First I would like to state that I have found the information on this site extremely helpful. I now have a clean pool with very little problem due to following the information I have found on this site! Pool stores love me!
Now I have a question I cannot find an answer for. I would like to know when muriatic acid is added to pool water, what happens to the acid. Is it used up? What is the resulting by-product. Or, What compounds that are left behind as a result of use. I have small children and this creates my concern, I want to know how safe is muriatic acid is. I know that muriatic acid lowers PH and TA (Yes I do know the procedure for lowering TA). I normally operate my AGP with a higher PH 7.8-8.0, high TA 240, and a high hardness of 340. Its my fill water from the well. I have been having a little trouble with scaling and would like to lower my PH and TA. Maybe! Thank you for the information on this site. I actually enjoy pool maintenance now .

The acidity of the water depends on the pH. Once the acid is added and allowed to mix and circulate, the final pH of the water is what determines what is safe.

There is no muriatic acid left circulating in the water. It is perfectly safe when used as directed. The only thing left over is a little bit of chloride, like from regular salt (sodium chloride).

Note: Concentrated muriatic acid is dangerous and must be handled with care. Take precautions to avoid contact with skin or eyes. Always have a plan for accidents or spills before handling.

As for the concern for the kiddos........I'll generally add 20 oz.s of acid at a time and jump in after 30 minutes after circulating.

Muriatic acid is hydrogen and chlorine. When added to the water it forms H3O+ and Cl−. Essentially it increases the hydrogen ion level and adds chloride ions. In the very long run that usually ends up as hydrogen gas and salt, depending on what else is added to the water.

I don't think one sees hydrogen gas. Usually one is adding acid to compensate for carbon dioxide outgassing so the acid lowers the TA over time as well. So if one is adding baking soda to keep the TA from falling too much, then the net result is just a salt (sodium chloride) build-up. The hydrogen ends up becoming a part of water from carbonic acid when carbon dioxide outgasses.

HCO₃^- ---> CO₂(g) + OH^-
(add HCl) ---> H⁺ + Cl^-
(add NaHCO₃) --> Na⁺ + HCO₃^-
-----------------------------
result is CO₂(g) + H₂O + Na⁺ + Cl^-
or carbon dioxide gas, water, and sodium chloride salt

This is very interesting! So after adding muriatic acid to my pool, the only thing "leftover" is salt. I now feel more comfortable about lowering my PH and TA.
Now what I find interesting is everything I add to my pool other than the CYA, seems to be some form of salt. The only chemicals I add to my water besides CYA is, chlorine and muriatic acid. Is this correct, am I basically performing water sanitation with salts? It appears to be safe to me.

Why would you think it wasn't?

Its just that muriatic acid is a strong acid and, I was concerned about having a pool full of "acid" after lowering TA.

Yeah, HCl is strong, but you're only adding a few ounces to thousands of gallons of water - quite frankly the equivalent of a drop in a bucket.

And stomach acid is partially HCl......your gut has a pH of about 2!

Pool water has lots of different components that in their pure and undiluted form, would be extremely dangerous. But in such dilute amounts, they exist to do us no harm and are actually beneficial. You can't really describe it as a "pool of acid" any more than you could call a glass of water as a glass full of hydrogen and oxygen, both of which are substances with significant hazards in their own elemental form.

People get caught up with associating "salt" with table salt. Salt is the product of any acid/base reaction (NaCl, KCl, CuSO4, etc...)

Can I just say this made me laugh out loud.

Yeah, but you wouldn't want to swim in your gut!

nor would you want to swim in any pool with a ph of 2