General Titration Theory

It would be folly for this text to provide comprehensive titration theory coverage. Most of the details following are based on extracts from Dick [43]. These wiU yield at least a picture of the essentials. Further details can be obtained from Chapter 5 of the same reference. 

From the above we have, using molarities instead of activities  

For any point in the titration between the start and the equivalence point we have, for a point of volume Vt  

The right member of the right-hand side represents [R]br, or [R] from the back reaction. When Keq is large (equilibrium for the reaction hes far to the right), and for titration points appreciably before the equivalence point, the contribution of [Rjbr may be ignored, and Equation.(n) reduces to  

2 Text, tables and illustrations in this section are taken from Analytical Chemistry , James G. Dick, McGraw-Hill, Inc., (1973), Chapter 5 (with permission). 

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Where potentiometric titrations, other than those involving pH measurement are concerned, such as precipitation, complexation, oxidation-reduction, nonaqueous media, etc., the data obtained will be in the form of E versus V. All of the titration theory, and that of titration curves, will apply to such titrations, as will the general methods of endpoint location. 

Tanford, C., Kirkwood, J. G. Theory of protein titration curves. I. General equations for impenetrable spheres. J. Am. Chem. Soc. 79 (1957) 5333-5339. 6. Garrett, A. J. M., Poladian, L. Refined derivation, exact solutions, and singular limits of the Poisson-Boltzmann equation. Ann. Phys. 188 (1988) 386-435. Sharp, K. A., Honig, B. Electrostatic interactions in macromolecules. Theory and applications. Ann. Rev. Biophys. Chem. 19 (1990) 301-332. 

An important reason for this lack of experimental work is that the zeta-potential cannot be easily determined independent of the electrophoretic mobility [284] however, in the case of proteins (as well as some other charged colloids), the intrinsic charge obtained by titration is a parameter that can be measured independent of the electrophoretic mobility. The charge obtained from electrophoretic measurements (i.e., the net charge) via the preceding theories is generally not the same as the charge obtained from titration (i.e., the in-... 

Tanford, C Kirkwood, JG, Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres, Journal of the American Chemical Society 79, 5333, 1957. 

This example shows also that the proton theory, in addition to being valid for aprotic solvents, also works for amphiprotic solvents, and so represents a more general theory. How in an acid-base titration the theory works out can be followed from the titration of a certain amount of HC1 gas introduced into pyridine as an aprotic solvent ... 

Tanford C, Kirkwood JG (1957) Theory of protein titration curves. I. general equations for impenetrable spheres. J Am Chem Soc 79 5333—5339. 

Although the ester mechanism is not yet generally accepted, the evidence accumulating since it was first put forward is in its favour, and the evidence which is alleged to be against it, or which has been interpreted in terms of ion-pairs in place of the ester, is certainly compatible with the ester theory [13, 14,15]. We note in passing an interesting application of the polymerisation of styrene by perchloric acid it was used as an indicator-reaction in the enthalpy titration of weak bases [16]. 

In Chapter 3, we supply the theory required for the modelling of chemical processes. Many of the example data sets used for both kinds of analyses are taken from kinetics and equilibrium processes. This reflects the background of both authors. In fact, this part of the book serves as a solid introduction to the simulation of equilibrium processes such as titrations and the simulation of complex kinetic processes. The example routines are easily adapted to the processes investigated by the reader. They are very general and there is essentially no limit to the complexity of the processes that can be simulated. 

K. Linderstrom-Lang, Compt. Rend. Trav. Lab. Carlsberg, 15, 1 (1924). The Ionization of Proteins. C. Tanford and J. G. Kirkwood, /. Am. Chem. Soc., 79, 5333 (1957). Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres. 

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