Alkalinity Calculations

[Daveacksh]

Hi,

Could someone please explain (by showing me the math) how this is actually calculated. Ex. If my pool (41000L) has a TA of 104ppm and I want to increase it to 150ppm, the calculators say I need 3.3Kg of Sodium bicarbonate. HOW IS THIS CALCULATED? Thank you.

OR why 680g/37854L pool will raise by 10ppm.

 

[mgtfp]

You need to know that TA gets measured in units of CaCO₃, which has a molar weight of 100g/mol. Sodium Bicarbonate is NaHCO₃ with a molar weight of 84g/mol.

If you add 680g of Bicarb to 37854 litres of water, you have 680g/(37854l x 84g/mol) = 0.00021389 mol/l of carbonates in your pool. Multiply with 100g/mol and with 1000 (to turn g into mg) and divide by 2 (CO₃^2- has two charges) and you get 10.7 mg CaCO₃ / litre, which we call 10.7ppm.

Then you need to consider the various carbonate equilibriums and that only HCO₃^- and CO₃^2- contribute to TA (the first one single, the second one double), but not H₂CO₃ or dissolved CO₂ as they have no charge, which is where a pH dependency comes in and a slight correction to the 10.7, but at pool pH most of the carbonates are HCO₃^- and the correction is small. (EDIT: Actually, the pH shouldn't even matter because what's missing in HCO₃^- and CO₃^2- will be compensated by a corresponding number of reduced H⁺, which contributes with a negative sign to TA.)

 

[an1vrsy]

 

[JamesW]

Then you need to consider the various carbonate equilibriums and that only HCO3- and CO32- contribute to TA (the first one single, the second one double), but not H2CO3 or dissolved CO2 as they have no charge, which is where a pH dependency comes in and a slight correction to the 10.7, but at pool pH most of the carbonates are HCO3- and the correction is small.

Since it is all bicarbonate added, no corrections are needed.

If some becomes H₂CO₃, it has to take a hydrogen ion, which maintains the same alkalinity.

HCO₃^- + H⁺ --> H₂CO₃

 

[mgtfp]

Since it is all bicarbonate added, no corrections are needed.

If some becomes H₂CO₃, it has to take a hydrogen ion, which maintains the same alkalinity.

HCO₃^- + H⁺ --> H₂CO₃

Thanks, James. I had (probably while you were typing your reply) come to the same conclusion and added an EDIT to my post.

 

[Daveacksh]

You need to know that TA gets measured in units of CaCO₃, which has a molar weight of 100g/mol. Sodium Bicarbonate is NaHCO₃ with a molar weight of 84g/mol.

If you add 680g of Bicarb to 37854 litres of water, you have 680g/(37854l x 84g/mol) = 0.00021389 mol/l of carbonates in your pool. Multiply with 100g/mol and with 1000 (to turn g into mg) and divide by 2 (CO₃^2- has two charges) and you get 10.7 mg CaCO₃ / litre, which we call 10.7ppm.

Then you need to consider the various carbonate equilibriums and that only HCO₃^- and CO₃^2- contribute to TA (the first one single, the second one double), but not H₂CO₃ or dissolved CO₂ as they have no charge, which is where a pH dependency comes in and a slight correction to the 10.7, but at pool pH most of the carbonates are HCO₃^- and the correction is small. (EDIT: Actually, the pH shouldn't even matter because what's missing in HCO₃^- and CO₃^2- will be compensated by a corresponding number of reduced H⁺, which contributes with a negative sign to TA.)

THANK YOU! I still don't get why it should matter that the carbonate ion has a -2 charge. In your calculation, you convert mol/L of sodium bicarbonate into mg/L of calcium carbonate by using the ratio of their molar masses (which I understand). Why divide by 2?

 

[mgtfp]

Because TA basically counts how many molecules in the water can accept a proton. And a carbonate ion can accept two protons.

 

[mgtfp]

You would have two add (in moles) only half the amount of CaCO3 to get the the same TA as when adding Bicarb. And your unit of measure for TA is how much CaCO3 would have given you the same TA.

 

[Daveacksh]

You would have two add (in moles) only half the amount of CaCO3 to get the the same TA as when adding Bicarb. And your unit of measure for TA is how much CaCO3 would have given you the same TA.

OK so it isn't simply ppm of CaCO3, it is ppm of "carbonate-as-a-base" as it were, and the carbonate ion is dibasic. Thank you very much for the clarification.

 

[mgtfp]

OK so it isn't simply ppm of CaCO3, it is ppm of "carbonate-as-a-base" as it were, and the carbonate ion is dibasic. Thank you very much for the clarification.

That's at least how I made sense of it when I dived into pool chemistry. But I think that's the right angle to look at it...

 

[AUSpool]

But why would you want to raise TA to 150ppm. And how did you get a current TA of 104ppm?