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Water salts when sparging

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There's never "nothing" in the mash *on average*, but my point was exactly that the average does not count.

Seriously, there's never "nothing" in the mash ever, not just on average.

Also, I don't think it's accurate to talk about alkalinity, assuming harshness is extracted as a function of pH. You still need 10^-5 mol of H+ to drop the pH of distilled water to 6. You just need more H+ if your water has non-zero alkalinity to neutralize.

The fact that you need more H+ to neutralize when the water has non-zero alkalinity nicely demonstrates why it's the alkalinity that's important, I think. Do we really think that adding 0.005 ml of lactic acid to 5 gallons of distilled water has any real impact, even though it reduced the water's pH to 5.5 (or whatever)? I mean, there is almost no buffering capacity in that acidified water.

Anyway, I'd recommend reading the paper I linked, and hopefully @mabrungard will comment.
 
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