Hydrate enthalpy method

Bashin A A and K Namboodiri 1987. A Simple Method for the Calculation of Hydration Enthalpies c Polar Molecules with Arbitrary Shapes. Journal of Physical Chemistry 91 6003-6012. 

A. A. Rashin and K. Namboodiri, A simple method for the calculation of hydration enthalpies of polar molecules with arbitrary shapes, J. Phys. Chem., 91 (1987) 6003-6012. 

Values for the changes in enthalpy during mutarotation reactions have been obtained by direct determination of the heats of combustion, corrected for heats of solution.196,197 The values thus obtained may be in error due to uncertainty in the heats of solution and of hydration. Enthalpy values may also be calculated from changes of the equilibrium constants with temperature,203,289,290 but, at present, the values may be in error, because of uncertainty as to the proportions of the constituents in the equilibrium. Hence, it is not surprising that, in some instances, there are substantial differences in the values for the thermodynamic constants obtained by the two methods. Some of the most reliable data are reported in Table XIV (see p. 56). 

An alternative method for obtaining thermod)mamic functions of hydration is based upon an arbitrary assignment of a value of Aj,ydIT°(H, g) = 0. From this starting point, and using values of Ahyd f for a range of ionic salts and the hydrogen halides, a self-consistent set of relative hydration enthalpies can be obtained. More sophisticated methods... 

Since DSC is a quantitative technique, the enthalpies determined for reactions can be used for analytical purposes. For instance, a method has been described whereby the water content in hydrate species can be determined using DSC techniques [35]. In this method, it was assumed that the enthalpy of binding n moles of water molecules in a hydrate is the same as that of n moles of water... 

Experimental Ionic Enthalpies of Hydration Obtained By Three Different Methods, in kcal/mole ... 

DSC instruments measure the heat flow into a sample as the temperature is ramped, in comparison to a reference standard. The melting temperature and enthalpy of fusion are quantified. The technique is not suitable for a significant proportion of pharmaceutical compounds because they decompose at the same time as melting. In solvates and hydrates the solvent will evaporate prior to melting which also limits the methods value. Sample size is typically 10 mg. 

CnmcntiniKil enthalpies of hydration of ions are those obtained by the first method, i.e. those using the convention that the enthalpy of hydration of the proton is zero. 

Generally, the first method has been used, and Table 2.9 gives the ionic radii, the radii derived from equation (2.43) from the appropriate values of the enthalpies of hydration, and the differences between the two radii. If an amount between 54 and 79 pm (the mean additive amount is 67 + 8 pm, i.e. one standard deviation) is added to the ionic radii, the Born equalion (2.43) gives realistic values for the absolute enthalpies of hydration of the ions of Table 2.8. 

The alternative method is to bring the equation (2.43) values into agreement with the estimated values of enthalpies of hydration of the same ions by optimizing their ionic charges. This approach yields the apparent charges given in Table 2.I0 for the ions under consideration. 

The same methods are used to estimate the enthalpies of hydration of the + 3 ions of Table 7.5. The appropriate ionic radii of the ions are given in Table 7.7. The radius of the Ga3 + ion (3dl0) is included, as the ion comes at the end of the series in which the 3d orbitals are increasingly occupied. 

After 1900 the direct determination of hydrate number was abandoned in favor of the second, indirect method. The indirect method is still in use today and is based on calculation of the enthalpies of formation of hydrate from gas and water, and from gas and ice. This method was originally proposed by de Forcrand (1902) who used the Clapeyron equation to obtain the heat of dissociation from three-phase, pressure-temperature data, as in the below paragraph. With this more accurate method many exceptions were found to Villard s Rule. The historical summary provided in Chapter 1 indicates that while the number of hydrated water molecules was commonly thought to be an integer, frequently that integer... 

Table 4.10 shows the literature values for hydrate numbers, all obtained using de Forcrand s method of enthalpy differences around the ice point. However, Handa s values for the enthalpy differences were determined calorimetrically, while the other values listed were determined using phase equilibrium data and the Clausius-Clapeyron equation. The agreement appears to be very good for simple hydrates. Note also that hydrate filling is strongly dependent on... 

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