Van’t Hoff method

The temperature dependences of solubilities of the trichlorides of lanthanum, praseodymium, and neodymium in aqueous ammonium chloride solutions (212) are so irregular that no estimate of solution enthalpies can be made from them by the van t Hoff method. 

Except for the direct van t Hoff method, the enthalpies of dihydrogen bonds can be estimated from the frequency shifts, Av (HX), or the integral intensity, A (XH), determined in the IR spectra for proton-donor components, HX ... 

As has been shown experimentally, the relationships 4.4. 6 can be used successfully for dihydrogen-bonded complexes [24]. In addition, despite their approximate character, they lead to enthalpy values that are usually close to those determined by van t Hoffs method. For example, applying eq. (4.4) to equilibrium equation (4.3) gives a —AH° value of 6.6 kcal/mol versus the 6.7 kcaFmol found using van t Hoffs method. 

Figure 16.9 The ratio of the effective calorimetric enthalpy to the enthalpy calculated by the van t Hoff method from optical measurements, plotted against the temperature of denaturation. The symbols represent the following proteins , metmyoglobin A, ribonuclease O, cytochrome c O, a-chymotrypsin , lysozyme. Reproduced by permission from P. L. Privalov, Adv. Prot. Chem., 33, 167 (1979).

Figure 3.29 shows the dissolution profile obtained during a solubility experiment for the amorphous form of a development compound. The initial dissolution of the compound is high but falls as the compound crystallizes and the equilibrium reaches that of a crystalline form of the compound. By measuring the solubility of polymorphs, the thermodynamic quantities involved in the transition from a metastable to a stable polymorph can be calculated. Experimentally, the solubilities of the polymorphs are determined at various temperatures, and then the log of the solubility is plotted against the reciprocal of the temperature (the van t Hoff method). A straight line results (the problem of non-linearity has been dealt with by... 

In view of the problems we have just seen which may arise in the determination of the heats of ionization of weak bases by the van t Hoff method, it is natural to consider whether these values might not be determined calorimetrically. Obviously, this cannot be done directly in dilute aqueous acid (the standard state) because weak bases are by definition not ionized in this medium. Unfortunately, there is no way that we know of to use free energy-enthalpy extrapolations across a range of aqueous acid solutions to estimate... 

The unconventional character of MH—HX hydrogen bonding demands the validity of equations (7) and (8) to be tested. Therefore, we calculated -AH values by van t Hoffs method, from H-bonds formation constants (KfOf Eq. 5) determined from the characteristic band intensity changes at different temperatures. The linear correlation equation between the logarithm of the formation constants and 1/T allows the calculation of the enthalpy (Eq. 9) and entropy values. 

In the van t Hoff method, the cmc of a surfactant is measured at different temperatures and the energetic parameters can be evaluated by the mass-action and pseudo-phase models (Attwood Florence, 1983, Moroi, 1992, Moulik et al, 1996, Chaterjee et al, 2001, 2002, Dan et al, 2008, 2009). For calculating thermodynamic parameters, we have used the following equations ... 

As described in Section 2, the concentration dependence of the provides an alternative van t Hoff method for determining thermodynamics. In this method, the transition AH and AS are obtained by equation 4 from the slope and intercept of a 1/Tm against lnCx/4 plot. Since the Tm is relatively insensitive to non-two-state behaviour and to the choice of baselines, 1/Tm versus logCj plots provide very reliable AH , AS , and AG s7 parameters (16), particularly if... 

Fig. 7.11 Grapliic determination of adsorption enthalpy and entropy from isothermal adsorption data measured at various temperatures, a Van t Hoff method applied to the adsorption equilibrium constant deduced from the parameter of a thermodynamic model like Henry or Langmuir fitting well the adsorption isotherms, h Clausius-Clapeyron or isosteric method the isosters he below a limit Une, which corresponds to the liquefaction equihbrium of the adsorptive...

Table 7.2 Comparison of adsorption enthalpies of p-xylene and m-xylene on NaY measured by calorimetry and estimated from adsorption isotherms using the Van t Hoff method...

---