Page 338 - Water and wastewater engineering

ION EXCHANGE 8-7

and

q j
Y j (8-12)
q T

where q T total exchange capacity of resin, eq/L.

Because a binary system involves only the presaturant ion and one other ion to be exchanged,

CT Ci C j (8-13)

and
q T q i q j (8-14)

Separation factors for commercially available strong acid cation exchange resins are given
in Table 8-1 .
A combination of Equations 8-7 and 8-8 yields

⎛
T
Ca K Ca qY Na ⎞ (8-15)
Na Na ⎜ ⎝ CX ⎟ ⎠
T Na
The implication of this equation is that, with q T constant, divalent/monovalent exchange
depends inversely on solution concentration and directly on the distribution ratio Y Na / X Na
between the resin and the water. The higher the solution concentration C T , the lower the
divalent/monovalent separation factor; that is, the selectivity tends to reverse in favor of the
monovalent ion as ionic strength (that is, a function of C ) increases. This is the theoretical
basis for regeneration of the cation exchange resin by the application of a high concentration
of sodium.
Rearrangement of Equation 8-8 with appropriate substitution of terms yields an expression
that allows the calculation of the resin phase concentration of the counterion of interest if the
binary separation factor and total resin capacity are known.

Cq
q i T
i j (8-16)
C C
i j i
j
i
where a i 1/ j .
The use of this expression in estimating the maximum volume of water that can be treated by
a given resin is illustrated in Example 8-1 .