Briefly, no, its not a good idea.
1). Distillation, for the home production of spirits, isn't legal. Pretty much, everywhere, worldwide. People will want to argue that point with some random national trivia, but in practical application, this is true everywhere. So lets just change your premise -- you want to distill impure water for ... stocking a survival kit, or something.
2). As a general rule, anything that's been used for laboratory chemicals is never, really, really, really, really, thoroughly cleaned out and then used for food. No one does that. There's no established protocols for that. Its not taught anywhere, and no one reputable has this experience. Someone will post eventually, years from now perhaps, says, "Oh yeah, i done that, jus' thre runs with the HCl and NaoH, and three runs trou the still throw awy runs. Is gud way. Dun all the time here in the bush." But that's not the same as I described above.