal}_{2} \) as an impurity. In this case one observes the disappearance of the sharp bands characteristic of \( \mathrm{PbHal}_{4}^{--} \) and their gradual transition into the bands of \( \mathrm{PbHal}^{+} \). In contrast to the preceding cases, no equilibrium between \( \mathrm{PbHal}_{4}^{--} \) and \( \mathrm{PbHal}^{+} \) is observed here: by gradual displacement and broadening, one band continuously passes into the other (Fig. 7), without leading to an intersection of the absorption curves, as occurred in the case of the equilibrium \( \mathrm{Pb}^{++} + \mathrm{Hal}^{-} \rightleftharpoons \mathrm{PbHal}^{+} \). Despite the displacement and broadening, the area of the absorption curve \( F \) (see Section 1), proportional to the probability of absorption of light by an individual center, retains its value. This probability increases in the sequence Cl, Br, I. For the bromine complexes of \( \mathrm{Ag}^{+} \) and \( \mathrm{Cu}^{+} \), the probability is approximately twice as large as for the chlorine complexes of the same cations. In all the changes in the degree of association of ions described here, no indications were found of the existence of undissociated \( \mathrm{PbHal}_{2} \) molecules in solution; none of the observed characteristic maxima can be assigned to it, although by analogy with the salts \( \mathrm{HgHal}_{2} \) (see Section 7), for which the absorption spectra of gaseous and dissolved molecules practically coincide, the absorption spectrum of the \( \mathrm{PbHal}_{2} \) molecule ought to have been observed in approximately the same region.
The halide salts of the divalent cation \( {}^{++}\mathrm{Cu} \) and of the monovalent cations \( \mathrm{Ag}^{+} \), \( \mathrm{Cu}^{+} \), \( \mathrm{Tl}^{+} \) behave analogously to the lead halide salts; the positions of the maxima of their complex ions are given in Table 5. The absorption spectrum of saturated aqueous sol—
* Such a spectral measurement of the degree of association was carried out in this simple particular case by Fromherz and Kun-Hou-Li.¹⁴ The degree of association of a saturated \( \mathrm{PbCl}_{2} \) solution (about 0.03 \( N \)), i.e., the ratio of the concentration of \( \mathrm{PbCl}^{+} \) ions to the total concentration of the salt \( \mathrm{PbCl}_{2} \), is 0.3, decreasing with dilution. For saturated solutions of \( \mathrm{PbBr}_{2} \) (about 0.02 \( N \)) and \( \mathrm{PbJ}_{2} \) (0.001 \( N \)), the degree of association
\[ \beta = \frac{\mathrm{PbHal}^{+}}{\mathrm{PbHal}_{2}} \]
is equal respectively to 0.3 and 0.6.
solutions of thallium salts* reveals absorption maxima belonging only to hydrated ions $\mathrm{Tl}^+$ and $\mathrm{Hal}^-$. Only in the case of TlCl was the presence of about 1% associated ions noted on the basis of spectral and cryoscopic data; their nature could not be clarified because of their negligible concentration. Thus, thallium halide salts should be regarded in aqueous solutions as completely dissociated into ions.
When thallium salts are dissolved in solutions of alkali-halide salts, characteristic maxima appear, given in Tables 5 and 6, attributed to the complexes $\mathrm{TlHal}_3^{--}$. As in the case of complexes of the ion $\mathrm{Pb}^{++}$, in addition to these maxima there are also second, considerably higher maxima lying in the shorter ultraviolet; it proved difficult to determine the wavelength of the latter because of the presence of a strong continuous absorption background in this region. Upon dilution of the original solution of the alkali-halide salt, these maxima undergo a gradual lowering, broadening, and pass into the maxima of the hydrated ion $\mathrm{Tl}^+$, characteristic of an aqueous solution of thallium salts. No points of intersection of the absorption curves, characteristic of equilibrium between complex ions of two different degrees of association, are observed here. The behavior of the thallium complex ions is thus similar to that of lead ions, with the difference that upon dilution no intermediate complex ion analogous to the ion $\mathrm{PbHal}^{+}$ is formed. The lesser tendency of the thallium cation toward association is explained by its smaller deforming action, connected with its larger size. The lesser stability of the complex ions $\mathrm{TlHal}_3^{--}$ is also indicated by the greater width of the absorption maxima in comparison with the maxima of the ions $\mathrm{PbHal}_4^{--}$ (Table 6). The greater width of the absorption maximum indicates a greater susceptibility of the electronic configuration of the absorbing system to external influences. As in the case of lead salts, there is no indication of the presence in the solution of a neutral molecule—in the present case $\mathrm{TlHal}$—as an intermediate stage between the hydrated cation of the diluted solution and the same cation, maximally saturated by the addition of halide anions from the solution of the alkali-halide salt.
In aqueous solutions of halide salts of divalent copper, when the concentration of halide ions increases above 2 mole/liter, a shift of the characteristic bands attributed to the complexes $\mathrm{CuHal}_4^{--}$ toward the red is observed; at the same time, in the region of longer waves, new broad bands appear which should apparently be attributed to more complex, possibly polynuclear, complexes. Analogous broad maxima, lying partly also in the visible region, also arise in a mixed solution of the salts $\mathrm{CuHal}_2 + \mathrm{CuHal}$ in a concentrated solution of various alkali-halide salts.\(^{15}\)
* TlCl (0.01 $N$), TlBr (0.002 $N$), TlJ (0.0002 $N$).
- In contrast to the weakly deforming ions Tl$^{+}$ and Pb$^{++}$, the cations Cd$^{++}$, Zn$^{++}$ and especially Hg$^{++}$ give in aqueous solutions not only stable complexes of the presumed composition HgHal$_4^{--}$ and CdHal$_4^{--}$, but also neutral molecules HgHal$_2$ and CdHal$_2$12, 14, 15. In the latter, the predominance of a homeopolar type of bond in this group of halide compounds is manifested. A saturated aqueous solution of HgCl$_2$ has, for example, on the basis of cryoscopic data, the following composition (in moles per liter):
\[ \begin{array}{cccccc} \mathrm{HgCl_2} & \mathrm{HgCl^{+}} & \mathrm{H^{+}} & \mathrm{Cl^{-}} & \mathrm{Hg^{++}} & \mathrm{HgCl_4^{--}}\\ 2.6\cdot 10^{-1} & 1.5\cdot 10^{-4} & 3.3\cdot 10^{-4} & 4.8\cdot 10^{-4} & 1\cdot 10^{-8} & 5\cdot 10^{-6} \end{array} \]
i.e., it consists practically of undissociated molecules. The salt HgJ$_2$, which is less soluble than HgCl$_2$, gives $1.3\cdot 10^{-4}$ mole/l of undissociated molecules in the saturated solution14.
Complex ions of the presumed composition MHal$_4^{--}$ are also obtained when dissolving the halide salts of Hg, Cd and Zn in solutions of alkali-halide salts. In this case, instead of the absorption bands of the undissociated molecule, a maximum appears in the region of longer waves, characteristic of the complex (Fig. 8a)*.
Table 7 gives the wavelengths of the maxima, as well as the value of the absorption coefficient for solutions of mercury-halide salts in water and potassium iodide.
TABLE 7
Wavelengths (in mµ) of the first maxima of solutions of mercury-halide salts
| Solvent | HgJ$_2$ λ$_{\max}$ | HgJ$_2$ lg $k_{\max}$ | HgBr$_2$ λ$_{\max}$ | HgBr$_2$ lg $k_{\max}$ | HgCl$_2$ λ$_{\max}$ | HgCl$_2$ lg $k_{\max}$ | Spectrum carrier |
|---|---|---|---|---|---|---|---|
| H$_2$O | 265 | 3.6 | 226 | 3.6 | <200 | — | Molecule |
| KHal solution | 323 | 4.4 | 245 | 4.5 | 228 | 4.5 | Complex ion HgHal$_4^{--}$ |
It is noteworthy that the absorption maxima of the complexes are considerably higher than the maxima of the undecomposed molecules. In addition, it should be noted that, with the exception of the iodides, the maxima of the complexes are narrower than the maxima of the molecular spectrum.
* The composition MHal$_3^{-}$ is also possible; direct measurements revealed the ions Hg$_2$Cl$_5^{-}$ and Hg$_3$Cl$_6^{--}$. The tendency toward complex formation increases for the iodides.
** See Fig. 5 in Fromherz’s review12.
A. N. TERENIN
The greater stability of the complex in the case of bromides and iodides, as compared with chlorides, is revealed by the fact that, upon a decrease in the concentration of halide ions achieved by dilution of the basic solution, the absorption maxima of the bromide and iodide complexes disappear more slowly than for chlorides. The greater stability of all these complexes follows from the fact that even at a dilution of 1:5000 the position and contour of the absorption bands remain practically unchanged. Upon further dilution the maximum characteristic of the complex ion disappears, and absorption characteristic of the undecomposed molecule \( \mathrm{HgHal_2} \) or \( \mathrm{CdHal_2} \) gradually appears. In the case of mercury salts, with such a change in the spectrum the absorption curves show a common point of intersection, indicating the presence of an equilibrium between two discrete species, i.e.
\[ \mathrm{HgHal_2} + 2\mathrm{Hal}^{-} \rightleftarrows \mathrm{HgHal_4}^{--}. \]
In the case of Cd salts, however, there is no such point of intersection, which indicates a smooth transition from the coordination ion \( \mathrm{CdHal_4}^{--} \), by gradual splitting off of halide ions, to the \( \mathrm{CdHal_2} \) molecule, without formation of any stable intermediate complexes of definite composition.
