While Li [0] is probably just about capable of reducing K [+I], this isn't going to happen at room temperature, at least not without a catalyst of
sorts.
At elevated temperature, KCl dissociates a bit: KCl ---> K + 1/2 Cl2. The lithium would then mop up the chlorine, form LiCl and heat and a
self-propagating reaction could be created, depending on the heats of formation of LiCl and KCl. Of course if you could distill the K off, you drive
the equilibrium to LiCl + K.
At RT there isn't enough energy in dissolved KCl +Li to allow reactive collosions, IMHO.
And finding a solvent for KCl that not reactive with lithium metal? Good luck with that...
This is not much more than a pipe dream...
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