What if everything you thought you knew about Ka and pKa dissociation constants was wrong?

[Silver_Is_Money]

I just learned something today. The potentially mega-major 'fly in the ointment' here is that all of the so-called dissociation "constants" are not constants at all. They are actually variables. They are highly temperature dependent "constants" that vary per the "Van 't Hoff equation". And (if I'm looking at this correctly) the temperature dependence "variance" itself seems to likely vary from one acid or base to the next, so clearly no easy fixed rate of slope type of correction/kludge is applicable.

For an exothermic reaction the degree of dissociation rises with rising temperature, and for an endothermic reaction the degree of dissociation falls with increasing temperature.

For acids and bases we are dealing with mainly to perhaps exclusively exothermic reactions.

The dissociation constants seen in text books for the various of weak acids are only valid at what I initially presume to be 20 degrees C. (subject to correction). Acids and bases can dissociate far more at higher temperatures.

Thus (for one example) the long valued presumption that Lactic Acid has an acid strength of 11.451 mEq/mL at specifically a pH target of 5.40 is only true at 20 degrees C. If mL of 88% Lactic Acid addition calculations required whereby to hit a target mash pH of 5.40 are firmly based upon this established 20 degree C. acid strength, and you are mashing at 67 degrees C., the strength of this acid is consequently shifted upward to some unknown degree, and likely (I presume, with a strong emphasis here upon presumption) more toward 88% Lactic Acids calculated molarity value of 11.78.

This could be a game changer.

 

[Silver_Is_Money]

The above may very well provide the explanation as to why a mash temperature pH measurement of 5.2 will be found to be a room temperature mash pH measurement within the ballpark vicinity of 5.4 to 5.45. And also as to why the measured degree of witnessed shift does not follow a "constant" (and thereby an easily quantifiable) pattern.

 

[Alan Reginato]

Basically it's why the reference value is for 20c. Many constants change with temp. So, the best approach is read and calculate with standards.
BTW, if you don't have a good pHmeter and don't calibrate it regularly, don't worth worry about it, unless the iodine test is positive past 30 min mash.

 

[hopjuice_71]

I just learned something today. The potentially mega-major 'fly in the ointment' here is that all of the so-called dissociation "constants" are not constants at all. They are actually variables. They are highly temperature dependent "constants" that vary per the "Van 't Hoff equation". And (if I'm looking at this correctly) the temperature dependence "variance" itself seems to likely vary from one acid or base to the next, so clearly no easy fixed rate of slope type of correction/kludge is applicable.

For an exothermic reaction the degree of dissociation rises with rising temperature, and for an endothermic reaction the degree of dissociation falls with increasing temperature.

For acids and bases we are dealing with mainly to perhaps exclusively exothermic reactions.

The dissociation constants seen in text books for the various of weak acids are only valid at what I initially presume to be 20 degrees C. (subject to correction). Acids and bases can dissociate far more at higher temperatures.

Thus (for one example) the long valued presumption that Lactic Acid has an acid strength of 11.451 mEq/mL at specifically a pH target of 5.40 is only true at 20 degrees C. If mL of 88% Lactic Acid addition calculations required whereby to hit a target mash pH of 5.40 are firmly based upon this established 20 degree C. acid strength, and you are mashing at 67 degrees C., the strength of this acid is consequently shifted upward to some unknown degree, and likely (I presume, with a strong emphasis here upon presumption) more toward 88% Lactic Acids calculated molarity value of 11.78.

This could be a game changer.

Just to make matters worse for you .. .. the traditional Van 't Hoff equation is an old(er) thermodynamic relationship that linearly relates the natural logarithm of the pKa with the inverse of the temperature. This holds true under only very specific conditions, i.e. when the change in heat capacity for the equilibrium is 0. This condition is almost never met meaning that this equation is not even that useful. If a full suite of thermodynamic parameters, including the change in heat capacity, for an acid/base dissociation is known then the pKa can be reliably predicted with changing temperature using more complex relationships. Probably more than you wanted to know ... ... but it highlights the complexity of the issue, particularly in a complex system like a mash.

 

[Silver_Is_Money]

This is the equation I was studying when I launched this thread. T1 and T2 are temperatures in Kelvins. K1 is the Ka dissociation constant at T1, and would be the Ka dissociation constant as it is most commonly reported in the textbooks. T2 would then represent your mash temperature in Kelvins, and K2 would be the mash temperature corrected Ka dissociation constant. Delta-H is the mash systems enthalpy, which is defined as the sum of the system's internal energy and the product of its pressure and volume, where H = U + pV. Symbol R is a constant derived from PV=nRT, or the ideal gas law. The idea here is to solve for K2, or the Ka value at mash temperature. T1 and T2 are easy to derive. Delta-H and R are the mysteries.

 

[hopjuice_71]

This is the equation I was studying when I launched this thread. T1 and T2 are temperatures in Kelvins. K1 is the Ka dissociation constant at T1, and would be the Ka dissociation constant as it is most commonly reported in the textbooks. T2 would then represent your mash temperature in Kelvins, and K2 would be the mash temperature corrected Ka dissociation constant. Delta-H is the mash systems enthalpy, which is defined as the sum of the system's internal energy and the product of its pressure and volume, where H = U + pV. Symbol R is a constant derived from PV=nRT, or the ideal gas law. The idea here is to solve for K2, or the Ka value at mash temperature.