For the salts \( \mathrm{ZnHal_2} \), complex formation is observed only in the case of \( \mathrm{ZnJ_2} \), with the appearance of a maximum at \(238\ m\mu\). For \( \mathrm{ZnBr_2} \) and, especially, \( \mathrm{ZnCl_2} \), apart from the band of the hydrated anion, no other bands are observed that would indicate the formation of complexes, even when these salts are dissolved in solutions of alkali-halide salts. The cation \( \mathrm{Zn}^{++} \) thus occupies an intermediate position between the cations of the alkali and alkaline-earth metals and the heavy-metal cations considered here.
As already mentioned above, the tendency toward complex formation increases in the sequence \( \mathrm{Zn} \to \mathrm{Cd} \to \mathrm{Hg} \) and \( \mathrm{Cl} \to \mathrm{Br} \to \mathrm{J} \). The formation of complexes in solutions can be detected independently by means of Raman spectra, which in these cases give the vibrational quanta of the resulting system[^31].
TABLE 8
Raman spectra of solutions of \( \mathrm{HgHal_2} \) salts
| Molecule | Solvent | \(\omega\) \((\mathrm{cm}^{-1})\) | Solvent | \(\omega\) \((\mathrm{cm}^{-1})\) | \(\dfrac{\omega(\mathrm{HgHal_4}^{--})}{\omega(\mathrm{HgHal_2})}\) |
|---|---|---|---|---|---|
| \( \mathrm{HgCl_2} \) | Ethyl acetate | 331 | Aqueous solutions \( \mathrm{KCl} \) | 266 | 0.83 |
| \( \mathrm{HgCl_2} \) | \( \mathrm{H_2O} \) | 320 | Aqueous solutions \( \mathrm{KCl} \) | 266 | 0.83 |
| \( \mathrm{HgBr_2} \) | Ethyl acetate | 205 | \( \mathrm{KBr} \) | 166 | 0.81 |
| \( \mathrm{HgJ_2} \) | Absolute alcohol | 150 | \( \mathrm{KI} \) | 126 | 0.82 |
An aqueous solution of \(\mathrm{HgCl_2}\) and solutions of \(\mathrm{HgBr_2}\) and \(\mathrm{HgJ_2}\) in acetic ether and alcohol* give single vibrational frequencies, undoubtedly belonging to \(\mathrm{HgHal_2}\) molecules. When these same salts are dissolved in solutions of potassium halide salts, new, likewise single, vibrational frequencies appear, amounting with rather great constancy to \(0.8\) of the preceding ones (Table 8).
For \(\mathrm{CdJ_2}\) the Raman spectrum indicates the formation of complexes of indefinite composition (a broad band in the spectrum) already in a concentrated aqueous solution of this salt, but a particularly sharp Raman frequency appears only upon dissolution in \(\mathrm{KJ}\). A definite frequency in the Raman spectrum is observed for \(\mathrm{CdJ_2}\) also in an alcoholic solution (the \(\mathrm{CdJ_2}\) molecule)**.
A detailed investigation of the absorption spectrum of dissolved molecules \(\mathrm{HgHal_2}\), \(\mathrm{CdHal_2}\), and \(\mathrm{ZnHal_2}\) was carried out by Scheibe and Lederle \(^{32,33}\). In view of the low solubility of these salts in water, ethyl alcohol had to be used for the most part as the solvent. In comparison with aqueous solutions, this circumstance does not introduce any substantial difficulty, since replacing alcohol by water causes a comparatively small shift of the absorption maxima belonging to \(\mathrm{MHal_2}\) and \(\mathrm{MHal_4}^{--}\), by \(3\)—\(6\,m\mu\) toward the ultraviolet.
In Fig. 8b are given the absorption curves of alcoholic solutions of \(\mathrm{HgJ_2}\), \(\mathrm{CdJ_2}\), and \(\mathrm{ZnJ_2}\) at intermediate concentrations.
The assignment of these maxima to undissociated \(\mathrm{MHal_2}\) molecules follows from the close coincidence of their position with the maxima of the absorption spectrum of gaseous \(\mathrm{MHal_2}\) molecules \(^{34}\). Such invariance of the spectrum upon transfer of the molecule into solution finds its explanation in the fact that these molecules are bound by forces of homeopolar origin and in the normal state constitute valence-saturated electronic systems, little subject to electrostatic influences on the part of the solvent molecules. Further, the process of absorption of light by these molecules does not lead them into a new stable electronic state, which could undergo strong distortion by the solvent, but causes their dissociation into \(\mathrm{MHal + Hal}\). The presence of identical absorption maxima both in vapors and in solutions agrees well with the conception of such a dissociation process taking place in solution. The second maximum of \(\mathrm{HgJ_2}\), situated toward higher frequencies, approximately 5 times higher than the first maximum. In its position it agrees well with the region of wavelengths that cause decomposition of the gaseous \(\mathrm{HgJ_2}\) molecule into excited-
* The choice of new solvents is due to the negligible solubility of the latter salts in water.
** Upon dilution of solutions of \(\mathrm{CdJ_2}\) and \(\mathrm{ZnJ_2}\) to \(10^{-4}\) normal, a band of the solvated ion \(\mathrm{J^-}\) appears; for \(\mathrm{HgJ_2}\) such dilution is still insufficient for dissociation. At very high concentrations of alcoholic solutions, as has already been mentioned, complex formation of \(\mathrm{MHal_4}^{--}\) ions is observed.
... radical HgJ* and the atom J. The same applies to HgBr₂, where, however, owing to the displacement of the entire absorption spectrum toward shorter wavelengths, the rise toward the second, higher maximum is only just indicated.
Fig. 8. Absorption maxima of halide salts of mercury and cadmium in various solvents
a
b
- HgJ₂ in ethanol
- CdJ₂ in ethanol
- ZnJ₂ in ethanol
Table 9 gives a comparison of the absorption maxima of the molecules MHal₂ in vapors and in solutions.³³
The halide compounds of metals of group V, Bi and Sb, are hydrolyzed in aqueous solutions, but in ethyl ether it is possible to obtain the spectrum of the undecomposed BiBr₃ molecule, consisting of a broad maximum,
TABLE 9
Comparison of the positions of the absorption maxima of \(M\mathrm{Hal}_2\) molecules in the gaseous phase and in solutions
| Molecule | Vacuum \(\lambda\) \((m\mu)\) | Vacuum \(\nu\) (eV) | Solvent \( \mathrm{H_2O}\) \(\lambda\) \((m\mu)\) | Solvent \( \mathrm{H_2O}\) \(\nu\) (eV) | Solvent \( \mathrm{C_2H_5OH}\) \(\lambda\) \((m\mu)\) | Solvent \( \mathrm{C_2H_5OH}\) \(\nu\) (eV) |
|---|---|---|---|---|---|---|
| \(\mathrm{HgJ_2}\) | 268 | 4.60 | 265 | 4.67 | 272.5 | 4.53 |
| \(\mathrm{HgJ_2}\) | 224 | 5.50 | — | — | 217.5 | 5.63 |
| \(\mathrm{HgBr_2}\) | 224 | 5.50 | 226 | 5.46 | 233 | 5.30 |
| \(\mathrm{CdJ_2}\) | 262 | 4.70 | — | — | 242 | 5.10 |
| \(\mathrm{CdJ_2}\) | 223 | 5.54 | — | — | \(<190\) | — |
| \(\mathrm{CdBr_2}\) | 227 | 5.70 | — | — | 211 | 5.85 |
| \(\mathrm{CdBr_2}\) | 197.6 | 6.26 | — | — | — | — |
| \(\mathrm{ZnJ_2}\) | 221 | 5.62 | — | — | 217 | 5.70 |
exactly coinciding with the absorption maximum of \(\mathrm{BiBr_3}\) vapor. An analogous coincidence also takes place for \(\mathrm{BiCl_3}^{65}\).
- From the experimental material considered above it follows that, when an excess of halide ions is present in the solution, the cations of heavy metals combine with them, forming complexes of quite definite composition, which give characteristic narrow maxima in the absorption spectrum and definite vibrational frequencies detected in the Raman spectra. Such complexes are formed the more readily and are the more stable, the greater the deforming action of the cations, i.e., the smaller the size and the larger the charge of the cation. Further, the ease of formation of the complex increases with increasing polarizability of the anion, i.e., in the sequence \(\mathrm{Cl^-} \to \mathrm{Br^-} \to \mathrm{J^-}\). In this same double sequence the characteristic absorption maxima belonging to the complexes are also displaced increasingly toward the red. In Fig. 9, the positions of the absorption maxima for the complexes considered above, as well as for hydrated cations, are given on an energy scale (electron-volts). The data are taken from Tables 2 and 5. Cations with a rare-gas electron shell, even when these cations have small dimensions (for example, \(\mathrm{Li^+}\)), do not give such complexes. For their formation it is essential that the outer shell of the cation consist of 10 \(d\)-electrons, i.e., that it represent a system less inert chemically than a closed rare-gas-type shell. In the case of the cations \(\mathrm{Hg^{++}}\), \(\mathrm{Cd^{++}}\), \(\mathrm{Zn^{++}}\), their interaction with halide anions has so intimate a character,
that in solutions of medium concentration there exist normal undissociated valence-bonded molecules \(MHal_2\).
