Reversibility Thermodynamic and Kinetic Analysis

The dissociation of hydrogen ions from the model compounds discussed in Section II is ordinarily a very rapid reversible reaction. Measurements by ordinary methods represent thermodynamic equilibrium. They are independent of time and independent of the direction in which the reaction is carried out. 

Large sections of protein titration curves are often equally time-independent and reversible, as, for instance, the acid part of the titration curve of (3-lactoglobulin shown in Fig. 2. Any such section of the titration curve will again represent thermodynamic equilibrium and it may be subjected to thermodynamic analysis, as outlined in Sections VI and VII. 

On the other hand, a titration curve may depend on the time between addition of acid or base and the pH measurement (as in the alkaline branch of Fig. 2). When this happens, the curve will also in general be irreversible. 

A titration curve may appear to be time-independent but irreversible, especially if a continuous titration method is employed in which successive increments of acid or base are added to the same solution for each successive pH measurement. A hypothetical example is shown in Fig. 8. When this situation occurs, a careful rerun of the curve, in which each experimental point is obtained with an entirely fresh solution, will usually show time-dependence, as shown by curves 3, 4, and 5 of Fig. 8. 

In many time-dependent situations a zero-time reversible curve (curve 6 of Fig. 8) may be obtained, i.e., reversed points obtained by keeping a solution at an extreme pH for various lengths of time, and then extrapolating to zero time of exposure to the extreme pH, may coincide with a forward titration curve, each point of which also represents an extrapolation to zero time. 

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