148
Chemical Oceanography, 4th Edition
K elect
NZ e Dr
lnD P T
lnD P
o (
)   (
) (
)
(
=
∂
∂
− ∂
∂
2 2
2
2
/
/
/ ) )
.
T
Z r
2
4 2
8 31 10
 
  = −
×
−
/
(4.21)
Similar differentiation of the solution component of Equation 4.16 with respect to temperature yields the electrostatic partial molal entropy (–∂G o /∂T = S o ) and heat capacity
–∂(S o /∂T)/∂T = ∂H o /∂T = C o
P .
S o (elect) = (NZ 2 e 2 /2Dr)(∂lnD/∂T) P = –9/65Z 2 /r
(4.22)
C elect
NZ eT
Dr
lnD T
lnD
P
o
P
(
)   (
) (
) (
=
∂
∂
− ∂
2
2
2
2
2
/
/
/ /
/
∂
 
  = −
T
Z r
P
)
.  
2
2
12 96
(4.23)
The partial molal properties of ions in solution contain a minimum of two terms, an intrinsic contribution and an electrical contribution. For example, for the partial molal volume
of an ion, we have
V o (ion) = V o (int) + V o (elect)
(4.24)
where the intrinsic partial molal volume V o (int) is equal to the size of the ion, V o (cryst) =
(4πN/3)r 3 = 2.52 r 3 (when r is expressed in Å units) plus the packing effects, and the electrostriction partial molal volume V o (elect) is the decrease in volume caused by ion–water
interactions. Thus, to plot the various partial molal properties versus Z 2 /r, one must estimate the intrinsic term. For V(int), one can use the semiempirical values from
V o (int) = 4.48 r 3
(4.25)
while for S o (int), one can use
S o (int) = 3/2 ln[AW]
(4.26)
–∆H°h (kcal mol
–1
)
380
400
420
440
460
480
500
520
540
Ca
Mn
Fe
Co
Ni
Cu
Zn
Figure 4.17
Values of the enthalpy of hydration for the transition metals.