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$$\ce{3Na2CO3 + 2FeBr3 + 3H2O -> 6NaBr + 2Fe(OH)3 + 3CO2}$$

Why $\ce{Fe(OH)3}$? Where do these $\ce{-OH}$ groups come from?

This is from a series of reactions in a Russian sample exam question.

P.S.

Following Ivan't hints, I've gone through the process of reaction, and I get some water in the right-hand side of the equation. I wonder why the answer has no water in the right-hand side.

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    $\begingroup$ From the reaction of the carbonate with water. $\endgroup$ – bon May 23 '16 at 8:50
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    $\begingroup$ Carbonic acid is a weak acid, $\ce{Fe(OH)3}$ is a weak base, so their salt hydrolyzes completely. $\endgroup$ – Ivan Neretin May 23 '16 at 8:52
  • $\begingroup$ @IvanNeretin - but isn't $\ce{Fe(OH)3}$ a salt? And I've just read that $\ce{Na2CO3}$ should only hydrolyze as far as $\ce{NaHCO3}$ without heating. $\endgroup$ – CowperKettle May 23 '16 at 9:01
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    $\begingroup$ You might have to review your definition of salt. As for $\ce{Na2CO3}$, it is a salt of a weak acid and a strong base, therefore it hydrolyzes only partially. $\endgroup$ – Ivan Neretin May 23 '16 at 9:03
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    $\begingroup$ A screenshot or picture of an exercise is not searchable. Please consider rewriting it, so that it can be of help for future visitors. You have been a member of this community for quite some time, but if you want to know more about mark-up, please have a look here and here. We prefer to not use MathJax in the title field, see here for details. $\endgroup$ – Martin - マーチン May 23 '16 at 9:21
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You have certainly already recognized $\ce{Na2CO3}$ as the base in your equation.

Did you also consider the following:
When $\ce{FeBr3}$ is dissolved in water, the hexaaqua complex $\ce{[Fe(H2O)6]^3+}$ is formed. This complex is fairly acidic: $$\ce{[Fe(H2O)6]^3+ + H2O<=> [Fe(H2O)5OH]^2+ + H3O+}$$

Ignoring ligand exchange processes, you might state that the $\ce{OH}$ groups come from the deprotonation of the water ligands of your initial complex.

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  • $\begingroup$ I see. $\ce{Na2CO3}$ creates a basic environment, because CO3 binds protons tightly and leaves a lot of OH(-) groups floating about. These groups deprotonate three of the H2O molecules from the $\ce{[Fe(H2O)6]^3+}$ complex, and we get $\ce{Fe(OH)3}$. Now it's much more clear, thank you! $\endgroup$ – CowperKettle May 23 '16 at 17:10
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Draw a lewis diagram of the molecules to give you visual clues. From a glance it looks like the halides that are connected to the iron take their electrons leave and then are captured in solution to the sodium molecules. (this wouldnt be such a great bond since its ionic and the sodium and bromine ions would really act more like spectators).

From thee the CO3 attacted to the Na would decompose to CO2 and the extra O would attach itself to the iron and and somewhere before or after that instant those oxygens would strip a hydrogen from the water.

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