Distilling anything requires precise temperture control ... not everything that polutes water boils off below the boiling point of water.. some stuff boils at higher temps ... while water is boiling, if water is the main part of the liquid, the water, by boiling, keeps everything at 212 degrees.. but as the ammount of water is reduced and any polutants by concentration start to become a sizeable fraction, the boiling point can change, with the extreme case being boiling a pot dry and anything that boils or turns to vapor will, when it reaches that temperture point, goes up with the water.. leaving only the minerals in the pot or kettle that have a higher vapor point than you can get on a stove .. 400-500 degrees or so.
You want just water, you control the temp a close as possible to 212 degrees, or you only boil off about half to two thirds of the liquid .. you never let it boil out dry. This is on top of driving off anything with a lower boiling point by letting the steam escape for the first 10 minutes of so of boiling.
That means recovering maybe half the liquid you started with... that is not what I call efficent, especially when you may have to chop wood or gather deadfall for fuel.
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