# How to understand the chemical formula of Prussian blue complex w.r.t its crystal structure?

Note: Just to be clear, I do not refer to "complex molecules" (i.e. "complex" as "complicated"), but to actual complexes.

I am trying to understand the structure of Prussian Blue based on its chemical formula (I ultimately want to explain why it is blue, but this is probably not relevant to this question). This formula is

$$\ce{Fe4[Fe(CN)6]3}$$

where the "first" iron is $$\ce{Fe(III)}$$ and the "second" is $$\ce{Fe(II)}$$ but that too is probably not relevant.

Now, having pretty much no experience with complexes, I would read this formula such that for every four $$\ce{Fe(III)}$$s, there are three $$\ce{Fe(CN)6}$$s – like this:

(Source)

So far, so good. But I am confused to how this relates to the actual 3-dimensional structure of Prussian Blue which apparently is something like this:

(Source)

I see that from each $$\ce{Fe}$$, six "bonds" extend to each other $$\ce{Fe}$$. These "bonds" are, I think, ligands and are actually $$\ce{N\equiv C}$$. This makes sense because we had $$\ce{Fe(CN)6}$$ in our original formula. However, there should be some $$\ce{Fe(III)}$$s, namely four for every three $$\ce{Fe-N\equiv C}$$. Also, a $$\ce{Fe(CN)6}$$ shouldn't be able to bond to another because this would mean that there were two $$\ce{N\equiv C}$$s between each $$\ce{Fe}$$. This, however, is not the case.

What am I missing here?

## 1 Answer

The structure of Prussian blue is not as regular as Jonas thought. It is basically cubic as Jonas has drawn. But Jonas's figure includes the same number of $$\ce{Fe^{II}}$$ as $$\ce{Fe^{III}}$$, which is impossible. There must be $$\ce{4 Fe^{III}}$$ for $$\ce{3 Fe^{II}}$$. So some $$\ce{Fe^{II}}$$ sites of the cubic structure drawn by Jonas must be empty. The real structure is described in a publication in French by G. Fornasier, Act. chimique 444-445, Oct. 20219, p.16 - 21

First the Prussian Blue includes $$15$$ water molecules. Its formula is $$\ce{Fe^{III}_4[Fe^{II}(CN}_6]_3$$·$$\ce{15 H2O}$$. It is basically Jonas's image, but with two $$\ce{Fe^{II}}$$ lacunes (black in Jonas's picture), one in the center of the horizontal upper face, and the second in the center of one of the vertical face of the cube. The CN groups that are binding each $$\ce{Fe^{II}}$$ atom to the 6 next $$\ce{Fe^{III}}$$ atoms are replaced around the lacunes by 6 water molecules.

Here is a description of the Prussian Blue, after G. Fornasier. The numbers $$2$$ and $$3$$ represent $$\ce{Fe^{II}}$$ and $$\ce{Fe^{III}}$$ respectively. The water molecule is like a V shape attached to a $$\ce{Fe^{III}}$$ ion. The two dotted loops are lacunes where $$\ce{Fe(CN)6]^{4-}}$$ have been removed in order to save the electric neutrality of the structure. Please observe that every $$\ce{Fe^{3+}}$$ ion is surrounded by $$\ce{6 N}$$ or $$\ce{O}$$ atoms from $$\ce{CN-}$$ groups, or from $$\ce{H2O}$$ molecules