When a catalyst is in the same phase or state as the reactant, an intermediate species is formed
Overall reaction of peroxodisulphate ions and iodide ions:
S2O82-(aq) + 2I- à 2SO42-(aq) +I2(aq)
Peroxodisulphate ions, S2O8 ions oxidise iron (II) to iron (III):
S2O82- (aq) + 2Fe2+ (aq) à 2SO42- (aq) + 2Fe3+(aq)
Then Fe3+ oxidises the I- to I2, regenerating the Fe2+ ions so that none are used up in the reaction:
2Fe3+(aq) + 2I-(AQ) à 2Fe2+(aq) + I2(aq)
Irons job here is to give an electron to the peroxodisulphate and then later on take one back from the iodide reactions.
Notice that without the iron catalyst the reaction occurs between two negatively charged ions, which repel, so a high activation energy for the reaction is needed. However involving the catalyst means that in both reactions the reactants are oppositely charged, this explains the lower activation energy and the increase in rate of reaction.
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