Titration calorimetry equilibrium constants

A primary use of titration calorimetry is the determination of enthalpies of reaction in solution. The obtained results may of course lead to enthalpies of formation of compounds in the standard state by using appropriate thermodynamic cycles and auxiliary data, as described in chapter 8 for reaction-solution calorimetry. Moreover, when reactions are not quantitative, both the equilibrium constant and the enthalpy of reaction can often be determined from a single titration run [197-206], This also yields the corresponding ArG° and ATS° through equations 2.54 and 2.55. 

Figure 11.4 Results of a hypothetical titration calorimetry study of the reaction A(aq) + B(aq) AB(aq), showing the dependence of the curve shape on the values (a) of the equilibrium constant for ArH° — 100 kj mol-1, and (b) of the enthalpy of reaction, for Kc = 100 (see text).

Isoperibol titration calorimetry was also extensively used by Drago s group [215] to determine enthalpies and equilibrium constants of a variety of reactions where acid-base adducts are formed. These results are the source of Drago s ECW model, which has been widely used to rationalize chemical reactivity [216-218]. 

J. J. Christensen, J. Ruckman, D. J. Eatough, R. M. Izatt. Determination of Equilibrium Constants by Titration Calorimetry Part I, Introduction to Titration Calorimetry. Thermochim. Acta 1972, 3, 203-218. 

Thus, the left side of Equation (12.23) is the result of a titration calorimetry experiment, and the right-hand side includes experimental quantities and the equilibrium constant K and AH. Therefore, the parameters AH and K can both be obtained by a nonlinear, least-squares fitting of the data to the relation that we have derived... 

Titration calorimetry depends on calculation of the extent of reaction from the quantity of heat evolved. Its successful application to a given system depends on (a) the equilibrium constant and the reaction conditions being such that the reaction occurs to a moderate extent (i.e., not to completion) and (b) the enthalpy of reaction being measurably different from zero. 

Titration calorimetry has been successfully employed in the determination of thermodynamic parameters for complexation (Siimer et al., 1987 Tong et al., 1991a). The technique has the advantage of employing direct calorimetric measurements and has been proposed as the most reliable method (Szejtli, 1982). It should be noted that the information derived from multistep series reactions is macroscopic in nature. In contrast to spectrophotometric methods that provide information concerning only the equilibrium constant(s), titration calorimetry also provides information about the reaction enthalpy that is important in explaining the mechanism involved in the inclusion process. 

Instead, a wide variety of spectroscopic and electrochemical titration methods are often employed to determine the equilibrium constants for a molecular recognition process at several different temperatures, which are then analyzed by the van t Hoff equation to give the thermodynamic parameters for the process. However, there is a critical tradeoff between the accuracy of the value obtained and the convenience of the measurement since the thermodynamic parameters, evaluated through the van t Hoff treatment, do not take into account the possible temperature dependence of the enthalpy change, i.e. heat capacity, and are less accurate in principle. In fact, it has been demonstrated with some supramolecular systems that the van t Hoff treatment leads to a curved plot and therefore the thermodynamic parameters deviated considerably from those determined by calorimetry.3132 Hence one should be cautious in handling thermodynamic parameters determined by spectroscopic titration and particularly in comparing the values for distinct systems determined by different methods. 

Eatough, D. J., Christensen, J. J., and Izatt, R. M. (1972a). Determination of equilibrium constants by titration calorimetry. II. Data reduction and calculation techniques. Thermo-chim. Acta 3, 219-232. 

Titration calorimetry was used to determine values of log,g K, A //° and AjS°, reported for the formation of NiS04(aq) for 25°C and 7 = 0. The data analysis is suspect because of a possible correlation between the value for the calculated equilibrium constant and the enthalpy of association. A good reassessment was reported by Powell [73POW], who pointed out that if the data of Izatt et al. were used with the association constant at 298.15 K set equal to the value from Nair and Nancollas [59NAI/NAN], then an enthalpy of ion-pair formation of 5.7 to 5.9 kJ-mol was obtained, not the reported 1.7kJ mol [691ZA/EAT]. 

Isothermal titration calorimetry (ITC) is almost the ultimate titration methodology in that this technique is based entirely upon titration of heat energy and then deconvolution of this information into equilibrium binding constant information. However, the real beauty of this technique is that it engages directly with the thermodynamics of receptor-ligand binding interactions. 

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