If one compares the positions of the maxima of the chloride complexes shown in Fig. 3 with the positions of the maxima of the corresponding hydrated cations, their relatively small difference is noteworthy: the maxima of the complexes for cations with a unit charge are shifted by approximately \(0.6\ \mathrm{eV}\) toward lower energies from the maxima of the hydrated cations. For cations with a double charge this shift is about \(1.5\ \mathrm{eV}\). The difference in the positions of the absorption maxima for chloride complexes and hydrated cations is considerably
Fig. 9. Position of the absorption maxima of hydrated cations and their complex halide ions
smaller than the difference in position for hydrated cations, on the one hand, and gaseous cations, on the other. Indeed, the difference in the latter case amounts to from 2 to \(10\ \mathrm{eV}\) (Table 3).
The maxima of bromide and iodide complexes are shifted still farther to the red, and the shift for iodides already reaches considerable magnitudes (Fig. 9).
This phenomenon may be interpreted, following Fajans, by the different deformability of the anions and by the difference in the deforming action of the cations. For cations with a double charge the shift of the absorption maximum is considerably greater than for cations with a single charge.
Thus replacement of the shell of water molecules surrounding the hydrated cation by chlorine ions does not cause any substantial change in the spectrum. Considering in Section 2 the spectrum of hydrated cations of heavy metals, we acknowledged that its considerable shift in comparison with the spectrum of the free cation can be explained by assuming a closer inter-
ABSORPTION SPECTRA OF ELECTROLYTE SOLUTIONS
penetration of the electronic systems of the cation and of the water molecules than is possible under a purely external electrostatic interaction and relatively weak deformations of the participants. All the more should such a close interaction take place for chlorine ions and, to an ever increasing degree, for bromine and iodine ions. Halide anions displace the shell of water formed around the hydrated cation and enter into direct contact with the latter, since the energy of this bond is greater than the hydration energy of the cation.
In halide complexes the electrons required by the cation to complete its external structure are supplied to it by easily polarizable anions. In hydrated cations this function is performed by less readily polarizable water molecules. In both cases a new electronic system is formed, possessing energy levels that are, of course, different from the levels of the free cation. To single out in such a common binding electronic system the individual shells of the separate ions constituting the complex appears difficult. If the bond in the complex is indeed of a homeopolar nature, then attempts to localize absorption bands in definite ions are doomed to failure in advance.
Fromherz, nevertheless, believes^11 that the first absorption maximum of a halide complex belongs to the cation, while the second, considerably (by a factor of 3.5–4) higher maximum, lying toward the side of shorter wavelengths, belongs to the halide ion. When hydrated ions combine into a complex, their absorption frequencies decrease. He explains this, in his opinion, primarily by the fact that the redward displacement of the absorption maxima of different complexes upon replacement of the cation and anions preserves the same sequence as is observed for hydrated cations and anions (Fig. 9). The closeness of the first absorption maxima of the complexes to the absorption maxima of hydrated cations and the similarity of their external appearance (the presence of a bifurcation in the case of Ag\(^+\)) are, in Fromherz’s opinion, sufficient grounds for assigning the first maxima of the complexes to an electronic transition in the cation. On the other hand, the unusual height of the second absorption maxima must, in his view, be correlated with the presence in the complex of several identical absorption centers, i.e., halide ions. Indeed, in contrast to PbHal\(_4^{--}\), in the case of the monohalide ion PbHal\(^+\) the first and second maxima have approximately the same height. Moreover, the second maximum for PbJ\(_4^{--}\) and TlJ\(_3^{--}\) is double, with the same separation between the components as occurs for J\(^-\).
However, all these arguments are not entirely convincing. The structural similarity of the bands of the hydrated cation with the first maxima of the halide complexes is due rather to the fact that the shell of water molecules surrounding the hydrated cation creates, with the outer electrons of the cation, such a
the same electronic configuration as is created by a shell of halide ions.
The increase of the absorption coefficient on passing to more distant ultraviolet maxima is a phenomenon of a general kind, also encountered in molecular systems, including those that do not possess a structural element repeated several times. It is possible that the second, more distant ultraviolet absorption maxima of the complexes are connected with the process of detachment of an electron or of splitting off an entire halide atom.
Finally, Fromherz\(^8\) himself points out that the absorption maximum of the complex \(\mathrm{Ag}_2\mathrm{J}^+\),* containing two cations \(\mathrm{Ag}^+\), has the same height as the maximum of the complex \(\mathrm{AgJ}_2^-\). If this absorption belonged to the cation, one would have expected the absorption to be twice as intense in the first case. Fromherz finds a way out of this difficulty by assigning the absorption not to the cation \(\mathrm{Ag}^+\), but to the \(\mathrm{Ag—J}\) bonds, the number of which is the same in both cases (\(\mathrm{Ag—J—Ag}\) and \(\mathrm{J—Ag—J}\)). Such a statement is equivalent to recognizing a homeopolar bond in these complexes. However, subsequently Fromherz\(^{11,13}\) rejects this explanation on the basis of the fact that the mixed complex \(\mathrm{PbBr}_2\mathrm{Cl}_2^{--}\)** gives only one absorption band at \(291.7\,m\mu\), occupying an intermediate position between the bands of \(\mathrm{PbCl}_4^{--}\) \((272\,m\mu)\) and \(\mathrm{PbBr}_4\) \((304\,m\mu)\). In his opinion, the existence of two different homeopolar bonds, \(\mathrm{Pb—Cl}\) and \(\mathrm{Pb—Br}\), in the complex should have led to two different absorption maxima, and he considers this argument decisive. Against this consideration, however, one may object that the coordination bond of ions in a complex, even if it is homeopolar, probably differs from the ordinary saturation of the principal valences of an ion. Especially in the case of symmetrically constructed, coordinatively saturated polyhalide complexes with a closed structure, one should expect a delocalized homeopolar bond. Such an assumption explains well the sharpness of the absorption bands, i.e. the small width of the maxima, comparable with that observed for the same complexes in crystals.
Along with such a delocalized homeopolar bond, there exists, of course, also a very strong interaction of electrostatic nature in these complexes.
An electrostatic bond between the participants of the complex, accompanied by little deformation of them, is excluded because the absorption spectrum of the complexes differs greatly in its position from the spectrum of the free ions. Consequently, for
* The complex ion \(\mathrm{Ag}_2\mathrm{J}^+\) is obtained upon dissolving \(\mathrm{AgJ}\) in a concentrated solution of \(\mathrm{AgClO}_4\), which gives, as was indicated earlier, \(\mathrm{Ag}^+\) ions. The absorption maximum of this complex ion is at \(245.5\,m\mu\).
** More precisely, \(\mathrm{Pb}^{++}\mathrm{Cl}_m^-\mathrm{Br}_n^-\), since the composition of the complex is not known; such a complex is obtained by dissolving \(\mathrm{PbBr}_2\) in a saturated mixed solution of \(\mathrm{KCl}+\mathrm{KBr}\).
for an explanation of the observed strong shift of the spectrum by electrostatic influences, it is necessary to assume a strong deformation of the electron shells of the ions composing the complex, which, however, is equivalent to admitting a homeopolar or covalent bond.
Naturally, deviations from this general case are possible both in the direction of approximation to a purely electrostatic type of bond and in the direction of a purely homeopolar bond. It is also possible that both kinds of bonds are present in the given complex separately. Thus, for example, Fromherz supposes that the complex $\mathrm{AgHal}_2^{-}$ has the structure $\mathrm{AgHal}\cdot\mathrm{Hal}^{-}$, where $\mathrm{AgHal}$ is a valence-bonded, homeopolar molecule, undoubtedly possessing a considerable dipole moment, while $\mathrm{Hal}^{-}$ is a halide ion associated with this molecule. As a result of their interaction, the region of the absorption spectrum of the molecule $\mathrm{AgHal}$, known for the vapor of this compound, is shifted to the ultraviolet side. The same occurs for the complex ions $\mathrm{Hal}_3^{-}$ in solutions, which are usually regarded as addition of the ion $\mathrm{Hal}^{-}$ to an undissociated homeopolar molecule $\mathrm{Hal}_2$*. As a result of the action of the negatively charged ion, the spectrum of the covalent molecule is shifted to the ultraviolet side. In Table 10 there are compared
TABLE 10
Absorption maxima (in m$\mu$) of trihalide complex ions$^{-35}$ $\mathrm{Hal}_2\cdot\mathrm{Hal}^{-}$ and gaseous molecules $\mathrm{Hal}_2$
(The numbers in parentheses give the spectral positions of the maxima in electron-volts)
| $\mathrm{Hal}_2\cdot\mathrm{Hal}^{-}$ | $\mathrm{Hal}_2$ (gas) |
|---|---|
| $\mathrm{Cl}_2\cdot\mathrm{Cl}^{-}$ 233 (5.30) |
$\mathrm{Cl}_2$ 338 (3.66) |
| $\mathrm{Br}_2\cdot\mathrm{Cl}^{-}$ 230 (5.36) |
$\mathrm{Br}_2$ 415 (2.97) |
| $\mathrm{Br}_2\cdot\mathrm{Br}^{-}$ 265 (4.66) |
|
| $\mathrm{J}_2\cdot\mathrm{Cl}^{-}$ — ? 245 (5.04) |
$\mathrm{J}_2$ 500 (2.47) 700 (1.76) |
| $\mathrm{J}_2\cdot\mathrm{J}^{-}$ 290 (4.26) 358 (3.45) |
the absorption maxima of the hydrated complex ions $\mathrm{Hal}_2\cdot\mathrm{Hal}^{-}$ with the absorption maxima of gaseous molecules $\mathrm{Hal}_2$. It should be noted that upon dissolution in indifferent liquids (benzene, hexane) the absorption maximum of halide molecules retains approximately the same position as it had for the gaseous state. For dipolar solvents the maximum is shifted—
* See reference 11.
