Selective Salt Recovery from Reverse Osmosis Brine - University of ...

chemical equation, in principle it has a thermodynamic significance and can represent
equilibria at high ionic strength.
For systems in which ions of the same valence are being exchanged, the
separation factor and the selectivity coefficient are identical. In systems in which the
valances of the exchange ions are different, Equation 5 can be used to convert between
the two.
Equation 2: Separation Factor, α (Equivalent based)
Equation 3: Ion Exchange Chemical Reaction ZA ZB ZB ZA
z RA + z B → z RB + z A
B A A B
Equation 4: Selectivity Coefficient Z
ZA ZB
B ZA
Equation 5: Conversion Between Separation Factor
and Selectivity Coefficient ( α )
K
( X ) × ( X )
α =
( X ) ×
( X )
B
A
Z
Z
Z
Z
9
B
A
B r A S
A r B S
⎡RB⎤ ⎡A⎤ =
⎣ ⎦ ⎣ ⎦
⎡
⎣
B ⎤
⎦
⎡
⎣
RA ⎤
⎦
A B
B A
Z −Z
B A
ZB
Z ⎛⎡RB⎤⎞ B B B
A = K ⎜⎣ ⎦⎟
A Z ⎜ B ⎟
⎡
⎣
B ⎤
⎝ ⎦ ⎠
Ion exchange resin selectivity is complicated by its dependence on several
parameters, but there are some general trends that can be recognized. Resins tend to have
more affinity for ions with greater charge due to increased electrostatic attraction. For
ions of equal charge, ions with a smaller hydrated radius are preferred. Hydrated radius
is dependent on the size to charge ratio of the ion. Larger ions have a greater surface area
over which to distribute charge density which reduces the field strength. For this reason,
they do not coordinate with water molecules as strongly as ions with smaller size to
charge ratios, which tend to have larger relative hydrated radii [5, 7]. This physical
explanation fits well with thermodynamic data from Marton [8] showing the dependence
of parameters go and g1 (which affect resin phase molar excess free energies) from
Equation 9.
The effect of ionic strength on selectivity can be difficult to predict due to
competing processes. When higher concentrations of ions exist in solution, neutral