[scanch]

I would like to use titration to make an approximation of the concentrations of primary acids in bread dough: carbonic (pKa 6.4,10.3), acetic (pKa 4.76), and lactic (pKa 3.86).

My plan is:

1) Log numerous data points of titrant added vs pH change from typical starting point of pH 3.5 to typical equivalence point of pH 8.2

2) At each data point use Henderson-Hasselbalch on each acid to create an equation linking pH change to acid concentrations.

For example, at pH 5.0 H-H predicts lactic acid, acetic acid, and carbonic acid ionizations to be 93%, 64%, and 4% respectively.  At pH 5.5 the ionizations are 98%, 85%, and 12% respectively.   If it takes 2 mmoles of NaOH to move the pH from 5.0 to 5.5, I can create the equation:

2 = (98%-93%)[Lactic] + (85%-64%)[Acetic] + (12%-4%)[Carbonic]

I can create multiple such equations for every addition of titrant.

3) Solve the system of equations to get an estimation of the actual concentrations.

Note: Because the flour buffering capacity is a significant distortion, I plan to run a control titration of flour only, using HCL to acidify to ph 3.5, and logging titrant added vs pH change data up through 8.2.  These values will then be subtracted from readings taken on fermented dough to isolate the pH response attributable to the primary acids.

I'd very much welcome thoughts on if this approach should work and what any flaws might be.

[Borek]

I have a feeling this system will be very sensitive to the inaccuracies in pH measurement, so errors will be too large for any practical application.

[scanch]

Thanks for the thoughtful observation.  I too am worried about this method's sensitivity to pH reading error.

As a first step, I've bought a meter rated at +/-.002pH with 5-point calibration.

But what I'm hoping really addresses this problem is how the method takes many (e.g. 50) readings across the entire pH range.  With this large set of simultaneous equations the errors of individual data points will "average out" in the best-fit process.  I get my concentration not from any particular data points but from matching the shape of the measured pH change curve against the shape of the theoretical pH change curve.

[Borek]

With this large set of simultaneous equations the errors of individual data points will "average out" in the best-fit process.

Assuming errors are random, and not systematic.

What is the ionic strength of the solution?

[scanch]

Yes.  I plan to calibrate the meter at 3.000, 4.000, 6.000, 8.000, and 9.000 to minimize systematic error.

I don't know the ionic strength, but I do know titrating to an equivalence point of pH 8.2 in one 115g sample of solution required up to 15g of ~0.1N NaOH.

[Borek]

If you don't know ionic strength, you don't know apparent Ka values, if you don't know apparent Ka values, your calculation of concentration ratio is systematically off, if it is systematically off - your final result is not worth paper it is written on.

I would love to be wrong, I like the idea.

[scanch]

Ooof, painful truth about ionic strength, I missed that.  I'm not ready to give up yet though.  I am keen to get results at least worth the paper they're printed on.

The contribution to ionic strength coming from the acetic, lactic, and carbonic concentrations I can bake in to my best-fit calculations so that consideration can be handled.

The flour in the solution is the ionic strength wildcard.  Flour contains trace amounts of a variety of organic acids and bases as well as 0.5-1.5% by weight of P, K, Ca, Mg (though not all in soluble form).

I estimate the total ionic strength of the solution including the primary acids could be in the .01-.1 range.

I came up with three different ideas on how to calculate flour ionic strength, I'm not sure which is most viable:

1) Add flour ionic strength as additional unknown to solve for among set of simultaneous equations.  Makes me queasy because feels like having this additional large degree of freedom could open the door to multiple correct solutions.

2) Calibrate conductivity meter to ionic strength using known NaCl solutions then measure conductivity of flour solution to determine ionic strength.

3) Add known amount of acid to flour solution and after correcting for flour buffering effects, determine pKa of acid and thus ionic strength of flour.

[Borek]

What about buffering the sample at very high ionic strength (like 1 or 2) with some inert salt? You may need some checking of Ka values, but it will be enough to do it once just to "calibrate the method".

[scanch]

Thanks for the idea.  I confess I don't understand how it would work though.

[Borek]

If you add a lot of inert salt, relative changes in the ionic strength will be small - that means changes in activities will be small also. That in turn means you can assume they are constant, and the error you are making is small, especially compared with the low ionic strength solution.

Note: change from 0.01 to .1 is tenfold, for 2.01 to 2.1 is 4.4%.

[scanch]

Got it.  But I thought the common equations that convert ionic strength to activity coefficient were only accurate enough below 0.1 ionic strength.  I thought they broke down above that so converting ionic strengths around 1 or 2 to activity coefficients and pKa's would require woolly rocket science.

[Borek]

Got it.  But I thought the common equations that convert ionic strength to activity coefficient were only accurate enough below 0.1 ionic strength.  I thought they broke down above that so converting ionic strengths around 1 or 2 to activity coefficients and pKa's would require woolly rocket science.

You are right - but it doesn't matter. Prepare high ionic strength solutions, titrate each acid separately to determine its apparent dissociation constant, and use this apparent dissociation constant in further calculations. This way you don't have to care about calculation of activity coefficients, you got them experimentally.

[scanch]

Got it.  Then I just need to add the same quantity of salt to all my titrations to recreate the conditions for that pKa.  Cool idea.

I may try that and a few of my ionic strength determination ideas as well to find out what approach ends up most accurate.  I'm heartened that I can assess the accuracy of any approach by adding known amounts of acetic and lactic acids to solutions and testing.