** Such ions are always obtained in aqueous solutions of medium and strong electrolytes in the presence of an excess of halide ions, especially in the presence of dissolved oxygen.
shifts by 50–60 mμ toward the ultraviolet, relative to its position in hexane.
In Fig. 9 are given the positions (on an energy scale) of the absorption maxima of complex halide ions, gaseous halide molecules, and hydrated halide ions (see Sec. 9).
The distance between the absorption maxima of the gaseous iodine molecule, equal on the energy scale to 0.8 eV, is well reproduced in complex ions containing iodine.
An entirely analogous shift of the spectrum of the gaseous molecules \(J_2\) and \(Br_2\) into the ultraviolet region is observed upon adsorption of these molecules on crystalline \(CaF_2\), and there are a number of grounds for supposing that the adsorption occurs on \(F^-\) ions. In the absorption spectrum of the adsorbed molecules \(J_2\) and \(Br_2\), consisting of two maxima, there appears the energy interval characteristic precisely of \(J_2\) and \(Br_2\).\(^{35}\) Thus in this case there is no reason to doubt that the absorption of light occurs in a deformed molecule and not in a halide ion.*
Fig. 10. Position of the absorption maxima of complex halide ions \(Hal_3^-\)
The absorption maxima of the halide complex ions considered above may also be subjected to an analogous interpretation.
* It would have been possible to ascribe the maxima of the complex ions \(Hal_2 \cdot Hal^-\) not to the molecule \(Hal_2\), but to the ion \(Hal^-\) entering into the composition of the complex. In this case the observed maxima must be compared with the absorption maxima of the hydrated anions \(Hal^-\), from which they may be obtained by a shift to the red (Fig. 10). Such an interpretation of the spectrum of \(J_3^-\) is given by Bonhoeffer and Harteck, who consider that under the action of light the process occurs:
\[
J_3^- \to J_2 + J\,(J')
\]
and that the absorption takes place in the \(J^-\) ion. The decisive argument in favor of this interpretation would be the presence of two maxima separated by the magnitude of the iodine interval (0.94 eV) in the case of the complexes \(Cl_2 \cdot J^-\) and \(Br_2 \cdot J^-\).
heavy metals: \(MHal_2^{-}\), \(MHal_3^{--}\), and \(MHal_4^{---}\). They may also be treated as the absorption spectrum of the homeopolar molecule \(MHal\) or \(MHal_2\) (known for the gaseous state of this molecule), shifted toward the ultraviolet as a result of the attachment of halide ions*. In Fig. 11
TABLE 11
Maxima of the absorption spectrum of halide compounds in the gaseous state
| Compound | Cl \(\lambda\) (m\(\mu\)) | Cl \(\nu\) (eV) | Br \(\lambda\) (m\(\mu\)) | Br \(\nu\) (eV) | J \(\lambda\) (m\(\mu\)) | J \(\nu\) (eV) | Notes |
|---|---|---|---|---|---|---|---|
| \(AgHal\) | 317 | 3.90 | 319 | 3.88 | 321 | 3.84 | Electronic transition of the discrete absorption spectrum (0,0 band) |
| \(ZnHal_2\) | — | — | — | — | 221 196 |
5.61 6.30 |
For chlorides and bromides there is continuous absorption in the short-wave ultraviolet |
| \(CdHal_2\) | — | — | (227) 197.5 |
(5.7) 6.26 |
262 223 207.5 |
4.71 5.54 5.95 |
For chlorides there is continuous absorption in the short-wave ultraviolet |
| \(HgHal_2\) | 181 | 6.82 | 224 195 |
5.52 6.33 |
268 224 162 |
4.60 5.51 6.40 |
|
| \(TlHal\) | 322 | 3.84 | 343 | 3.60 | 381 | 3.24 | Electronic transition of the discrete absorption spectrum (0,0 band) |
| \(PbHal_2\) | 364 325 267 |
3.39 3.80 4.62 |
(414) 308 (247) |
(2.98) 4.01 (5.0) |
(518.5) 400.5 288 238 |
(2.38) 3.08 4.29 5.19 |
* In agreement with such an interpretation, among other things, is the fact that the vibration frequency in the complex \(HgH_4^{--}\) differs little from the vibration frequency of the molecule \(HgH_2\) in solution (both frequencies are determined from the Raman spectrum), namely: the former is about 0.8 of the latter (Table 8).
such an attempt at comparison has been made. The data for gaseous molecules are given in Table 11.
For the halide compounds of Zn, Cd, and Hg, Fig. 11 also gives the positions of the maxima of the corresponding salts in alcoholic solution (Table 9).
As can be seen from Fig. 11, the maxima of the complex polyhalide ions of Ag, Tl, and Pb are shifted toward higher energies in comparison with the electronic transitions of gaseous halide molecules; moreover, not only is the sequence of the positions of the chloride–bromide–iodide maxima preserved, but also the relative magnitude of the intervals I—Br, Br—Cl; the absolute magnitude of these intervals is greater for the complex ions. Thus the complex polyhalide ions Ag, Tl, and Pb could be regarded as homeopolar molecules AgHal, TlHal, and PbHal\(_2\), perturbed by the electrostatic action of the excess negative halide ions. In this case the structure of the complexes will be represented as: AgHal·Hal\(^{-}\), TlHal·Hal\(^{-}\), PbHal\(_2\)·Hal\(^{-}\).
Fig. 11a. Comparison of the absorption maxima of gaseous and dissolved molecules with the absorption maxima of complex halide ions of the same metals
For the complex ions of the metals Zn, Cd, and Hg, the maxima are shifted toward lower energies with respect to the maxima of the molecules MHal\(_2\), and therefore the interpretation of the spectrum given above for the complexes of Ag, Tl, and Pb is not applicable in this case. Evidently, in the complexes of the metals Zn, Cd, Hg the bond between the components is of only one type.
Spectrum displacement, i.e. distortion of energy levels, is too extensive a subject to be exhausted in this review, which is devoted to another question.
For the absorption spectra of complex ions of Cr, Fe, Ni, Pd, Pt, etc., containing not only halide anions but also radicals (CN) and even whole molecules (NH\(_3\), NO\(_2\)), there is at present an extensive literature, a review of which could constitute the contents of an entire article. We refer those interested to works devoted to this question\(^{36}\).
On the basis of what has been set forth in the preceding sections, we arrive at the conclusion that the elementary process occurring in hydrated cations and in polyhalide complex ions under the action of light in the region of the absorption spectrum under consideration consists in the transition of the common electronic system of these ions from the normal state to some excited energy level, which may be written as follows:
Fig. 11b. See Fig. 11a.
\[ h\nu + M_{\mathrm{aq}}^{+} \longrightarrow (M_{\mathrm{aq}}^{+})^{*} \]
\[ h\nu + M^{+}\mathrm{Hal}_{n}^{-} \longrightarrow (M^{+}\mathrm{Hal}_{n}^{-})^{*} \tag{1} \]
Absorption of hydrated anions
9. The absorption spectrum of hydrated halide anions (\(\mathrm{Hal}_{\mathrm{aq}}^{-}\)) is obtained in pure form in solutions of strong electrolytes, i.e. solutions of halide salts of alkali and alkaline-earth metals, completely dissociated into ions\(^{32,37,8}\). In the case of halide salts of heavy metals it is obtained only in very dilute solutions and, moreover, together with the spectrum of the hydrated cation, which falls approximately in the same spec-
tral region^11–15. An essential feature of the absorption spectrum of the solvated halide anion is the presence of two high absorption maxima with an interval \(\Delta \nu\), in good agreement with the difference of the terms of the normal and metastable halogen atom (Table 12 and Fig. 12)^38.
Fig. 12. Absorption spectrum of the hydrated ion \(J^{-}\).
Strictly speaking, distinctly separated maxima are observed only in the case of the iodine ion; in the case of the bromine ion only one maximum is observed, which, however, may be represented as the coalescence of two maxima separated by the magnitude of the atomic interval \(\Delta \nu \simeq 4000\ \text{cm}^{-1}\). In the case of the ion \(\mathrm{Cl}^{-}\), and still more so \(\mathrm{F}^{-}\), the difference of the atomic terms is so small that it is not possible to detect any splitting of the maximum.
Analogous double absorption maxima with a frequency interval corresponding to the difference of the terms of the halide atom are observed in crystals of alkali-metal halide salts^40. The maxima in aqueous solutions of the mixtures, however, are on average \(30\ m\mu\) to the red of the positions of the maxima in crystals.
