Fitting a model to titration of a weak base with a strong acid

Question

I need to determine the inflection point of a titration curve adding a a standardized strong acid to a weak base.  This is usually an asymmetric sigmoidal curve.  I can take an empirical approach: fit  the three standard models (Gompertz 3P, Gompertz 4P, and Logistic 5P) for such curves and evaluate the fit, choose the best model and its predicted inflection point.  The fit is not bad around the inflection point.  Has anyone developed a custom model from chemical first principals that might give a better fit?  An interactive solution would be fine at this point.

K PO4 Titration.jmp

Mark_Bailey · Answer

By the way, there is an excellent short series of posts to the JMP Blog about fitting nonlinear models by Susan Walsh in JMP Technical Support. The link takes you to the last post, which contains links to the earlier posts in the series.

Very well done and very informative!

PeteW · Answer

Yes, thank you, Mark. I was hoping that someone may have already done the work to develop the theoretical model. I'm a great fan of not re-inventing the wheel. If the wheel need inventing and I have the time to do it, it is great to know that JMP can fit a custom model to data. Thanks, again.

Pete

Mark_Bailey · Answer

As you said, your initial attempts at empirical model building yield reasonable estimates of the inflection point. Given that the extremes of the response are asymptotes, I tried several logistic models. The logistic curve with five parameters exhibits the lowest AICc and provides for the asymmetric curve you requested.

If a theoretical model can be found and it is different from the choices in either the Fit Curve platform menu or the Model Library in the Nonlinear platform, then a custom model can be fit. See Help > Books > Predictive and Specialized Modeling > Chapter 13: Nonlinear Regression.