I've never had a problem with tap water and reptile eggs, but that doesn't mean that it can't be a problem. Since the distilled water issue has been covered, then I guess I'll throw in some other information that is well known to aquarium enthuiasts.
I have forgotten how to apply my highschool chemistry lessons, so I simply remember these simple things, taken from wikipedia (en.wikipedia.org/wiki/Chloramine:
"Aquarium owners must remove the chloramine from their tap water because it is toxic to fish. Aging the water for a few days removes chlorine but not the more stable chloramine, which can be neutralised using products available at pet stores.
Many animals are sensitive to chloramine and it must be removed from water given to many animals in zoos."
Chlorine was once the norm for municipal water treatment, but now, chloramine has become the standard........therefore, the old rule of letting the water stand before aquarium use doesn't apply to chloramine-treated water. You need to use direct chemical measures to remove chloramine---->>>>> I use "Prime," a Seachem product.
If you want to make sure the water won't kill the eggs, then you should treat it as you would aquarium water.......the pH tolerances of different egg species are completely unknown to me!
Shane
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