CHAPTER 1 . Sea Water as an Electrolyte
19
to a solution that has no structure (Fig. 1.15). The free energy, enthalpy and entropy of
transferring an ion for a vacuum to the solution can be determined from the equations:
LlG h (kcal mot l ) = _(Ne 2 Z 2 / 2r)(1- 1 / D) = -163.9Z2 / r
(1.21)
Mi h (kcal mor l ) = (Niz2/ 2r)[l - 1/ D - T / D(alnD / aT)p] = -166.8Z 2 / r (1.22)
LlSh (cal mot l K- l ) = (Ne 2 Z 2 / 2r)(alnD / aT)p= -9.65Z 2 / r
(1.23)
where D is the dielectric constant, N is Avogadro's number, r is the radius (A = 1 X 10- 8 cm),
Z is the charge, e is the electrostatic charge, T is the absolute temperature and P is the
pressure. The free energy of hydration for a number of cations as a function of Z2/r is
shown in Fig. 1.16. The agreement is reasonable, but is better if the radius is increased
by 0.85 A. This can be attributed to the average inter-sphere radius of the firmly bound
waters of hydration. The ion-dipole and quadrupole models attempt to account for
the interactions of water molecules with individual ions. A more simplistic model can
be developed by examining the differences in the properties of the water molecules in
the electrostricted region (Fig. 1.17) and the waters in the bulk solution. One can look
at the electrostriction as the region where the volume is decreased due to the interactions of the water molecules with a given ion. If one uses the continuum model, the
volume of electrostriction (cm 3 mor l ) is given by:
V(elect) = (Ne 2 Z 2 / 2Dr)(alnD / ap}y= -4.2Z 2 / r
(1.24)
One can model the partial molal volume of an ion in water as being composed of
two components:
V(ion) = V(int) + V(elect) = a? + bZ 2 / r
(1.25)
where the V(int) is related to the size of the ion in space = (4/3)Nllf = 2.52?, with r in
A and V(elect) = -4.2Z2/ r. The fit of the measured values of V(ion) as a function of
Z2/r in Fig. 1.18 gives values of a = 4.48 and b = -8. These values are larger than those
Fig. 1.15. The hydration of an
ion
Vacuum
Solution
Na+
19
to a solution that has no structure (Fig. 1.15). The free energy, enthalpy and entropy of
transferring an ion for a vacuum to the solution can be determined from the equations:
LlG h (kcal mot l ) = _(Ne 2 Z 2 / 2r)(1- 1 / D) = -163.9Z2 / r
(1.21)
Mi h (kcal mor l ) = (Niz2/ 2r)[l - 1/ D - T / D(alnD / aT)p] = -166.8Z 2 / r (1.22)
LlSh (cal mot l K- l ) = (Ne 2 Z 2 / 2r)(alnD / aT)p= -9.65Z 2 / r
(1.23)
where D is the dielectric constant, N is Avogadro's number, r is the radius (A = 1 X 10- 8 cm),
Z is the charge, e is the electrostatic charge, T is the absolute temperature and P is the
pressure. The free energy of hydration for a number of cations as a function of Z2/r is
shown in Fig. 1.16. The agreement is reasonable, but is better if the radius is increased
by 0.85 A. This can be attributed to the average inter-sphere radius of the firmly bound
waters of hydration. The ion-dipole and quadrupole models attempt to account for
the interactions of water molecules with individual ions. A more simplistic model can
be developed by examining the differences in the properties of the water molecules in
the electrostricted region (Fig. 1.17) and the waters in the bulk solution. One can look
at the electrostriction as the region where the volume is decreased due to the interactions of the water molecules with a given ion. If one uses the continuum model, the
volume of electrostriction (cm 3 mor l ) is given by:
V(elect) = (Ne 2 Z 2 / 2Dr)(alnD / ap}y= -4.2Z 2 / r
(1.24)
One can model the partial molal volume of an ion in water as being composed of
two components:
V(ion) = V(int) + V(elect) = a? + bZ 2 / r
(1.25)
where the V(int) is related to the size of the ion in space = (4/3)Nllf = 2.52?, with r in
A and V(elect) = -4.2Z2/ r. The fit of the measured values of V(ion) as a function of
Z2/r in Fig. 1.18 gives values of a = 4.48 and b = -8. These values are larger than those
Fig. 1.15. The hydration of an
ion
Vacuum
Solution
Na+