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222 CHAPTER 2

Fig. P2.2

24. (a) Calculate the dipole moment associated with water in the hypothesis of fully
ionic OH bondings (i.e., considering a –2e charge on the O atom and a + 1e
charge on each H atom; e = elementary charge taken without sign). Draw the
associated vector (refer to Fig. P2.2). (b) Knowing the dipole moment of water,
write down an equation expressing it in terms of f the fractional charge on either
end of the dipole and x the distance between the center of charge and the atomic
nucleus. (c) Determine f and x in the hypothesis of a tetrahedrical angle HOH
and draw the corresponding vector T. (Mussini)

25. (a) Write an expression for the potential in a point P of the electric field created
by a dipole. (b) Then write an expression for the potential energy of the
ion–dipole interaction. (c) Calculate the potential energy, of an ion-dipole
interaction (in between water and a z-valent cation, as
a function of the distance r, the ion charge the angle I and the relative
permittivity (d) Perform a complete calculation for the limiting cases
r = 2 Å, and r = 6 Å, Assume that the relative positions
are as in Fig. P.2.3 and the negative end of the water dipole faces the positive
ion. (e) Assuming the intermediate values to increase exponentially, draw a
complete versus r characteristic in the interval 2 < r < 6, and mark the region

Fig. P2.3