I want to extract the $\ce{KI}$ component of the Lugol solution, is there a method to do it? If not, how can I make a $\ce{KI}$ solution?
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As you know you have to remove the others species like $\ce{I2}$ and $\ce{I3-}$. $\ce{I3-}$ I'm quite sure it exists only in solution so simply evaporating the water from Lugol 's solution you should eliminate it. To remove completely $\ce{I2}$ you have to do some others steps.
$\ce{KI}$ is produced industrially by treating iodine with $\ce{KOH}$.(see Wikipedia for reference).
$$ \ce{3I2 + 6KOH -> 5KI + KIO3 + 3H2O}$$
So I think the simple way is to treat Lugol's solution with $\ce{KOH}$ make an ice bath to precipitate $\ce{KIO3}$, filter the solution to remove it and than evaporate water. You can also try to remove iodine by means of active carbon I know this method is used to purify water see ref and ref. You can try evaporating the Lugol's solution and re-crystalize it and than eventually try different solvents to solubilize one of the compounds and leave the other as precipitate but if think is quite difficult to find a better solvent than water (as you know iodine is very insoluble in water instead $\ce{KI}$ is very soluble).
If you want to make the $\ce{KI}$ from your self here there are two Home experience:
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$\begingroup$ A very clear exposition, can I use other thing than $KOH$ to treat Lugol's solution? $\endgroup$– PedroSep 15 '13 at 17:43
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$\begingroup$ I don't know I'm sorry! Maybe you can do something with $K_2CO_3$ and/or $KHSO_3$... Of curse if you use active carbon you don't need it... $\endgroup$– G MSep 15 '13 at 18:28