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How does potassium iodate react with hydrogen iodide? What is the internal driving force? Which reaction mechanism does it belong to?
The driving force of all chemical reactions is energy advantage.

Potassium iodate is a strong oxidant in acidic solution, while iodine ion is a medium-strength reducing agent. In acidic solution, strong oxidant meets strong reductant, and the reaction is beneficial in energy.

KIO3 + 6HI = KI + 3I2 + 3H2O

Belonging to the neutralization reaction in redox reaction.