View attachment 721862

Yeah, the thing about that is it assumes that the change in enthalpy (deltaH) is constant with changing temperature (deltaT). For reactions that occur in aqueous solution this is very rare and the deltaH varies with temperature, in other words, there is a non-zero change in heat capacity (deltaCp), which is defined as the change in deltaH with deltaT. Taking deltaCp into account for mash pH calculations would be incredibly difficult, I would think.

 

[Silver_Is_Money]

Reactions are only "reversible" to the precise measure by which all of the stoichiometric equilibrium components of said reactions remain within the Wort and are not otherwise altered or consumed in "side reactions". This perspective lends credence to much greater validity in the taking of mash pH's at mash temperature as opposed to cooling the Wort sample down to room temperature. What is meant here is that the only way a pH measured at room temperature can be considered valid is if absolutely nothing that was going on reaction-wise while at mash temperature was in any possible way altering the reaction component counts or removing the same via evolution as a gas or even via azeotropic evaporation or by side reactions. If for mildly acidified water the measured rise with such cooling is measured to be 0.35 pH points (as is textbook reported), while for Wort the rise is only measured to be perhaps 0.2 pH points (also seen, albeit with much concerning and seemingly un-explainable variance), this indicates that for the case of the Wort some unquantifiable measure of the reactions taking place at mash temperature could not be reversed with cooling. If nothing hindered or altered the critically requisite reaction reversibility, Wort would (upon cooling) act like mildly acidified water and the room temperature pH would be 0.35 pH points above the mash temperature pH.

The tentative conclusion here is that math models using Ka's and/or pKa's that are textbook grounded in room temperature values whereby to predict mash pH are doomed to have some degree of error associated with not knowing and thereby not using the appropriate temperature altered Ka's/pKa's.

 

[Silver_Is_Money]

There is a way to apply a direction to the error induced by the temperature variability in 'Ka', and there may be a means to ballpark quantify a magnitude for it as well.

If a room temperature "spring forward" of 0.35 pH points is implied via the application of the textbook Ka for room temperature pH measure while acidifying a Wort, but only on the order of 0.22 pH points (Weyermann) to 0.25 pH points (AJ deLange) is in practice observed as the "spring forward", then the directionality is such that over-acidification occurs, and the ballpark magnitude of the over-acidification is on the order of (0.35-0.22) to (0.35-0.25) with respect to pH points. The result being that actual measurement will potentially wind up being 0.10 to 0.13 pH points to the low side, and if this line of reasoning is valid (whereby with this being merely my think as I type theory, such validity is clearly open to challenge and verification or falsification) then the primary tendency when acidifying during the mash while using an otherwise math model sound and un-kludged software would be to instead find measured room temperature cooled results to be 0.10 to 0.13 pH points lower than target. For a target of 5.40 one would expect to quite often actually measure 5.27 to 5.30.

10^-5.30/10^-5.40 = 1.26 (inferred from AJ deLange)
10^-5.27/10^-5.40 = 1.35 (inferred from Weyermann)

This might imply that grist buffering is on the quantifiable magnitude order of 26% to 35% lower at mash temperature vs. room temperature. Or alternately it may imply that on the order of 26% to 35% less acid than calculated should be added to the mash water. Or these may be one and the same.

I believe (subject to correction) that D.M. Riffe has tentatively observed that as much as a 40% reduction in grist buffering may be required whereby to bring software and room temperature mash pH readings into line with real world observation. But I might add that Kai Troester observed that the degree of grist "crush" (or mill gap) plays a significant part here as well. So a combined pH shift error due to Ka variability with respect to temperature plus real world crush vs. Congress Mash pulverization (which I have discussed elsewhere, and which is the source/logic behind MME's "Grist Buffer Multiplier") may elevate the inferred 26% to 35% to something more on the order of 40% as per D.M. Riffe. What I had formerly called the D.M. Riffe "kludge" (in a very friendly and not negative way, while simultaneously personally agreeing with it, albeit for questioning the specific 40% magnitude of it) may have its root grounded within all of the reasoning found within this thread (or then again, the reasoning may lie partially to fully elsewhere).

 

[Silver_Is_Money]

Anyone attempting to seek a solution to the Van 't Hoff equation whereby to solve for the mysterious and elusive Delta-H/R may find it helpful to know that based upon a few of the basic math rules for natural logs:

ln(K2/K1) = ln(K2) - ln(K1)

(and)
K1 = e^-ln(K1)

(and)
K2 = e^-ln(K2)

(and)
e = 2.7182818284590.... = Euler's number

 

[Gnomebrewer]

While this is all interesting to read from a chemistry point of view, it really doesn't make any practical difference to brewing (although I can see that it'd be important for your software, Larry). We're talking a 3% mEq/L difference (approximately), but our mash pH simply isn't that precise to start with when we consider variation in malt batches, variation of source water (unless using DI), absorption of water into salts etc. A 3% change in acid for a 5gallon batch of pale ale for me means a difference of 0.1mL!