In both cases this presence of absorption maxima with a frequency interval characteristic of the energy levels—
TABLE 12
Maxima of the absorption spectrum of hydrated halide anions
| \(\mathrm{Hal}^{-}\) | \(\lambda\) (\(m\mu\)) | \(\nu\) (eV) | \(\lg k_{\max}\) | \(\Delta \nu\) (\(\text{cm}^{-1}\)) | Difference of terms of Hal atoms (\(\text{cm}^{-1}\)) | Difference of terms of Hal atoms (kg cal) |
|---|---|---|---|---|---|---|
| \(\mathrm{Cl}^{-}\) | 181 | 6.84 | \(\sim 4.0\) | — | 885 | 2.5 |
| \(\mathrm{Br}^{-}\) | \(\sim 190\) | 6.50 | 4.03 | \(\sim 3000\) | 3680 | 10.5 |
| \(\mathrm{Br}^{-}\) | 193 | 6.34 | 4.04 | \(\sim 3000\) | 3680 | 10.5 |
| \(J^{-}\) | 194 | 6.35 | 4.1 | \(\sim 8000\) | 7600 | 21.7 |
| \(J^{-}\) | 226 | 5.46 | 4.1 | \(\sim 8000\) | 7600 | 21.7 |
gies of the halide atom, gives a key to the interpretation of the process caused by the absorption of light: evidently, under the action of light, the halide atom is set free in one way or another in its normal or metastable state. Let us note that both states are components of one and the same doublet term \(({}^2P_{1/2}\) and \({}^2P_{3/2})\), differing little in energy. Therefore there is no basis for expecting any specific difference in their behavior.
It remains to clarify in what precisely this process of liberation of a halide atom in solution consists.
The first explanation, given by Franck and Scheibe \(^{38}\), was that under the action of light photoionization occurs, i.e., the detachment of an electron from the hydrated halide ion \(\mathrm{Hal}_{\mathrm{aq}}^{-}\), with its transformation into a halide atom either in the normal state (the first absorption maximum), or in the metastable state (the second maximum):
\[ \left. \begin{aligned} \mathrm{Hal}_{\mathrm{aq}}^{-} + h\nu_1 &\longrightarrow \mathrm{Hal}_{\mathrm{aq}} + e_{\mathrm{aq}},\\ \mathrm{Hal}_{\mathrm{aq}}^{-} + h\nu_2 &\longrightarrow \mathrm{Hal}^{*}_{\mathrm{aq}} + e_{\mathrm{aq}} \end{aligned} \right\} \tag{2} \]
\((\mathrm{Hal}^{*}_{\mathrm{aq}}\)—a hydrated metastable halide atom).
The energy required for detaching an electron from a halide ion in the gaseous state, i.e., the so-called electron affinity energy of the halide atom, is at present well known (Table 13).
TABLE 13
Energy for detachment of an electron from a gaseous halide ion \(^{41*}\)
\[ \mathrm{Hal}^{-} + E \longrightarrow \mathrm{Hal} + e \]
| \(\mathrm{Cl}^{-}\) | \(\mathrm{Br}^{-}\) | \(\mathrm{J}^{-}\) | |
|---|---|---|---|
| \(E\) (eV) | 3.75 | 3.53 | 3.22 |
| \(E\) (kg cal.) | 86 | 81 | 74 |
For the hydrated ion the strength of the bond of the electron with the halide atom, and consequently the detachment energy \(E_{\mathrm{aq}}\), will already be different. To calculate it, Franck and Scheibe \(^{38}\) made use of the following cycle, represented visually in the form of an energy diagram for the iodine ion in Fig. 13.
* Fervén and de Boer \(^{42}\) give the following values (in kg cal.), based on more accurate data:
\[ 83\ (\mathrm{Cl}^{-}),\quad 77.2\ (\mathrm{Br}^{-}),\quad 69.9\ (\mathrm{J}^{-}) \]
A. N. TERENIN
This process consists of the following stages:
1) to transfer an ion from solution into the gaseous state, i.e. for the process
\[ \mathrm{Hal}_{\mathrm{aq}}^{-} \longrightarrow \mathrm{Hal}^{-}, \]
an expenditure of hydration energy equal to \(H\) is required;
2) to detach an electron from the gaseous ion, the affinity energy \(E\) is necessary; as a result we obtain a system consisting of a free atom \(\mathrm{Hal}\) and an electron \(e\);
Fig. 13. Energy cyclic process for the photoionization of the hydrated ion \(J^{-}\).
3) now we transfer the atom and the electron separately into the solution; in this process the hydration energy of the halide atom \(S_{\mathrm{Hal}}\) and the hydration energy of the electron \(S_e\) are liberated; both these quantities are unknown and can be estimated only approximately.
As a result we obtain in the solution the separated and hydrated halide atom \(\mathrm{Hal}_0\) and electron \(e_{\mathrm{aq}}\). It would seem that the difference of the levels \((\mathrm{Hal}_0 + e_{\mathrm{aq}})\) and \((\mathrm{Hal}_{\mathrm{aq}}^{-})\) would give us the value of the quantum \(h\nu\) required to detach an electron in solution. In fact this is not so: the halide atom, lacking a charge, does not exert upon the surrounding dipolar water molecules the orienting action that the ion \(\mathrm{Hal}^{-}\) exerts. Around the latter there is formed a quite definite configuration of water dipoles, absent in the case of the atom, which is also indicated by the subscript 0 in \(\mathrm{Hal}\).
Meanwhile, when a light quantum acts on the hydrated ion \(\mathrm{Hal}^{-}_{\mathrm{aq}}\), the process of light absorption takes place so rapidly that the state \((\mathrm{Hal}_{\mathrm{aq}}+e_{\mathrm{aq}})\) is reached before the water dipoles have time to become disoriented. Consequently, at the first moment after absorption of light the halogen atom \(\mathrm{Hal}'_{\mathrm{aq}}\) is surrounded by oriented water molecules, which only subsequently, as a result of thermal motion, gradually lose their orientation. The index aq on \(\mathrm{Hal}\) denotes such a state of the hydration shell, different from its normal disordered state, denoted by the sign 0. However, in order to produce around the atom the same orientation of the water dipoles as they have around the ion, it is necessary to expend an additional potential energy \(P\), caused by the fact that dipoles turned with like charges to one side will, naturally, repel one another. Only after expending this energy \(P\) do we obtain from the level \((\mathrm{Hal}^{0}+e_{\mathrm{aq}})\) the level \((\mathrm{Hal}_{\mathrm{aq}}+e_{\mathrm{aq}})\), which is the final level in the act of light absorption. The arrow \(h\nu\), closing the entire energy cycle, represents the magnitude of the quantum required to detach the electron from the hydrated halide ion and observed experimentally in the form of the first absorption maximum. The magnitude of the energy \(P\), as well as the hydration energies \(S_A\) and \(S_e\), can be obtained only approximately.
Proceeding from very simplified assumptions, which proved to be incorrect, Franck and Scheibe\(^{38}\) estimated \(S_e\) at \(18.5\ \mathrm{kg\ cal}\) and \(P\) at \(7.5\ \mathrm{kg\ cal}\), and obtained good agreement between the calculated value of \(h\nu\) and the position of the absorption maximum observed in solution. However, Pauling\(^{39}\) showed that \(S_e\) has a considerably larger value, namely \(88\ \mathrm{kg\ cal}\), whereas \(P\) is close in magnitude to the entire hydration energy \(H\) and is approximately \(50\ \mathrm{kg\ cal}\). As a result, a sharp discrepancy is obtained between the calculated and observed quanta \(h\nu\), which is shown in Fig. 13, relating to the iodine ion.
The failure of such a calculation shows that the absorption maxima of hydrated anions cannot be explained by the simple process of photoionization (2). On this basis, Franck and Haber\(^{43}\) put forward another interpretation, consisting in the fact that absorption of a light quantum does not cause removal of the electron beyond the limits of the hydrated anion, but only its transfer to one of the water molecules bound to the anion, which thereby dissociates into a hydrogen atom and a hydroxyl ion:
\[ \mathrm{Hal}^{-}\cdot\mathrm{H{-}OH}+h\nu \longrightarrow \mathrm{Hal}+\mathrm{H}+\mathrm{OH}^{-}. \tag{3} \]
In other words, the electron passes to the positive part of one of the water molecules facing the anion and, as it were, neutralizes its charge; as a result all the bonds break, and a hydroxyl ion appears in the solution.
The energy of the quantum \(h\nu\) causing this process can in principle be obtained from the dissociation energy \(D\) of the \(\mathrm{H_2O}\) molecule
on H—OH and the difference in the electron affinities of the halide atom and the hydroxyl according to the equation
\[ h\nu = D + (E_{\mathrm{Hal}} - E_{\mathrm{OH}}) + X, \]
where \(X\) is the reserve of potential energy possessed by the system \((\mathrm{Hal}, \mathrm{H}, \mathrm{OH}^{-})\) at the first moment of absorption (analogously to what was said above with respect to \(P\)). It is possible, however, to calculate \(h\nu\) from this equation only for a gaseous system, for which the data entering into it are known or can be estimated with a greater or lesser degree of approximation.
For the case of a solution, all the quantities indicated in this equation must refer to the hydrated state, which strongly changes all the energy relations of the gaseous system. Since such data for solutions are unknown, any calculations for comparison with experiment are as yet impossible.
