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You'd think astatine would oxidize (take the electron from) iodide, but At is a weaker oxidizer than I, so that's out. However, if you look at the I2 and KI reaction, it forms KI3. KI3 contains a cluster of three iodine atoms, one of which has an extra pair of electrons. None of the lighter halogens do this, but trends indicate that astatine wouldn't be bothered too much by the extra pair. Thus, the reaction probably looks like this:

K+ + I- + At2 --> K+ + At2I-

Or more simply: KI + At2 --> KAt2

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