CHAPTER 1 • Sea Water as an Electrolyte
Fig. 1.17. The volume of electrostriction for ions in water
Electrostricted
region
21
compressible (oV(int) / oP = -K(int) = 0), one can determine the number of water
molecules hydrated to a given ion by:
V(elect) = h(VE - VB)
(1.26)
where h is the hydration number, VE is the volume of water in the electrostricted region and VB is the volume of bulk water (18.015 cm 3 mor l ).
The differentiation of Eq. 1.26 yields the compressibility of electrostriction:
K(elect) = K(ion) = -oV(elect) / oP = h(oV B / oP) = -hV B f3s
(1.27)
where f3s = -(1/ V B)(OV B / oP) (45.25 X 10- 6 bar-I). By rearranging Eq. 1.27, one has:
h = -K{ion) / VBf3s
(1.28)
Combining equations we have:
V(elect) = -[VE - VB) / VBf3s1K(ion) = -kK(ion)
(1. 2 9)
A plot of V(elect) as a function of K(ion) is shown in Fig. 1.19 and yields a value of
k = 5000 bar, which is in reasonable agreement with the continuum model (4800 bar).
This value of k yields a value of VE - VB = -3.9 cm 3 mOrl. Using VB = 18 cm 3 mor\ we
obtain V E = 14 cm 3 mor l for the volume of waters in the hydrated region. This is larger
than the crystal volume of 6.6 cm 3 mor l or the volume corrected for packing
of 11.8 cm 3 mOrl. This means that the water molecules in the electrostricted region
are not tightly packed. Hydration numbers calculated from Eq. 1.26 yield values
of 3 to 4 for monovalent ions, 6 to 9 for divalent ions and 15 for trivalent ions (Millero
1996 ).
Fig. 1.17. The volume of electrostriction for ions in water
Electrostricted
region
21
compressible (oV(int) / oP = -K(int) = 0), one can determine the number of water
molecules hydrated to a given ion by:
V(elect) = h(VE - VB)
(1.26)
where h is the hydration number, VE is the volume of water in the electrostricted region and VB is the volume of bulk water (18.015 cm 3 mor l ).
The differentiation of Eq. 1.26 yields the compressibility of electrostriction:
K(elect) = K(ion) = -oV(elect) / oP = h(oV B / oP) = -hV B f3s
(1.27)
where f3s = -(1/ V B)(OV B / oP) (45.25 X 10- 6 bar-I). By rearranging Eq. 1.27, one has:
h = -K{ion) / VBf3s
(1.28)
Combining equations we have:
V(elect) = -[VE - VB) / VBf3s1K(ion) = -kK(ion)
(1. 2 9)
A plot of V(elect) as a function of K(ion) is shown in Fig. 1.19 and yields a value of
k = 5000 bar, which is in reasonable agreement with the continuum model (4800 bar).
This value of k yields a value of VE - VB = -3.9 cm 3 mOrl. Using VB = 18 cm 3 mor\ we
obtain V E = 14 cm 3 mor l for the volume of waters in the hydrated region. This is larger
than the crystal volume of 6.6 cm 3 mor l or the volume corrected for packing
of 11.8 cm 3 mOrl. This means that the water molecules in the electrostricted region
are not tightly packed. Hydration numbers calculated from Eq. 1.26 yield values
of 3 to 4 for monovalent ions, 6 to 9 for divalent ions and 15 for trivalent ions (Millero
1996 ).