The interpretation of the absorption expressed by equation (3) is very plausible in connection with the discovery, in direct experiments, of analogous processes in the gaseous phase[^44]. Namely, when electrons were passed through various dipolar gases \((\mathrm{H_2O}, \mathrm{HCl})\), the appearance of negative ions was observed, which could be explained only by the decomposition of the molecule as a result of electron attachment, according to the schemes
\[ \mathrm{e} + \mathrm{HCl} \longrightarrow \mathrm{H} + \mathrm{Cl}^{-}, \]
\[ \mathrm{e} + \mathrm{H_2O} \longrightarrow \mathrm{H} + \mathrm{OH}^{-}. \]
Since these processes are endothermic, for them to occur the electrons must possess additional kinetic energy.
We turn to the absorption spectra of other negative ions. The anion \(\mathrm{OH}^{-}\), according to refractometric data, exhibits approximately the same polarizability as the ion \(\mathrm{Cl}^{-}\), and gives approximately the same hydration energy as the latter (about \(50\ \text{kcal/mol}\)). Both anions are more strongly polarized than water molecules. The similarity of the \(\mathrm{OH}^{-}\) and \(\mathrm{Cl}^{-}\) ions is also manifested in the absorption spectrum: the hydrated \(\mathrm{OH}^{-}\) ion, present in aqueous solutions of strongly dissociated alkalis \((\mathrm{NaOH}, \mathrm{Ca(OH)_2}, \mathrm{Ba(OH)_2})\), gives an absorption maximum at \(186\ m\mu\) \((\lg k_{\max} \sim 3.6)\), situated close to the absorption maximum of the hydrated \(\mathrm{Cl}^{-}\) ion, lying at \(181\ m\mu\)[^45].
The analogous ion \(\mathrm{SH}^{-}\) has an absorption band with a maximum at \(227\ m\mu\) \((\lg k_{\max} = 3.65)\)[^46]. The hydrated anion \(\mathrm{S}^{--}\) likewise gives a maximum. The nature of the elementary process caused by absorption of light in the case of these anions has not yet been clarified.
Sulfate ions \(\mathrm{SO_4}^{--}\), bisulfate[^46], and also bisulfite[^47] absorb noticeably only in the short-wave ultraviolet region and do not reveal any selective maxima that could aid in interpreting the process.
The sulfite ion \(\mathrm{SO_3^{--}}\) gives continuous absorption, beginning at about \(265.5\,m\mu\) and increasing continuously toward shorter waves, without showing maxima. Franck and Haber\(^{48}\) attribute this spectrum to a photodissociation process analogous to (3), namely:
\[ \mathrm{SO_3^{--}\cdot H_2O + h\nu \longrightarrow SO_3^- + H + OH^- .} \]
The anions \(\mathrm{NO_3^-}\), \(\mathrm{NO_2^-}\), \(\mathrm{CrO_4^{--}}\), \(\mathrm{MnO_4^{--}}\) are stable complexes that do not substantially change their absorption spectrum in passing from the crystalline state into solution. The absorption spectrum of the hydrated ion \(\mathrm{NO_3^-}\), to which a particularly large number of investigations\(^{48}\) has been devoted, consists of two maxima: a weaker one at \(302\,m\mu\) \((\lg k_{\max}=0.8—0.9)\) and a considerably more intense one at \(193.6\,m\mu\) \((\lg k_{\max}=4.08)\).
The frequency difference of these maxima is \(2.3\ \mathrm{eV}\), which is close to the difference between the terms of the normal \(({}^3P)\) and metastable \(({}^1D)\) terms of the oxygen atom, equal to \(1.96\ \mathrm{eV}\). In addition, it is known that alkali-metal nitrates in solution decompose into nitrite and oxygen. Hence the observed absorption maxima of the \(\mathrm{NO_3^-}\) ion may with high probability be assigned to the primary photochemical processes\(^{49}\)
\[ \mathrm{NO_3^- + h\nu \longrightarrow NO_2^- + O({}^3P),} \]
\[ \mathrm{NO_3^- + h\nu_2 \longrightarrow NO_2^- + O({}^1D).} \]
Crystals of nitrates exhibit analogous absorption, where the evolution of oxygen and the formation of nitrite have likewise been established\(^{49}\). In this case the dissociating action of light depends on the orientation of the light vector, being maximal when the latter is located in the plane of the triangle occupied by the \(\mathrm{O}\) atoms.*
Analogous detachment of \(\mathrm{O}\) atoms apparently also occurs for the other oxygen-containing anions in the ultraviolet part of their absorption spectrum. The characteristic spectra of the ions \(\mathrm{CrO_4^{--}}\), \(\mathrm{MnO_4^{--}}\), \(\mathrm{UO_2^{--}}\)\(^{50,51,52}\), located in the visible region and having a band structure, undoubtedly belong to “shielded” electronic transitions occurring in the electron shell surrounding the central metal cation.
* In some contradiction to this interpretation is the fact that at low temperatures the continuous band of the \(\mathrm{NO_3^-}\) ion with a maximum at \(302\,m\mu\) shows a structure (vibrational?),\(^{50}\) indicating excitation of an electronic transition in the \(\mathrm{NO_3^-}\) ion rather than its decomposition under the action of light. It is possible, however, that lowering the temperature exerts a stabilizing influence on the electronic state, which only at a higher temperature can pass into an unstable state (analogous to the process of induced predissociation in gases). Moreover, the appearance of structure in the maximum of continuous absorption could have been caused by peculiarities of the photodissociation process occurring in the crystal lattice.
The greater sharpness of the bands, in comparison with hydrated cations of the same metals, leads to the conclusion that the lone electrons of the oxygen atoms form, with the outer electrons of the central cation, a symmetrical shell, sufficiently well shielded from external influences by the electron systems of the four oxygen atoms.
Under these conditions one may also expect reverse emission of the absorbed light in the form of fluorescence. Indeed, the uranyl anion, whose absorption spectrum even in solution is characterized by sharp bands, gives a similarly constructed fluorescence spectrum[^52].
Fluorescence is also observed for complex anions containing, as the central ion, cations of rare-earth atoms (see Section 11).
Shift of the absorption maxima
10. An increase in the concentration of solutions of strong electrolytes, i.e., halide salts of alkali and alkaline-earth metals, does not cause significant changes in the absorption spectrum analogous to those that occur for halide salts of heavy metals.
An increase in the concentration of \(J^{-}\) ions, produced by raising the concentration of the dissolved salt to \(10\ \mathrm{mol/l}\), causes no shift of the absorption maxima belonging to this ion. The only phenomenon observed in this case consists in a slight broadening of the maximum with increasing concentration, more precisely—a shift of the lower part of the absorption-coefficient curve toward the red side. An analogous, but smaller, broadening with preservation of the position of the maximum is observed for the ion \(\mathrm{Br}^{-}\)[^9]. However, the addition of an excess of \(\mathrm{Cl}^{-}\) ions, achieved by dissolving iodide or bromide in a concentrated solution of \(\mathrm{MgCl}_{2}\) or \(\mathrm{CaCl}_{2}\), causes a small but nevertheless distinct parallel shift of these maxima, with preservation of their contour, toward the ultraviolet side[^10]. The magnitude of the shift is proportional to the concentration of \(\mathrm{Cl}^{-}\) ions and, when the latter is \(10\ \mathrm{mol/l}\), reaches, for the iodine ion, \(6\ m\mu\); for the bromine ion the magnitude of the shift is still smaller. An analogous concentration shift of the maximum toward the ultraviolet side is also observed for \(\mathrm{Cl}^{-}\) ions upon a simple increase in the concentration of a solution of chloride alone. Addition to \(J^{-}\), instead of \(\mathrm{Cl}^{-}\), of an excess of other anions, such as, for example, \(\mathrm{F}^{-}\), \(\mathrm{SO}_{4}^{--}\), causes an even greater shift of the iodine maximum, the magnitude of the shift \(\delta\lambda\) being arranged in the following sequence:
\[ \delta\lambda = 1(\mathrm{Cl}^{-}) : 1{,}9(\mathrm{F}^{-}) : 2(\mathrm{SO}_{4}^{--})^{10}. \]
It is remarkable that the nature of the cation, also present in the solution in excess, has no specific influence either on
the magnitude of the broadening, nor the magnitude of the shift of the absorption-spectrum maxima of the halide anions.
Only for chlorine ions and for cations with a double charge, i.e., the chlorides of alkaline-earth metals, is there observed a certain dependence of the displacement of the maximum on the nature of the cation, consisting in the fact that the magnitude of the ultraviolet shift \(\delta \lambda\) in the sequence: \(\mathrm{Ba}^{++} \to \mathrm{Sr}^{++} \to \mathrm{Ca}^{++} \to \mathrm{Mg}^{++}\) becomes progressively smaller. Since the deforming action of the barium ion, owing to its large size, should be minimal, such a result can be explained only by the fact that, in contrast to \(\mathrm{Cl}^{-}\) ions, the cations \(\mathrm{M}^{++}\) cause a shift of the absorption maximum toward the red, increasing in the indicated sequence of cations and compensating the ultraviolet shift produced by the chlorine anions. Probably, cations with a single charge exert a similar, but smaller, action, which escapes observation \(^{10}\)*.
The retention by the absorption maxima of hydrated anions \(\mathrm{J}^{-}\) or \(\mathrm{Br}^{-}\) of their position with increasing concentration of these ions, and their independence of the nature of the cation, indicate that the ions \(\mathrm{J}^{-}\) and \(\mathrm{Br}^{-}\) are completely covered by a shell of water molecules, which is so firmly bound to the anion that the external perturbing action of other ions may be neglected. The asymmetric position of the dipole in the water molecule, namely the proximity of the positively charged hydrogen nuclei to the periphery of the molecule, explains the circumstance that anions are more firmly bound to the surrounding water molecules than are cations having the same sizes, as follows also from their hydration energies.
