HYDRATION OF IONS 253 



calculate the hydration energy: the interaction energy of the ion with water 

 molecules outside the primary layer and the energy required to disrupt 

 the water structure — these are difficult to estimate accurately. From 

 the expression derived by Moelwyn-Hughes (1949), assigning D = 3, the 

 interaction of the ion with water molecules outside the primary layer re- 

 sults in a potential energy of — 5.6 kcal/mole; using Eq. 6-58 and assuming 

 interaction with ten water molecules outside the primary layer results 

 in — 7.0 kcal/mole. If it is assumed that the six water molecules in the 

 primary layer have each lost one of their interactions with neighboring 

 water molecules, the energy required would be + 13.3 kcal/mole. Thus 

 approximately + 7.0 kcal/mole must be added to the sum obtained from 

 individual interactions, giving — 71.7 kcal/mole for the over-all potential 

 energy. If this can be equated with the experimental hydration energy 

 of — 75.8 kcal/mole, it may be concluded that this treatment has led to 

 at least the right magnitude and indicates the relative importance of 

 the different interactions. Moelwyn-Hughes (1949) has calculated hydra- 

 tion energies of several ions by a similar method, neglecting dispersion 

 energy and disruption of water structure and assuming that the repulsion 

 energy varies with d^~^, and has arrived at values close to the experimental 

 ones. It may be observed that the calculations within the primary water 

 layer assumed a value of D = 1; the correspondence between the results 

 and the experimental values indicates that this assumption is valid for 

 interactions at small distances. Perhaps the principal value of such calcu- 

 lations lies in the resulting appreciation of the inadequacies of our know- 

 ledge and the stimulus this gives for theoretical and experimental advances 

 in interactions at the molecular level. 



It has been stated that the K"*" ion is close to the size of the water mol- 

 ecule and hence probably enters substitutionally into the water structure 

 without disturbing the structure (Brady and Krause, 1957). However it 

 is not the size of the ion that is most important but its charge and the orient- 

 ing effect the ionic field has on the surrounding water molecules. The al- 

 teration in water structure brought about by such ions is attested by 

 electrostriction. 



Two other treatments of the hydration energy will be mentioned because 

 they illustrate the relative contributions made by the various interactions 

 and also show how different approaches and assumptions can lead to sim- 

 ilar results. Buckingham (1957) assumed a hydration number of four 

 for the univalent ions and an orientation of the water wherein the dipole 

 is on a line with the center of the ion. The total interaction energy was 

 written as the sum of a variety of terms representing the different forces 

 involved: 



fP = (Pdiv + ^Quad + Vi + fd + (Pl + fPo + fPh + (Pr (6-77) 



The subscripts refer to the following: 9?^,^ to the ion-dipole interactions, 



