Oxidation state of tungsten in W3O8

Recently I came across this equation:


$$\ce{WO\_3 +SnCl\_2 +HCl\rightarrow W\_3O\_8 + H\_2SnCl\_6 +H\_2O}$$ 


The compound $\ce{W\_3O\_8}$ that appears in the right hand side of the equation seems to be mixed oxide. Normal calculation of the oxidation state of W in the compound yields $\ce{\frac{16}{3}}$ which is a fraction. A google search on the compound does not give any good results too.


So, is $\ce{W\_3O\_8}$ a mixed oxide? What are the oxidation states of the different tungsten atoms?




**TL; DR**: If you are forced to list the formal oxidation states, then with a high level of confidence it's tungsten(V,VI) octaoxide $\ce{W^{VI}W^V2O8}$. However, the real product of this reaction would be a number of non-soichimetric tungsten(IV,V,VI) oxides. Formation of molecular oxoclusters or peroxo compounds is very unlikely.




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Reduced tungsten oxides are generally non-stoiciometric. Glemser et al. [[1](https://doi.org/10.1002/zaac.19643320511)] reduced tungsten(VI) oxide hydrates $\ce{WO3 \* H2O}$ and $\ce{WO3 \* 2 H2O}$ with $\ce{Zn}$ in $\ce{HCl}$ to the blue tungsten oxide hydrates of the general formula $\ce{WO\_{3‐x}(OH)\_x}$ $(x → 0.5)$ with the lowest reducing degree of $2.65$, which is very close to the one in $\ce{W3O8}$ $(8/3 = 2.6(6))$.


I would expect that $\ce{SnCl2}$ in acidic media would have comparable reducing effect. With the moderately mild reducing agent such as tin(II) chloride there is very little chance of ending up exclusively with $\ce{W3O8}$. Also, a presence of a reducing agent also eliminates a possibility of the formation of the peroxo-compounds, so that with a high level of confidence we are dealing with oxide $\ce{O^2-}$ ligand.


I find it equally improbable that any cluster formation takes place. For the existence of a polyoxotungstate cluster the terminal $\ce{W=O}$ bonds must be "disarmed" in order to prevent further olation/oxolation and aggregation into bulk metal oxide. This is often achieved via the template effect, however even reduced by 1 to 6 electrons forms of 12-heteropolytungstates $\ce{[(P,Si)W12O40]^3-}$, the phosphate- or silicate-templated Keggin structure — one of the most stable — only exist briefly in solution [2, pp. 341–343]. In the presented system there is no suitable anion to preserve the three-membered $\ce{W3O8}$ ring, and it's very likely going to hydrolyze quickly.


To sum these thoughts up, the more appropriate way to write the reaction would be


$$\ce{n WO3 + SnCl2 + 4 HCl → W\_nO\_{3n-1} + H2SnCl6 + H2O}$$


where $\ce{W\_nO\_{3n-1}}$ is homologous series analogous to the mixed-valence tungsten blues. On crystallographic level this can be seen as withdrawal of oxygen atoms from $\ce{WO3}$, which is isostructural to [$\ce{ReO3}$](https://en.wikipedia.org/wiki/Rhenium_trioxide) (Fig. 1a). New point defects are eliminated by introducing a crystallographic shear (CS, Fig. 1b). As the reduction proceeds, the octahedra $\ce{[WO6]}$ in this structure changing from corner-sharing to edge-sharing motif (Fig. 1c). (Caption and adapted illustration from [3, p. 1086].)



> 
> [![Crystallographic shear in WO3](https://i.stack.imgur.com/kkDZr.png)](https://i.stack.imgur.com/kkDZr.png)
> 
> 
> **Figure 1.** Crystallographic shear in $\ce{WO3}$ (**a**) the idealized structure
> of $\ce{WO3}$, drawn as corner-shared $\ce{WO6}$ octahedra, squares in projection (**b**) {102} CS planes (arrowed), consisting of blocks of four edge-shared octahedra (**c**) {103} CS planes (arrowed), consisting of blocks of six edge-shared octahedra.
> 
> 
> 


It's impossible to deduce exact oxidation number for such structure with floating stoichiometry, but sure enough an *average oxidation number* of tungsten can be found trivially from the $\ce{W\_nO\_{3n-1}}$ formula:


$$\text{O.N.}(\ce{W})\cdot n - 2(3n - 1) = 0 \qquad\to\qquad \text{O.N.}(\ce{W}) = 6 - 2/n,$$


e.g. for $\ce{W3O8}$ $\text{O.N.}(\ce{W}) = 6 - 2/3 = 5.3(3)$. Boundary case $n = 1$ dictates the lowest $\text{O.N.}(\ce{W}) = 4$, so that $\ce{W\_nO\_{3n-1}}$ phase consists of a mixed-valence oxide with various ratios of $\ce{W(VI)}:\ce{W(V)}:\ce{W(IV)}$. Exact ratio is to be determined from [XPS](https://en.wikipedia.org/wiki/X-ray_photoelectron_spectroscopy)/[XANES](https://en.wikipedia.org/wiki/X-ray_absorption_near_edge_structure) analysis for a given specimen; spectrophotometry would be difficult to implement as tungsten oxides have negligible solubility in most solvents unless some peroxide or $\ce{HF}$ is added. Exact location of the reduced tungsten centers can be averaged by finding CS areas with [EM](https://en.wikipedia.org/wiki/Electron_microscope)/[PXRD](https://en.wikipedia.org/wiki/Powder_diffraction) analysis.