The displacement of the iodine and bromine maxima under the action of other anions, which bind the water molecule more strongly, is evidently caused by some phenomenon of competition among anions that changes the number of water molecules and the strength of their bond with the ions \(\mathrm{J}^{-}\) and \(\mathrm{Br}^{-}\).
The insignificance of the observed effects of broadening and displacement of the absorption bands leads, first of all, to the conclusion that, in contrast to the solutions of salts of heavy metals considered above, the association of ions of opposite signs here does not consist in the formation of complexes, but leads only to their accumulation, or to the formation of “swarms” (Schwärme) of ions, which retain unchanged both the structure of their closed electron shells and the configuration of the water molecules surrounding them \(^{10,12}\). The comparatively weak interaction of the hydrated ions is manifested precisely in the insignificance of the spectral effects of displacement and broadening caused by an increase in the concentration of ions in solution**.
* Lederle \(^{33}\) supposes that, when the concentration of \(\mathrm{CaCl}_{2}\) is increased, it is precisely the \(\mathrm{Ca}^{++}\) cations that act, producing an ultraviolet shift of the \(\mathrm{J}^{-}\) band.
** It might be objected that, nevertheless, association of the ions does occur, but that the absorption bands characteristic of complexes should lie in a shorter-wavelength region of the spectrum than that which is accessible
The indicated shifts of the absorption bands are wholly inconsistent with those changes of refraction with concentration which are observed in strong electrolytes. Specifically, refraction decreases with increasing concentration by 1–2‰, and the magnitude of this decrease is greatest for iodine and depends strongly on the cations, being greatest in the case of lithium. Meanwhile, the small shifts of the absorption maxima toward the ultraviolet, mentioned above, should cause a decrease in refraction ten times smaller. Thus, for example, a shift of the maximum of the ion \(J^{-}\) by \(0.4\,m\mu\) toward the ultraviolet, with its height preserved, could have caused a decrease in refraction in the visible region not exceeding 0.75‰; in fact, the observed change in refraction in this region under the same conditions is 12.5‰. With a parallel shift of the absorption maximum of the ion \(Cl^{-}\) by \(4.5\,m\mu\), which occurs for a \(10\,N\) solution of LiCl, the refraction should have decreased only by 5.2‰ instead of the actually observed 17.7‰.
Such a discrepancy between the shift of the absorption band and the change in refraction may be explained, in Fromherz’s opinion,\(^{9}\) by the fact that the height of the absorption maximum, i.e. the value \(k_{\max}\), is determined with an accuracy only up to 15%. With such insignificant accuracy, unaccounted changes in the value of \(k_{\max}\), occurring with increasing concentration, are possible, and consequently changes in the probability of absorption, which also determines the magnitude of the dispersion and refraction. Finally, another possible explanation of the discrepancy between the refractometric and absorption data lies in the assumption that, under the action of dissolved ions, with an increase in their concentration, the refraction of the water itself changes owing to deformation of its molecules or a change in its structure.\(^{11}\)
It is known, for example, that when the degree of polymerization of water molecules changes, the infrared bands and absorption spectra shift toward shorter wavelengths. A similar conclusion about a change in the structure of water under the action of dissolved ions can also be drawn on the basis of the Raman spectrum.\(^{53}\) However, Fajans does not consider it possible to reduce all observed—
observations to this. Against such a consideration Fromherz\(^{10}\) adduces the argument that the first absorption bands of gas-like molecules of MHal (halide salts of alkali metals) lie in the region of the far ultraviolet, namely: iodides 324 and \(270\,m\mu\), bromides 275 and \(254\,m\mu\), chlorides \(245\,m\mu\), and the nature of the cation has no specific influence on the position of these bands.
Upon hydration of a salt molecule, not accompanied by its electrolytic dissociation, the absorption spectrum should occupy an intermediate position between the spectrum of the gas-like molecule and the spectrum of the hydrated anion; for example, in the case of the hydrated molecule NaJ, a double absorption maximum should have been observed, located between the maxima at 324 and \(270\,m\mu\) of the gas-like NaJ molecule and the maxima at 226 and \(194\,m\mu\) of the hydrated iodine ion. Such a maximum, however, is not observed.
given refractometric effects only to changes in the refraction of water*.
The position of the absorption bands of the ion \(J^-\) in alcoholic solutions likewise is completely independent of the nature of the cation \(^{32,33}\).
The interpretation of the absorption spectrum of the hydrated halide ion, given in the preceding section, leads one to expect a shift of this spectrum on passing to other solvents, since the values of the energy quantities entering into the equation that determines the magnitude of the absorbed light quantum will be different than for water. The position of the first absorption maximum of the ion \(J^-\) upon changing the solvent is given in Table 14 \(^{33}\).
TABLE 14
Position of the maximum of the absorption band of the ion \(J^-\) in various solvents
| Solvent | \(\mathrm{CH_3CN}\) | \(\mathrm{H_2O}\) | \(\mathrm{CH_3OH}\) | \(\mathrm{C_2H_5OH}\) | \(\mathrm{C_3H_7OH}\) |
|---|---|---|---|---|---|
| Dipole moment of the solvent \((\times 10^{18})\) | 3.1 | 1.8 | 1.7 | 1.7 | 1.7 |
| \(\lambda_{\max}\) \((m\mu)\) | 244.1 | 226.2 | 219.1 | 217.0 | 215.5 |
With increasing dipole moment of the solvent, a shift of the absorption band of the iodide ion toward the red is observed. Evidently, in a nonpolar solvent, for example hexane, the absorption maximum of the iodide ion would occupy some limiting position in the region of wavelengths shorter than \(216\,m\mu\). Since the alcohols possess almost the same magnitude of the dipole moment, the decrease in the magnitude of the red shift on passing to the more complex alcohols may be attributed to an increase in the size of the molecule, which causes removal of the dipole group of the hydroxyl to a greater distance from the halide anion. The dependence on the dielectric constant of the solvent is less distinct: acetonitrile, by the magnitude of its dielectric constant, should be placed between methanol and ethanol.
The less readily observable absorption maximum of the ion \(\mathrm{Br^-}\) shifts analogously to the iodide maximum.
With an increase in the temperature of an aqueous solution from 17 to \(75^\circ\), the absorption is distinctly shifted toward the red, and the first absorption maximum of the iodide ion is lowered. An analogous and equal-in-energy shift is undergone also by the long-wavelength edges of the absorption bands of the ions \(\mathrm{Br^-}\) and \(\mathrm{Cl^-}\) \(^{33}\).
* A comparison of refractometric and absorption data for gaseous salts has been made in the series of works of Fajans’s laboratory, which constitute an entire notebook (Z. physik. Chem. B. 24).
In contrast to the spectra of solvated halide ions, the absorption bands of dissolved homopolar molecules, when the polarity of the solvent is increased, undergo a shift into the ultraviolet region from their normal position in hexane. Such is the behavior, for example, of the absorption bands of the alkyl halides \(C_2H_5Br\) and \(C_2H_5J\), associated with the process of photodissociation, in which a halogen atom is split off,\(^{1,33,56}\) (Table 15).
TABLE 15
Position of the maximum of the absorption band of \(C_2H_5J\) in various solvents
| Solvent | \(C_6H_{14}\) | \(CCl_4\) | \(C_2H_5OH\) | \(H_2O\) |
|---|---|---|---|---|
| Dipole moment | 0 | 0 | 1.7 | 1.8 |
| \(\lambda_{\max}\) \((m\mu)\) | 259 | 256.5 | 256 | 251 |
The molecules \(ZnJ_2\), \(CdJ_2\), \(HgJ_2\) behave similarly; their absorption maxima, likewise ascribed to photodissociation with the splitting off of a \(J\) atom, shift toward shorter wavelengths on passing from an alcoholic to an aqueous solution.
The dependence on the magnitude of the dipole moment here, however, is not as distinct, as is seen from Table 16 for \(CdJ_2\).
TABLE 16
Position of the maximum of the absorption band of the molecule \(CdJ_2\) in various solvents
| Solvent | \(CH_3OH\) | \(CH_3CN\) | \(C_2H_5OH\) | \(C_3H_7OH\) |
|---|---|---|---|---|
| Dipole moment | 1.7 | 3.1 | 1.7 | 1.7 |
| \(\lambda_{\max}\) \((m\mu)\) | 238.8 | 240.5 | 241.8 | 242.1 |
The characteristic absorption maximum of the \(NO_3^-\) anion, located in aqueous solutions at \(302\ m\mu\), is shifted from this position for solvents with a smaller magnitude of the dipole moment, such as, for example, methanol and chloroform, toward longer wavelengths, analogously to the case of the homopolar molecules \(C_2H_5Br\) and \(C_2H_5J\), dis-
dissociating under the action of the absorbed light with the detachment of a halogen atom. In the case of \(NO_3^-\), as we saw in the preceding section, photodissociation likewise occurs under the action of light, with the detachment of an O atom.
The difference in the direction of the shift of the absorption band upon changing the polarity of the solvent, observed for halide ions, on the one hand, and for the above-enumerated cases of photodissociation, on the other, may be attributed precisely to the circumstance that in the former case, as a result of the action of light, an electron is transferred from the atom to the solvent molecule bound to it, whereas in the case of homopolar molecules and the \(NO_3^-\) ion a neutral atom is detached, experiencing no additional electrostatic interactions with the solvent molecules.
