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108 CHAPTER 2

difference in their absolute heats of hydration is obtained by
subtracting Eq. (2.53) from Eq. (2.52). Since the signs of the dipole term,

the Born charging term,

and the induced dipole term,

are invariant with the sign of the charge of the ion, they cancel out in the subtraction
(as long as the orientation of a dipole near a cation is simply the mirror image of that
near an anion). The quadrupole term, however, does not cancel out because it is
positive for positive ions and negative for negative ions. Hence, one obtains 29

It is seen from this equation that the quadrupolar character of the water molecule would
make oppositely charged ions of equal radii have radius-dependent differences in their
heats of hydration (Fig. 2.32). Further, Eq. (2.38) has given

By combining Eqs. (2.38) and (2.54), the result is

Thus, the ion–quadrupole model of ion–solvent interactions predicts that if the
experimentally available differences in the relative heats of
solvation of oppositely charged ions of equal radii r i are plotted against one
should get a straight line with a slope From Fig. 2.36, it can be seen that

29
Expression (2.54) is based on the assumption of the radius independence of
–1
(gram ion) and the constancy of n with radius over the interval concerned.