EQUILIBRIUM DISTANCE (l ^ FROM ^j 271 



made for three cases: (a) assuming the water shell does not enter into the 

 closest approach, in which case Tq = 3.0 A and x may be taken as 0.133 

 as derived above; (6) assuming the atmosphere ions and the involved ions 

 do not lose their primary hydration, in which case r^ = 10.2 A (diameter 

 of two water molecules being 7.2 A) and x can be taken as 12, since it 

 must be somewhat larger than Tq, and (c) neglecting the ionic atmosphere 

 entirely, which would apply when the ionic strength is very low or when 

 the charged group is within a large inhibitor molecule and uninfluenced 

 by the free ions in the solution. The energy equation for the first case 

 may be written as: 



199go.i33(3-d_^) 291e«-i33<^-<*e' 1652 , ,, , 



kcal/mole (6-110) 



d,{Qd, - 7) de*iQde - 1)- d, 



and similar equations may be written for the other situations. The energy 

 contributed by each type of interaction at various distances for the three 

 cases considered are shown in Table 6-18 and the total interaction energy 

 is calculated. Figure 6-16 shows the variation of qc^ or AF with the equili- 

 brium distance. This is not a potential energy-distance plot in the ordinary 

 sense, but gives the conditions only at equilibrium separation. From these 

 curves one may determine d^ from the experimental value of AF. It may 

 be seen that whichever assumption is made regarding the closest approach 

 of the ionic atmosphere, there is not a great difference in the results, ex- 

 cept at low interaction energies when the equilibrium distances will differ 

 by as much as 1 A. Preference here will be put on curve B since it is likely 

 that the atmosphere ions approach the interacting ions at their closest 

 with two layers of water molecules between them. The — NHg"^ and —COO 

 ionic groups, however, can lose their hydration layers upon interaction. 

 These curves will be applied to experimentally determined interaction 

 energies in the following sections. 



George (1959) suggested that there are two types of association between 

 ions in aqueous solution. In the first type there is a loss of the hydration 

 water in the association process, in which case the entropy change is 

 related to the entropy of hydration. This appears to apply to associations 

 of cations with singly-charged anions, such as CF, Br", F", 0H~, and HCOg . 

 In the second type the association does not involve a loss of the hydration 

 water and the various entropy and energy terms that are related to the 

 hydration are not so important. This would apply more particularly to 

 the doubly charged cations and anions, such as'the sulfates of Mg"^"*", Ca"^"^, 

 Ba"^"*", and Pb"*""^. It was felt that a simple coulombic treatment might be sat- 

 isfactory for associations of the second type, but that the disturbances in 

 water structure occurring in associations of the first type would complicate 

 the situation. Yet Eigen (1957) from the relaxation spectra of 2:2 electro- 

 lytes in aqueous solution had concluded that specific ionic interactions 



