I always brew with a not insignificant quantity of alkalinity in my mash liquor and a lesser quantity in my sparge liquor. All of it the result of natural action of rainwater on limestone including calcium and magnesium but not as metals. Alkalinity is sometimes added by brewers when their liquor has too little or no naturally occuring alkalinity...
This is, in most cases, a good thing as it means less acid needs to be added. Most brewers will not tolerate high levels of alkalinity in their liquor. It is when lots of dark malts are used or the base malt is of low alkalinity or a combination of the two that some base has to be added in order to achieve proton balance at a reasonable mash pH. Now if one wants lots of chloride or sulfate and happens to have lots of alkalinity in his source he can add acid with the anion he want's and Bob's your uncle. But most breweries would decarbonate by lime treatment, RO or membrabe treatment to get the bulk of the bicarbonate out (leaving the remainder, perhaps, to be cancelled with acid to give desired anion levels). A brewer wanting extra Ca++ or SO4-- can alos take the tack of adding sodium bicarbonate, sodium carbonate, calcium hydroxide, potassium hydroxide, etc. and then neutralizing their alkalinity with hydrochloric or sulfuric acid (remember in this context that 'neutralize' does not mean to bring to pH 7 but rather the desired mash pH). This results in replacement of the alkali species (OH)-, CO3--, HCO3-, with, respectively, water and carbon dioxide which escapes. IMO it's easier to just add the desired salt.
and because of the difficulty of getting calcium carbonate to dissolve, then potassium or sodium carbonate or bicarbonate is commonly used. We know (bi)carbonate witll raise wort pH,
We know bicarbonate will raise pH whenever the pH without it is less than 8.3 for it is an alkali for any pH less than that (and an acid if if pH >8.3). Carbonate ion is more strongly alkaline and OH- stronger still and will act as a base for any pH we might ever expect to have to deal with.
Some but not all calcium bicarbonate forms apatite meaning some alkalinity goes into the boiler where during the boil it will precipitate and its influence of pH will be lost.
Calcium carbonate/bicarbonate does not form apatite. Apatite (C10(PO4)6(OH)2) is formed from the calcium ion, water and
biphosphate ions released from the malt. It happens even if all the hardness is permanent hardness (no bicarbonate). Apatite formation starts in the mash tun and completes (to the extent that it is going to complete) in the kettle. When apatite is formed it precipitates as it is extremely insoluble even at mash and kettle pH. In its formation protons are released. These protons will be picked up by any proton absorber (base) in the system and as a result the pH goes down.
In the case of sodium and potassium based alkalinity, they will not be precipitated and the effect will be different. I then wondered if naturally alkaline water were added to the kettle to raise pH and extraction at the beginning of the boil it might extract more from the hops but would also have dropped out by the time the wort was transferred to the FV.
Were you to add water with appreciable temporary calcium hardness and appreciable alkalinity to the kettle the pH would immediately go up as the bicarbonate absorbs protons from the mash. At the same time you have provided more calcium to participate in apatite precipitation releasing protons and reducing the pH rise somewhat. The definition of RA as alkalinity - calcium_concentration/3.5 tells us that the bicarbonate is 3.5 times more effective at increasing alkalinity than apatite formation is at reducing it. The other reaction that will take place if hard, alkaline liquor is heated is the precipitation of chalk by Ca++ +2HCO3- ---> CaCO3 + CO2 + H2O. Note that no protons are released or absorbed in this reaction. Thus precipitation of chalk does not ostensibly result in a change in pH. But the calcium/carbonate system does want to be in equilibrium with the CO2 content of the atmosphere and so naturally heads towards pH 8.3 though it may take a long time to get there. This will not pull 100 hL of wort to pH 8.3 however because of all the other stuff in it.
Summary: Wort in kettle at pHi. Add hard, alkaline liquor. pH immediately rises. As the boil commences apatite precipitates lowering pH a little but not back to pHi. Chalk precipitates. This has minimal effect on pH. The net effect would be the same as if you added the extra liquor at mash in.