Partition of a microcomponent (C) between solid solution consisting of two macrocomponents (A) and (B), and aqueous solution has been formulated as,
In D
CAB=x
AInP
CA+(1-x
A)InP
CB + (x
A-α)InD
AAB+g
EAB/RT
where D
CAB represents the partition coefficient of microcomponent C of a solid solution, (A, B)N; P
CA and P
CB stand for the coefficients of C between AN (or BN) and aqueous solution, respectively, referred to the asymmetrical standard state system; D
AAB is the coefficient of A between BN and solution, referred to the symmetrical standard state system; g
EAB is the excess free energy of mixing for the solid solution, (A, B)N, which is here assumed to be a regular solid solution; x
A is the mole fraction of A in the solid solution; α is the parameter of substitution of any A in the solid for a C in aqueous solution in the following ion ex- change equilibrium,
C
aq+αAN
ss+(1-α)BN
ss=αA
aq+(1-α)B
aq+CN
ss where subscripts, aq and ss, refer to aqueous and solid solution phases, respectively. The value of can be obtained from
a/(1-α)=(k
fAC)/(k
fBC)•(x
A)/(1-x
A)=(k
bAC)/(k
bBC)•(y
A)/(1-y
A) (0≤α≤1)
where k
fAC and k
fBC represent the second order forward rate constants, and k
bAC and k
bBC, the corresponding backward rate constants of the following ion exchange equilibrium,
[numerical formula]
and y
A represents the mole fraction of A in solution. These formula were applied to ion exchange equilibrium systems with a cation exchange resion and aqueous phase.
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