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Assuming that your CYA wasn't really extreme (I assumed 40 ppm) then 1.5 quarts (6 cups) of Muriatic Acid (31.45%) in your 13,600 gallon pool with a pH of 7.9 and a TA of 216 should have resulted in a pH of 7.4 and a TA of 203. So the numbers that your pool store then gave you of 7.8 and 176 do not make sense.
Furthermore, if you were to start at 7.8 and 176 and then add 1 gallons of acid, you would end up with a pH of 6.9 and a TA of 141. So that is too much to add.
I would be very suspect of the numbers you are getting from the pool store. Get an accurate test kit such as the Taylor K-2006 or Ben's kit and test the pool water yourself.
As for lowering the TA, follow Ben's Lowering Your Alkalinity procedure which is the only truly effective way to lower the TA. The advice from pool stores to simply add acid without first lowering the TA and aerating is just plain wrong and ineffective.
My guess is that your pH is already on the low side, but that due to carbon dioxide outgassing (due to the high TA and low pH combination) the pH will rise (and the TA will stay the same). So again, get a decent test kit and test the water yourself and then follow Ben's procedure to get your TA down.
Keep us posted with how it goes.
Richard
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