Page 337 - Water and wastewater engineering

8-6 WATER AND WASTEWATER ENGINEERING

For the cation exchange of calcium and sodium expressed in Equation 8-2 , the equilibrium constant
would be expressed as

2
C ( Na ) q Ca
Ca
K (8-7)
Na 2
C ( q )
Ca
Na
The greater the selectivity coefficient ( K ), the greater is the preference for the ion by the
exchange resin. Commercial exchange resins used in water treatment tend to prefer (1) ions of
higher valence, (2) ions with smaller solvated volume, (3) ions with greater ability to polarize,
(4) ions that react strongly with the exchange sites on the resin, and (5) ions that do not form
complexes (Helfferich, 1962).
For process design evaluation, separation factors are used rather than selectivity coefficients.
The binary separation factor is a measure of the preference of one ion for another ion. It may be
expressed as
i YX j
i
(8-8)
j
i j
XY
i
where j separation factor
Y i resin phase equivalent fraction of counterions
X j equivalent fraction of presaturant ion in aqueous phase
X i equivalent fraction of counterion in aqueous phase
Y j resin phase equivalent fraction of presaturant ion

The equivalent fraction in the aqueous phase is calculated as

X i C i (8-9)
C T

and

C j
X j (8-10)
C T

where C T total aqueous ion concentration
C i aqueous phase concentration of counter ion, eq/L
C j aqueous phase concentration of presaturant ion, eq/L
Similarly, for resin phase

q i
Y i (8-11)
q T