It occurred to me this morning that perhaps another way to explain why lactic acid doesn't neutralized bicarbonate 1:1 might be to use the scheme I came up with for Palmer in his book on water in order to explain the acid/base chemistry of the mash. Its also the basis of the TQ paper on mash pH estimation. The basic concept is to let the titration curve of the materials involved tell the story. In this case the material in question is lactic acid (the other material is carbonic acid). To get the titration curve for lactic acid we would put a millimole of it in a beaker with a liter of water and add strong base in increments recording the pH after each addition. If we plotted the mEq of strong base added against the y axis and the resulting pH against the x axis we would get a plot that looks like the one below. This is similar to the carbonic acid plot in John's book except that it has two steps and one riser (with the pK at the inflection point of the riser) and the carbonic acid plot has three steps and two risers (with the two pK's at their inflection points). A plot for phosphoric acid (in the book), with its three protons, has 4 steps and 3 risers with the 3 pK's at their inflection points).
The numbers on the y axis represent the number of milliequivalents of base added and the total charge on the lactate (Lac-) ion in the water at equilibrium after the base has been added and has reacted with the acid:
HLac + Na+ + (OH)- ---> Na+ + H2O + Lac-
A reacting acid (HLac) molecule gives up its proton to the base (OH)- forming water and acquiring a negative charge in the process. IOW it becomes an Lac- ion. Not all acid molecules do this. The fraction that make the sacrifice depends on the final pH hence the curve. The fraction that do is given by the magnitude of the charge. Thus we see that if the final pH > 6.5 or so nearly all the lactic molecules have transitioned and Lactic acid is, in such cases, a strong acid. Conversely if pH < 1 very few molecules do and Lactic acid is a weak acid.
At mash pH we are almost to the point where we can call lactic acid strong as the y axis values are close to -1 in that region. At the same time it is clear from the curve that if we neutralize bicarbonate (or any other form of alklinity) to pH 5 with lactic acid that only 94% of the acid we added has reacted and we had better add a bit extra if we want to get rid of a specified amount of alkalinity. The amount is
mmol_acid_needed = mEq_alkalinity_to_be_removed/reading_from_graph
From yesterday's post it is probably clear that reading_from_graph = f1(pH) and that is indeed the case which also reveals how the graph was prepared. Put another way, the graph reading gives you the fraction of the added acid that reacts at a given pH and 1 minus the reading, f0(pH), gives you the fraction that didn't react.
I really hope that makes it clear how this works. Note that the same issue arises with phosphoric acid. Mash pH lies in the middle of the step between the first two pK's of phosphoric acid and thus the charge is ~-1. John and I debated this one quite a bit and he finally decided that he was just going to say that 1 mmol of phosphoric acid would wipe out 1 mEq of alkalinity but just as that isn't the case with lactic, it isn't the case with phosphoric. If you want 1:1 exactly you'll have to go to a strong acid (WRT mash pH) such as sulfuric acid with one negative pK and the other 1.92 or hydrochloric with one negative pK.
The numbers on the y axis represent the number of milliequivalents of base added and the total charge on the lactate (Lac-) ion in the water at equilibrium after the base has been added and has reacted with the acid:
HLac + Na+ + (OH)- ---> Na+ + H2O + Lac-
A reacting acid (HLac) molecule gives up its proton to the base (OH)- forming water and acquiring a negative charge in the process. IOW it becomes an Lac- ion. Not all acid molecules do this. The fraction that make the sacrifice depends on the final pH hence the curve. The fraction that do is given by the magnitude of the charge. Thus we see that if the final pH > 6.5 or so nearly all the lactic molecules have transitioned and Lactic acid is, in such cases, a strong acid. Conversely if pH < 1 very few molecules do and Lactic acid is a weak acid.
At mash pH we are almost to the point where we can call lactic acid strong as the y axis values are close to -1 in that region. At the same time it is clear from the curve that if we neutralize bicarbonate (or any other form of alklinity) to pH 5 with lactic acid that only 94% of the acid we added has reacted and we had better add a bit extra if we want to get rid of a specified amount of alkalinity. The amount is
mmol_acid_needed = mEq_alkalinity_to_be_removed/reading_from_graph
From yesterday's post it is probably clear that reading_from_graph = f1(pH) and that is indeed the case which also reveals how the graph was prepared. Put another way, the graph reading gives you the fraction of the added acid that reacts at a given pH and 1 minus the reading, f0(pH), gives you the fraction that didn't react.
I really hope that makes it clear how this works. Note that the same issue arises with phosphoric acid. Mash pH lies in the middle of the step between the first two pK's of phosphoric acid and thus the charge is ~-1. John and I debated this one quite a bit and he finally decided that he was just going to say that 1 mmol of phosphoric acid would wipe out 1 mEq of alkalinity but just as that isn't the case with lactic, it isn't the case with phosphoric. If you want 1:1 exactly you'll have to go to a strong acid (WRT mash pH) such as sulfuric acid with one negative pK and the other 1.92 or hydrochloric with one negative pK.