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What does the salt $\ce{K3Fe(CN)6}$ change to when it is dissolved in water? I mean, I think its going to ionize, but in what way? Is there a way to know this? I tried to search the web but wasn't able to find the answer.

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In water it should dissociate into $\ce{K+}$ and $\ce{[Fe(CN)6]^3-}$. This is because the $\ce{Fe}$ forms an octahedral complex with $\ce{Fe}$ at the centre and six $\ce{CN-}$ ions distributed around this each at 90 degrees to one another. This ion is sufficiently stable that it will not dissociate in water. The bonding is due to $\mathrm d$ orbitals on the $\ce{Fe}$. All undergraduate inorganic text books will give details of this. The Wikipedia page on ferricyanide gives pictures of the complex's geometry.

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