Question
Transition metals can act as catalysts because these can change their oxidation state. How does Fe$(III)$ catalyze the reaction between iodide and persulphate ions?

Answer

Transition metals can act as catalysts because these can change their oxidation state.
The reaction between iodide and persulphate ions catalyzes by Fe is as follows:
$2 I^{-}+S_2 O_8^{2-} \xrightarrow{Fe(III)} I_2+2 SO_4^{2-}$
Role of $Fe ( IIII )$ ions:
$2 Fe^{3+}+2 I^{-} \longrightarrow 2 Fe^{2+}+I_2$
$2 Fe^{2+}+S_2 O_8^{2-} \longrightarrow 2 Fe^{3+}+2 SO_4^{2-}$

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