It should be noted that the position of the absorption maximum of \(NO_3^-\), in contrast to what was said at the beginning of this section concerning \(Hal^-\) ions, depends quite distinctly on the nature of the cation*, and Galbán and Eisenbrand\({}^{48}\) established that the cations \(Li^+\), \(Na^+\), \(NH_4^+\), \(K^+\) shift the maximum toward the ultraviolet side, while the cations \(Rb^+\), \(Cs^+\), (tetraalkylammonium)\(^+\) shift it toward the red. The formal explanation given by Galbán\({}^{48}\) is based on the well-known considerations of Fajans concerning the deformability of ions; namely, it is assumed that the cations shifting the absorption band of \(NO_3^-\) possess greater deformability than the \(NO_3^-\) ion. In reality, of course, the position of the band in aqueous solution should by no means be regarded as normal. The absorption band of the \(NO_3^-\) ion, if it could be obtained by dissolving nitrates in hexane, would have to lie at considerably longer wavelengths than those observed in aqueous solution; with the increase of the deforming action of the cations in the sequence: (tetraalkylammonium)\(^+\) \(\to\) \(Cs^+\) \(\to\) \(Rb^+\) \(\to\) \(K^+\) \(\to\) \(NH_4^+\) \(\to\) \(Na^+\) \(\to\) \(Li^+\), the maximum of the \(NO_3^-\) ion is correctly shifted toward the ultraviolet side, water, in its electrostatic action on this ion, falling between \(Rb^+\) and \(K^+\)\({}^{33}\).
In dilute aqueous solution of \(HNO_3\) the same band at \(302\,m\mu\) is observed, characteristic of the \(NO_3^-\) ion; however, with increasing concentration this band gradually disappears, passing into a broader band with a suggestion of a maximum between 275 and \(270\,m\mu\). The latter maximum is also observed for nitric acid dissolved in a nondissociating solvent—hexane, and also for esters of this acid, for example ethyl nitrate. On this basis Samuel\({}^{28}\) considers that the group \(-O-NO_2\) possesses two different absorption spectra depending on whether it is
* A cation-dependent shift is also experienced by the absorption band of the \(NO_3^-\) ion in the crystal lattice\({}^{50}\).
A. N. TERENIN
the bond between the oxygen atom and the substituting group (H, metal atom, alkyl radical) is ionic or homeopolar. The maximum at 275 mμ must be assigned to homeopolar [[unclear: continuation cut off]]
A. N. TERENIN
then by emission of part of the absorbed energy. With the exception of the ion \(\mathrm{UO_2^{--}}\), for which an anomalously long duration of the excited state was obtained, the duration of the excited state proves to be a quantity of the same order as in the case of gaseous atoms and molecules, i.e. equal to \(10^{-7}—10^{-8}\) sec. The quantum yield of fluorescence in most cases is less than unity, which indicates an interaction of the anion with the molecules of the solvent, leading to the dissipation of the absorbed quantum in the form of thermal energy without radiation.
In the case of the anion \(\mathrm{Pt(CN)_4^{--}}\), which has two absorption maxima, fluorescence is excited only in the long-wave, comparatively weak maximum lying at 280 mμ; absorption of light in the considerably higher second maximum at 255 mμ, characteristic of the anion under consideration, does not excite fluorescence. Apparently, this latter maximum is connected with a process of photoionization or photodissociation of the ion \(\mathrm{Pt(CN)_4^{--}}\). The fluorescence spectrum lies in the visible region and consists of a broad band with two distinct maxima at 555 and 525 mμ.
The absorption spectra of the cations of the rare earths have, as was mentioned above, a discrete character and extend from the visible into the far ultraviolet region, where, beginning at 200 mμ, a continuous absorption band appears[^63]. In the case of \(\mathrm{Ce^{+++}}\), the structure of the absorption spectrum, situated in the region \(\lambda < 250\) mμ, made it possible to identify it with the transition of the single electron \(4f\), shielded by the outer shell \(5s^2 5p^6\), to the level \(5d\), corresponding to the periphery of the ion[^64]. The latter circumstance is consistent with the diffuseness of the absorption maxima, which exhibit a noticeable dependence on the nature of the foreign molecules and ions surrounding the cerium cation.
By analogy one may suppose that for the remaining trivalent ions of the rare earths as well, the discrete and continuous absorption situated in the region of the short-wave ultraviolet (\(\lambda < 250\) mμ) is caused by the transition of one electron from the \(4f\) shell to the \(5d\) level. The discrete absorption, consisting of very narrow bands and occupying the visible and near-ultraviolet region, is assigned to electronic transitions taking place within the same \(4f\) shell and connected, for example, with a change in the spin direction of one of the electrons[^64]. As was mentioned in Section 5, such an explanation had already been advanced for \(\mathrm{Cr^{+++}}\) ions[^26], where the corresponding electrons (\(3d\)) are located at the periphery of the ion, whereas in the case of the rare earths they are screened by the outer shell \(5s^2 5p^6\). This latter circumstance explains the considerable sharpness of the absorption bands in the visible and nearest ultraviolet region, which is preserved even in solutions.
ABSORPTION SPECTRA OF ELECTROLYTE SOLUTIONS
...that is, either in the region of the visible and nearest ultraviolet absorption bands of these ions, or in the region of the more distant ultraviolet, \(\lambda < 250\,m\mu\).*
In accordance with the interpretation of the various absorption regions given above, one may suppose that in the first case an electronic transition is excited only within the \(4f\) shell. This explanation is confirmed by the immediate proximity of the region of excitation and the region of emission, which in the case of such complex systems as hydrated—and possibly also complex—ions need not necessarily coincide, but, as is observed for organic molecules, exhibit a Stokes shift.
On the other hand, excitation of the same visible spectrum in the far ultraviolet is caused primarily, apparently, by the transition of one \(4f\) electron to the \(5d\) state, and only upon its return to the \(4f\) shell does the same electronic transition occur that could be excited directly in the first case. The ions \(\mathrm{Ce}^{+++}\), \(\mathrm{Pr}^{+++}\), \(\mathrm{Nd}^{+++}\), \(\mathrm{Er}^{+++}\), excited in the short ultraviolet, also fluoresce in aqueous solutions; however, the emission in this case consists of broad continuous bands extending from the visible region (approximately from \(410\,m\mu\)) into the ultraviolet region\(^2\). It is possible that in this case the transition \(5d \to 4f\) also manifests itself, since the character of the spectrum agrees with the expected strong perturbation of the \(5d\) level due to the peripheral position of the electron in this state.
It is highly noteworthy, however, that the details of the structure of the fluorescence bands of the \(\mathrm{Tb}^{+++}\) ion in solutions depend on the nature of the anion, and also that fluorescence of the \(\mathrm{Eu}^{+++}\) ion is observed exclusively in the presence of at least a small amount of \(\mathrm{SO}_4^{--}\) ions. These facts apparently indicate that in these cases the carrier of fluorescence is not the hydrated cation, but a complex consisting of the cation and acid anions. To what extent this point of view can be extended to all cases of fluorescence of rare-earth ions is still unclear, but it is very probable that, for the possibility of unimpeded emission of light by the ions—especially in the case of ultraviolet excitation transferring a \(4f\) electron to the periphery of the ion—an additional protective shell formed by the electrons of the anions is necessary. This circumstance could also explain the absence of quenching of the fluorescence of rare-earth ions upon addition of an excess of halide anions.
Undoubtedly, fluorescence in electrolyte solutions will make possible a more detailed penetration into the mechanism of those processes that occur with ions under the action of light.
* In view of the weaker absorption in the first region as compared with the short-wave ultraviolet, fluorescence in the former case can be observed only in a sufficiently concentrated solution.
References Cited
- A review of the literature on the absorption spectra of electrolyte solutions up to 1928; see the articles: Ley, Handb. d. Physik, Bd. XXI, 1, 14—16; 2, 1—11, 1929.
In Russian there is a review by A. I. Brodskii, “Optical methods for the study of electrolyte solutions,” Uspekhi khimii, 1, 712, 1932. See also the book: Bonhoeffer and Harteck, Fundamentals of Photochemistry, Moscow, 1935, p. 148.
-
Halban and Siedentopf, Z. physik. Chem., 100, 20, 1922. Halban and Eisenbrand, Z. wiss. Phot., 25, 138, 1928. See also Beyger, Optical Methods in Chemistry (Goskhimtekhizdat), 1934, ch. VII; and Handb. d. Exper. Physik, Bd. XIX, 9, § 1, 2, 1928.
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Forbes and Elkins, J. Am. Chem. Soc., 56, 516, 1934.
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Ley, Z. anorg. Chem., 173, 287, 1928; Cu(ClO₄)₂.
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Kato, Sci. Papers, Inst. Phys. Chem. Res. Tokio, 12, 1930; 15, 161, 1931.
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Volbert, Z. physik. Chem., A 149, 382, 1930; AgClO₄.
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Doehlemann and Fromherz, Z. physik. Chem., A 171, 353, 1934; aqueous solutions of Cd(ClO₄)₂, Zn(ClO₄)₂, Cu(ClO₄)₂, CdHal₂, ZnHal₂, and CuHal₂ mixed with MHal and MHal₂.
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