50    BINARY AND TERNARY EQUILIBRIA OF CATIONIC ION
EXCHANGE
Richard J. Vamos, Supervising Engineer
DePaul & Associates, Inc.; Chicago, Illinois 60622
Charles N. Haas, Betz Chair Professor
Drexel University, Philadelphia, Pennsylvania 19104
INTRODUCTION
Ion exchange processes are used extensively in water and wastewater treatment. Typical applications of ion exchange are the removal of hardness in drinking water supplies, removal of metals from
rinsewaters, and the production of ultra-pure water for industrial or laboratory use. Most applications of ion exchange are columnar processes which must be designed on the basis of pilot scale
testing, because of the inadequacies of the design equations. The fundamental design equations for
such columnar ion exchange processes require information concerning both the kinetics of the process, and the system equilibrium distribution. Typically, these design equations assume that the
exchanger selectivities for the system's ions are constant. However, it was discovered early on in the
research of ion exchangers that exchanger selectivities typically vary with the composition of the ion
exchanger.1-2 Furthermore, there is little data on the variation of these binary selectivities in ternary or
higher order systems. This data is important, as most applications of ion exchange involve systems
with more than two exchangeable ions. Therefore, to improve the a-priori design of ion exchange
processes, a better understanding of the variation of ion exchange selectivity in binary and ternary
systems is required.
FOCUS
This study focused on modeling the binary and ternary ion exchange equilibria of the Na+ '-Cd + 2-
Cu + 2 system on the strong acid, synthetic ion exchange resin, Dowex 50W-X8. The variation of the
binary and ternary ion exchange selectivities was accounted for by employing resin phase activity
coefficients which varied with resin phase composition. The ability of two different equations using
binary interaction parameters to model the variation of the resin phase activity coefficients with
composition was compared. These equations were the Wilson3 equation, and the Margules4 equation.
Binary equilibrium data was reduced to determine the binary equilibrium constants, and the binary
resinate activity coefficient parameters. Using the binary equilibrium constants and resinate activity
coefficients parameters, predictions of the ternary system equilibrium distribution were made and
compared to the observed ternary data. An error in variables method (EVM) was applied to reduce the
binary and ternary data.
BACKGROUND
Consider the following general binary ion exchange reaction between soluble phase species A, and
B, and an ion exchange resin (Res):
zBARes + zABzB a zABRes + zBAzA (1)
For ion exchange reactions in dilute solutions, it is generally assumed that the free energy change due
to solvent transfer between the solution and the exchanger, and the free energy change due to
exchanger imbibement of co-ions, can be neglected.5 Under these conditions, an equilibrium constant
can be defined for Equation 1 as:
-AG
K "ST" =     fB*ANB*A 7a2b [a*a]»b
e"        C fAZBNAZB 7BA [BZB]*A
46th Purdue Industrial Waste Conference Proceedings, 1992 Lewis Publishers, Inc., Chelsea, Michigan 48118.
Printed in U.S.A.
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