# Fitting titration curve

To simulate the action of gastric $\ce{HCl}$, we have titrated 100 ml of a meal with 0.1 N $\ce{HCl}$. To plot the data, use (R-code)

vol = read.table("http://menne-biomed.de/uni/volph.txt",sep="\t",header=TRUE)
plot(vol$vol,vol$pH,pch=16,type="l",main="Titration of 100 ml meal with 0.1 N HCl")


I am trying to determine, for example, how much 1N $\ce{HCl}$ I need to add to get a pH of 1.5; if I understand correctly, I have to fit the Hasselbalch equation.

Being a statistics guy, the numerics is no problem, I just do not understand how to get the terms in that equation together with my data.

• I don't quite understand what your problem is. Could you specify your question a bit further? – Antimon Oct 22 '12 at 13:01
• In the Hasselbalch equation, I know the pH, I want to know the pK, but how do I associate the [HA] and [A-] (or their ratio) with my partial titration curve? Or, more naively: how do I get pK from my titration curve (which remains in the acid all the time, the substance is not stable in alcaline). – Dieter Menne Oct 22 '12 at 13:09
• Could you also give us information about the concentration of your inital sample? Did you add any acid before the titration in order to make the solution acidic? – Antimon Oct 22 '12 at 15:15
• No, that's a standard meal, chocolate drink with some Ca that acts as a weak buffer, so initial pH is 5.4 as indicated in the data. The final question is inverted: we have measured the pH of the meal in the stomach (in addition to actual volume), and want to know the amount of protons "pumped" (see drug proton-pump-inhibitor). – Dieter Menne Oct 22 '12 at 16:02

## 1 Answer

The best thing would be if you went back to the mass action law, considered all reactions that take place ($\ce{Ca}$ buffer!) and derived a formula for your specific problem. The Henderson-Hasselbalch equation actually does exactly that for a one-component acid/base system with a single protonation stage. Remember that the concentrations that occur in the mass-action law are those at chemical equilibrium, not the initial ones; i.e. for any component $C$, the eq. concentration is $[C] = [C]_0 - \Delta_C$. The problem at hand is then to find how the changes in concentration depend on the added volume of titer.

If you just took the Henderson-Hasselbalch equation (equating the change in concentrations with the added concentration of $\ce{HCl}$), you do not include the $\ce{Ca}$ buffer, which will probably play an role in this. (You get a $pK_a$ of around 0.7, which I guess is a bit on the strong side ...)

One more thing I just noticed: You apparently added 100 mL of titer to 100 mL of sample. That's kind of bad, because you'll also have to consider how the change of overall volume affects your concentrations (effectively the pH) during titration.

• Thanks, yes, I am aware that the concentration has to be corrected, but that's the easy part, because it is standard numerics. If I understand you (and this is in agreement with what I read), it's hopeless to get anything from this titration curve, if I do not know what is going on inside. The Ca buffering is one I know of, but there may be others. – Dieter Menne Oct 23 '12 at 12:39
• There are basically two components in your system: The Ca buffer and your sample. (The HCl dissociation can be considered complete, so you won't have to bother with that.) So you can get a $pK_a$ from your titration, if you also include the Ca buffer. However, if there is indeed more than one component partaking in the reactions, you only get "effective" values and concentrations out, valid only for the pH region you have investigated. Do you have any information about the composition of that meal? – Antimon Oct 23 '12 at 12:57
• Effective values are fine; I believe we do know the concentrations, but the required range is not covered. I think one should redo the titration using 1N HCl so that the whole required range will be covered. – Dieter Menne Oct 23 '12 at 13:08
• Sounds like a good idea, experiment always beats extrapolation. Just remember to pay attention to the Ca concentrations, and you should be fine. (Unless I am forgetting something, which may always happen ...) – Antimon Oct 23 '12 at 13:16