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What is the explanation for the two possible reactions of $\ce{H2O2}$ with $\ce{KI}$ in acid media (iodide-catalyzed decomposition of hydrogen peroxide or iodide oxidation by hydrogen peroxide) and what determines the prevalence of one over the other?

It is known that if the hydrogen peroxide is concentrated, the pathway which results in the decomposition of hydrogen peroxide is favored. Otherwise, the iodide oxidation is predominant.

Two well-known chemistry demonstrations (elephant's toothpaste and the iodine clock) rely on these reactions.

The first one involves the decomposition of hydrogen peroxide

$$ \ce{2H2O2 ->[\ce{KI}] 2H2O + O2} $$ which is believed to occur through the following mechanism $$ \ce{H2O2 +I- + H+ -> HOI + H2O} $$ $$ \ce{HOI + H2O2 -> H2O + O2 +I- + H+} \text{(rate-determining step)} $$

On the other hand, the reaction that happens in the iodine clock is $$ \ce{H2O2 + 3 I- + 2 H+ -> I3- + 2H2O} $$

I would like to understand this phenomenon based on thermodynamic or kinetic data, since I could not find an explanation for it.

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