The calcium SHOULD neutralize the acid, but....do NOT add anything without a full set of tests:
Free Chlorine/FC
Combined Chlorine/CC
pH
Total Alkalinity/TA
Calcium Hardness/Calcium/Hardness/CA
Stabilizer/Cyanuric Acid/CYA
A new pool that needs acid usually need CYA as well. Therefore, a good all-purpose tool is using Tri-Chlor as your chlorine for a while. It will add chlorine, acid and CYA which you will need.
You don't need to "neutralize" the acid if your pH is correct--in the 7.3-7.8 range. You don't need to worry about it even if it's 7.0-7.2.
Your goal should be to have your TA in the 80-125 ppm range--baking soda does that, but has little effect on raising pH. But too high a TA is bad for a concrete pool. Vinyl is less sensitive--you could go to 180 to 200 with vinyl.
You need to measure Calcium as well--you want your calcium to be at least 200ppm but no more than 400ppm. Again, vinyl owners don't worry.
Chlorine and CYA are a balancing act and you can look up the "Best Guess" table here for correct combos.
But don't just assume you need to add acid, then "acid neutralizer" to your new pool without testing pH--pH tells you what you need to do.
For raising pH, many people here use ordinary 20 Mule Team Borax--it raises pH, without adding to the TA , is relatively safe to use, and is cheap, and available in the detergent section of any supermarket.
For raising both pH and TA, you use soda ash--"pH UP" at pool stores--very expensive. But, next to the Borax is Washing Soda (also Arm&Hammer) which is the same thing as pH Up, but even cheaper than Borax. Don't confuse it with Baking Soda--Washing Soda is in a Yellow box, not an Orange one.
I rarely use it because I rarely have to raise my TA, and I use Baking soda when I do.
Be forewarned: TA rises when pH rises, and falls when pH falls, so adding Borax will cause TA to rise, but (and I KNOW this is confusing) it's not actually increasing TA. Soda Ash, on the other hand will increase TA as well.
It's very easy to raise TA, but darned difficult to lower it, so you measure TA when pH is normal.
I hope this all helps. Most importantly, if you add chemicals without testing you will be very, very sorry very quickly.
Wal-Mart has a cheap kit that tests everything, but has a limited chlorine test.
Taylor sells its K2006 kit which is everything you need. Leslie's on-line sells the equivalent "FAS-DPD Chlorine Service Test Kit." Expect to spend $60 to $80 on such a kit and it's the best bargain you ever get on your pool--especially a nice, new inground concrete pool that you spent 5 figures on.
TroubleFreePools also sells a similar kit, but I haven't any personal experience with it.
Also, as a new pool owner, pool stores will see you as sheep to be sheared, so don't get "Pool Stored". They'll warn you about scary things like "Total Dissolved Solids" and "Phosphates". It's all nonsense that we've seen here year after year. Phosphates and a "Phosphate neutralizing annual contract" are the latest scam. 99.9% of the time ANY problem can be fixed without worrying about Total Dissolved Solids or Phosphates. They will also tell you Bleach is bad for your pool. The only thing bleach is bad for is their profits--and most sell liquid chlorine which is nothing more than bleach.
Good luck!
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