Volume Changes Accompanying Titration

New and more precise measurements of volume changes have been made recently by Kauzmann and co-workers (Kauzmann, 1958 Rasper and Kauzmann, 1962 Kauzmann et al., 1962). These measurements show 

Volume Change for the Binding of Hydrogen Ions by Carboxylate Groups at 30°C and Ionic Strength 0.16  

Kauzmann and co-workers measured AF for the addition of ions to proteins below pH 5. Normally only carboxyl groups are titrated in this range of pH, so that the results represent AF values for the reaction 

Kauzmann and co-workers also measured AF for the addition of 0H ions to proteins from pH 5 to pH 10 or above. These values mostly represent AF for the reactions 

In small molecules containing basic nitrogen atoms, the value of AF for the reaction 

---

This same explanation clearly cannot be invoked to account for the observed pK values of imidazole groups, since these pK s differ from expectation in the wrong direction. This result should perhaps not be taken too seriously since the intrinsic pK s of protein imidazole groups are relatively imprecise. Moreover, there is some question about the expected pK of an imidazole group (Table I, h). On the other hand, the volume changes which accompany dissociation of imidazole groups, to be discussed in Section VIII, are also anomalous, and the over-all conclusion must be that some effect of protein structure on the titration of imidazole groups has so far been overlooked in theoretical treatments of the problem. 

It is clear from this discussion that the measurement of volume changes which accompany titration of proteins and of model compounds represents a potentially fruitful area of research. It would be of special interest to have available AF values for synthetic polypeptides (or for naturally occurring substances such as a-corticotropin), which exist in aqueous solutions in a randomly coiled conformation. 

The major advantage of protein adsorption studies on high surface area materials is that changes of some extensive properties which accompany the process of adsorption are large enough to be directly measured heat of adsorption through microcalorimetry 141), uptake or release of small ions by a combination of electrokinetic methods and titration 142), thickness of adsorbed layer or an increase of the volume fraction of solid phase by a hydrodynamic method like viscometry 143). Chromatographiclike analysis can also be applied to protein adsorption 144). 

A potentiometric titration belongs to chemical methods of analysis in which the endpoint of the titration is monitored with an indicator electrode that records the change of the potential as a function of the amount (usually the volume) of the added titrant of exactly known concentration. Potentiometric titrations are especially versatile because indicator electrodes suitable for the study of almost every chemical reaction used in titrimetry are now available. This technique is also frequently used in the study of operational conditions of visual titrimetric indicators proposed for general use in chemical analysis, as well as in the study of numerous reactions, such as protonation and complexation, which find their application not particularly in analytical measurements. The course of the potentiometric titration curve provides information not only about the titration endpoint position, but also the position and shape of the curve that may provide data about the processes accompanying the titration reaction. Another advantage is that the necessary apparatus is generally less expensive, reliable, and readily available in the laboratories. 

The increase of x is accompanied by a decrease of the unit cell volume (see Table 1). Our results indicate that this volume variation is mainly governed by the change in the electronic configuration of the Mn ion rather than ionic radii considerations. Indeed according to iodometric titration, the increase of x promotes the reduction of manganese. For the x = 0.7 composition the sample is slightly overstoichiometric whereas for x > 0.8 the samples are oxygen deficient this anion deficiency results in contraction of the unit cell volume. 

---