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Ferric Acetate (II) and (III) are "mordants," which intensify wood staining in direct proportion to the tannin concentration in the wood. Some wood stainers add tea to increase the tannin content and thereby make the stain darker. How does Ferric Acetate act as a mordant in this case of ebonizing (web archive) wood?

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A mordant is a substance used to set dyes on fabrics or tissue sections by forming a coordination complex with the dye which then attaches to the fabric or tissue (source).

Tannin is a biomolecule consisting of many carbohydrate and polyphenol residues with plenty of hydroxyl and carboxyl groups. Tannic acid is a common type of tannin:enter image description here

$\ce{Fe^{2+}}$ and $\ce{Fe^{3+}}$ form colored complexes with these oxygen-containing functional groups. These iron-tannin complexes change the color of the wood. The color intensity increases with tannin content of the wood and can be increased by the addition of tannin-rich tea. Structures with a varying coordination sphere of iron are formed, some of which are shown here (sources: 1 and 2):

enter image description here

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