1. Zymotechnia Fundamentalis is there because I like history, brewing
historic brews, and because it sounds cool and refers to "Fundamental
Yeast Technology".
2. Lactic acids reacts 1:1 with bicarbonate ion, it doesn't matter
what the pKa is. If you have 100 molecules of lactic acid, but only
one reacts with bicarbonate, it reacts with one molecule of bicarbonate.
3. pKa is the negative log of the Ka, which is ratio that tells you
the relative amounts of substances in solution when the solution
*is at equilibrium*. If I place 1 mole of lactic acid in water solution
such that the total volume is 1 liter, it dissociates:
CH3CH(OH)CO2H -------> CH3CH(OH)CO2- + H3O+
The ratio [CH3CH(OH)CO2-][H3O+]/[CH3CH(OH)CO2H], where the square
brackets mean concentration of the substance in the brackets in moles/liter,
is equal to 1.4 x 10^-4, which is a pretty small number, typical for
carboxylic acids, and is called the Ka. The negative log of this number
is 3.85 and it is called the pKa. However, this ratio does not tell you the absolute
amount of any of these substances. I began with 1 mole lactic acid, that
means x amount dissociates, and since the amount of lactate has to equal
the amount of H3O+, [x][x]/[1-x] = 1.4 x 10^-4. Since 1 mole is much
greater than 1.4x10^-4, you can ignore the x in the denominator and
get a close answer by just writing x^2 = 1.4x10-4, or x = 1.18 x 10^-2.
That means that there is about 1-0.018 = 0.982 moles of lactic acid
remaining *at equilibrium*. But in the case of the reaction with bicarb,
there is something continually removing the [H3O+] from the reaction,
thus *disturbing the equilibrium*.
For now, let's call it The Leprechaun (and hope that he's not a racist
leprechaun...). Let's say The Leprechaun removes all of the [H30+] and
replaces it with Na+, that means we are back to the beginning, but we are
starting with 0.982 moles of lactic acid instead of 1.0. So now the equation
is [x][x]/[0.982-x] = 1.4 x 10^-4, so now x^2 = (0.982)(1.4 x 10^-4), so
x = 0.0117, and we have 0.982-0.0117 = 0.970 moles of lactic acid remaining.
Do you see what happens? The Ka value never changes, but the lactic acid is
consumed until The Leprechaun stops taking the H3O+. In this case, "The Leprechaun"
is the loss of CO2 to the atmosphere. At the elevated temperatures of mashing
and then boiling wort, for all intents and purposes all of the CO2 is lost, and
all of the lactic acid would be consumed if an equal molar amount of bicarbonate
were present, *even if the pKa was 14 instead of 3.85*.
4. This is just an example of Le Chatelier's principle, explained in any
general chemistry text, usually as the last topic in the chapter on
equilibria. If you want to prevent the lactic acid from completely reacting
and rely on the pKa, you would put the system under pressure and prevent the
CO2 from escaping. I learned this from Masterton + Slowinski, I've taught it
from Zumdahl and Chang, but really any intro chem text should have this information.
5. You are confusing the chemistry that occurs in closed aqueous systems and
acids and bases that don't form gases that escape, such as phosphate ions, with
the CO2 system, where the system is open and some of the reactants/products can escape.
Ray