Now, to the $\ce{W3O8}$. In fact, it's already been synthesized by Zakharov et al. as follows [[4](https://doi.org/10.1107/S0108768193005701)]:



> 
> The sample examined was prepared by partial reduction of $\ce{WO3}$ with carbon at high temperature in combination with high pressure. The reaction occurred between the graphite container material and a pressed tablet of $\ce{WO3}$ in a closed system ($T = \pu{1773 K}$, $P = \pu{50e5 kPa}$). [...] The product obtained was a mass containing minute dark-red crystallites. The colour suggested that considerable reduction had taken place.
> 
> 
> 


and two phases were characterized with EM/PXRD. Authors also suggest that $\ce{W3O8}$ can hardly be obtained under ambient conditions:



> 
> The two phases, both of composition $\ce{W3O8}$ $(\ce{WO\_{2.667}})$, do not appear in the binary $\ce{W-O}$ system at ambient pressure. $\ce{W3O8(I)}$ has a structure of the $\ce{U3O8}$ type (Andresen, 1958), which is denser than that of $\ce{W3O8(II)}$. The latter has a new type of structure, although some features are shared with other previously known tungsten oxides ({102} CS structures).
> 
> 
> 


[![W3O8(I)](https://i.stack.imgur.com/KxgDp.png)](https://i.stack.imgur.com/KxgDp.png)


**Figure 2.** Idealized polyhedral representation of $\ce{W3O8(I)}$


[![enter image description here](https://i.stack.imgur.com/ca5Pw.png)](https://i.stack.imgur.com/ca5Pw.png)


**Figure 3.** Idealized polyhedral representation of $\ce{W3O8(II)}$


So, there are two possible combinations for the formal $\text{O.N.}$s:


1. $1~\ce{W(VI)} + 2~\ce{W(V)}$;
2. $2~\ce{W(VI)} + 1~\ce{W(IV)}$.


Unfortunately, oxidation states are not mentioned in the article and I haven't found any citeable sources with the determination of oxidation numbers for $\ce{W3O8}$, but the XPS studies of [uranium octaoxide $\ce{U3O8}$](https://en.wikipedia.org/wiki/Triuranium_octoxide) indicated the presence of two oxidation states, $\ce{U(VI)}$ and $\ce{U(V)}$, in a $1:2$ ratio, respectively. Since phase $\ce{W3O8(I)}$ is isostructural, there is a high chance that the scenario 1, $1~\ce{W(VI)} + 2~\ce{W(V)}$, is quite plausible.


Having the CIFs of both structures at hands, I've been trying to perform bond-valence analysis, but with the [common tabulated empirical parameters](https://www.iucr.org/resources/data/datasets/bond-valence-parameters) I haven't reached any meaningful results. Mixed-valenced tungsten and molybdenum oxides often contain delocalized $\mathrm{d}$ electrons, making bond-valence analysis alone less meaningful [[5](https://doi.org/10.1016/0022-4596(85)90256-7)].


### References


1. Glemser, O.; Weidelt, J.; Freund, F. Genotypische Oxidhydrate des Wolframs. Zur Frage der Wolframblauverbindungen. *Zeitschrift für anorganische und allgemeine Chemie* **1964**, 332 (5–6), 299–313. <https://doi.org/10.1002/zaac.19643320511>.
2. Advances in Inorganic Chemistry and Radiochemistry; Emeléus, H. J., Sharpe, A. G., Eds.; Advances in inorganic chemistry and radiochemistry; *Academic Press: New York*, **1967**; Vol. 10. ISBN 978-0-08-057859-0.
3. Encyclopedia of Inorganic Chemistry, 2nd ed.; King, R. B., Ed.; *Wiley: Chichester, West Sussex, England ; Hoboken, NJ*, **2005**. ISBN 978-0-470-86078-6.
4. Sundberg, M.; Zakharov, N. D.; Zibrov, I. P.; Barabanenkov, Y. A.; Filonenko, V. P.; Werner, P. Two High-Pressure Tungsten Oxide Structures of $\ce{W3O8}$ Stoichiometry Deduced from High-Resolution Electron Microscopy Images. *Acta Crystallographica Section B Structural Science* **1993**, 49 (6), 951–958. <https://doi.org/10.1107/S0108768193005701>.
5. Domenge`s, B.; McGuire, N. K.; O’Keeffe, M. Bond Lengths and Valences in Tungsten Oxides. *Journal of Solid State Chemistry* **1985**, 56 (1), 94–100. <https://doi.org/10.1016/0022-4596(85)90256-7>.


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Note that $\ce{W3O8}$ is a **non-stoichiometric compound** and it is not that simple compound you may think. It has a very complex structure as such its oxidation state is very difficult to calculate. I am not going in details about the structure of the compound and I will only mention it a non-stoichiometric compound actually a oxygen-deficient cluster. 


Please give a good read to [Xin Huang *et.al.*, *J. Phys. Chem. A* **2006,** *110*, 85-92](http://pubs.acs.org/doi/abs/10.1021/jp055325m), the link that @JM97 has posted. It says that the $\ce{O-O}$ is much longer than normal oxide bond and so it is assumed to be a peroxo bond $\ce{O2^2-}$. Now, peroxide has oxidation state of -1. So, **assuming** $\ce{W3O8}$ to **be a simple compound** (no stoichiometric defect or any kind of defect), the oxidation state is: 


$$3x + 8(-1) = 0$$
$$x = +{8/3}$$


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