Q: Theoretically determine the pKa of creatine monohydrate

I'm writing a paper about determining the pKa of an amino acid using a pH sensor. In one of the investigations, 5g creatine monohydrate is dissolved in 10mL 0.1M HCL and titrated with 0.1 M NaOH. I found the pKa using the first and second derivatives of the pH vs volume graphs. But is there a way to determine it theoretically (as in by calculation)? I have attempted to find a theoretical measure for the pKa but my instructor told me it's irrelevant as it only considers the dissociation of the weak acid or only the dissociation of HCL. Keep in mind the strong acid is neutralized first before the creatine (Le Chatelier's principle) and it was experimentally determined 4 mL of NaOH was needed to neutralize the weak acid (from first and second derivative graphs) and the pH at the first peak which is for the HCL was 4.5. This pH is the pH of un-titrated creatine as all the NaOH was added before was used to neutralize the HCL.

In an attempt to find a theoretical value for pKa to compare with our results I wrote an equation for the reaction of the creatine molecule with hydroxide from the added NaOH titrant and wanted to ice the ICE box method. My instructor told me non of the calculations made are reliable as there is no source for the chemical equation I wrote. The equation is balanced, and the law of conservation of charge is present. We looked at the creatine molecule structure and there are 3 ionizable functional groups (we ionized only 1) yet my instructor refused to add the equation until we know the number of hydroxide ions that react. He emphasized how this is not about balancing and is impossible to find on my own so I should get it from somewhere to be certain of the stoichiometric ratios and execute my calculations accurately. The equation I wrote is

〖 C_4 H_9 N_3 O_2〗_((aq)) 〖+ OH^-〗_((aq))→〖+ C_4 H_8 N_3 O_2^+〗_((aq)) 〖+ H_2 O〗_((l))

(C_4 H_9 N_3 O_2 ) HCL+H_2 O ⇌ H_3 O^++(C_4 H_8 N_3 O_2 )^- HCl

I know this is tough, but another approach to solving this is through simulation models that use calculations based on the expected pH from experimental.

https://en.m.wikipedia.org/wiki/Protein_pKa_calculations. Though I don't know where to start with the info all of this!

if you need any variables in the solution that I didn't provide you can write them as a variable.

Thank you very much

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