By Peter Meyers
Summary: Water softening is an inherently efficient process. This is true for the service cycle, where sodium ions on the resin are exchanged for hardness ions in the water. And, unlike most chemical reactions, it’s true during the reverse exchange, or regeneration, where sodium ions in the brine are swapped for hardness ions on the resin. Few chemical processes are efficient in both directions. The reason for water softening efficiency is a phenomenon called selectivity reversal that’s caused by changes in the solution concentration when the ion exchange reaction involves ions of unequal valence. The principal of selectivity reversal underlies all ion exchange theory and is the science behind the art of softening water.
This article has been divided into two parts. Part 1 is presented here and Part 2 will be in next month’s issue. Part 1 concentrates on the qualitative theory, while Part 2 focuses on mathematical relationships of water softening. The theory of selectivity reversal isn’t “intuitively obvious” and can be difficult to master. Keep in mind that low total dissolved solids (TDS) favor divalent hardness ions while high TDS favors monovalent ions such as sodium. In water softeners, cation exchange resins remove hardness very efficiently when the TDS is low, and regenerated efficiently when the TDS is very high.
When salts such as sodium chloride (NaCl) dissolve into water, they form ions. Ions are atoms (or groups of atoms) with a different number of electrons than protons. Ions that lose electrons carry a positive charge and are called cations, while those that gain electrons carry a negative charge and are called anions. Overall, a solution of dissolved salts must contain the same equivalent number of cations as anions—the total number of electrons and protons is always equal. Solutions that contain excess hydrogen ions (H+) are called acidic, while solutions that contain hydroxide ions (OH-) are called basic. Large numbers of hydrogen and hydroxide ions cannot co-exist in water because they combine to form water molecules (H+ + OH- = HOH or H2O). “Valence,” which is the difference between the number of electrons and protons in an ion, is used to describe the combining—or attractive—capacity of a substance such as an ion. Monovalent ions have a single electron charge and divalent ions have a double electron charge.
In nature, all things seek balance—so when an element has an unbalanced charge, it seeks to attract or release that which brings it into balance. Thus, when we perform calculations using the number of ions in a solution, we need to make certain we account for the same number of electrons as protons. When comparing the concentration of various ions in solution, this needs to be expressed in terms of the number of ions—and/or the equivalent number of electron differences. In chemistry, we use the term “molarity” to describe the number of ions and “normality” to describe the number of electron differences. Molarity (M) is equal to concentration of a substance in grams per liter (g/L) of solution, divided by molecular weight of the substance. Normality (N) is defined as the concentration of a substance in g/L of solution, but divided by that substance’s valence and its molecular weight.
Ion exchange selectivity
Ion exchange resins are solid plastic materials with acidic or basic properties. Cationic resins are anionic in nature and have a permanent negative charge. The negative charge needs to be balanced by an equal positive charge. Thus, a cation resin attracts cations (and conversely, an anion resin is cationic—or has a positive charge—and attracts anions).
A resin’s preference for one ion over another is called selectivity. Ion exchange selectivity increases with an upward shift in swelling pressure, hydrated ionic radius and valence. We can observe and predict selectivity with some degree of accuracy, though an exact mathematical model of selectivity has never been mastered. The numerical expression of the selectivity coefficient defines the preference of an ion exchange resin for one ion compared to another. This expression can be manipulated mathematically in comparison to other mass action relationships—solubility products, for example (see Figure 1).
The presentation of the formulas is a little scary. We’ll save it for Part 2 of this discussion. Meanwhile, keep in mind that the math is the dream of theoretical scientists who could fill a chalkboard with equations. Manipulation of the selectivity formula itself isn’t terribly important nor necessary for understanding how a water softener works. However, the model’s best feature is it demonstrates the theory of selectivity reversal, which is fundamental to understanding why ion exchange softening works efficiently.
As long as the valences of both ions involved in an ion exchange reaction are the same, the concentration units cancel each other out. Only the ratio of ions is important to the selectivity coefficient. The TDS of the solution and of the resin aren’t factors in the selectivity relationship. If the valence of the ions is different (for example, if one ion is monovalent and the other is divalent), however, then both the total concentration of ions in solution (TDS) and the capacity of the resin become factors in the selectivity calculation. For exchanges of unequal valence, the TDS of the solution and of the resin both play a major role in the calculation of selectivity.
The term coined to describe the relationship that exists for a constant TDS in an exchange involving divalent (hardness) ions for monovalent (sodium) ions is “apparent selectivity.” The apparent selectivity—for hardness over sodium—for a given resin decreases as the TDS increases. The difference between the selectivity coefficient and apparent selectivity can be quite dramatic, as illustrated in Figure 2.
Of course, the problem with an ion the resin likes a lot is how to get that ion off the resin during regeneration using some other ion the resin doesn’t like as much. If hardness easily displaces sodium from the resin during the service cycle, then pushing hardness back off the resin with sodium during the regeneration cycle will be difficult unless we can reduce the resin’s preference (selectivity). We can reduce the selectivity the selectivyt for hardness by using higher brine concentrations during the regeneration cycle.
Again, we take up the case of water softening. During regeneration, we use monovalent sodium ions (from the sodium chloride or Na+ + Cl-) to drive divalent calcium ions (Ca+2) off the resin. If we try to do this at a low TDS, the exchange is very unfavorable because the resin prefers calcium to sodium by a wide margin. However, if we increase the TDS of the brine solution, the apparent selectivity for hardness (calcium and magnesium) over sodium decreases. In some cases, we can actually increase the TDS enough to make the exchange favorable in both directions! This phenomenon is known as selectivity reversal.
The concept of selectivity reversal may be difficult to comprehend on an intuitive basis. A good model for understanding it, though, is found in the next section.
Applying the model
Monovalent ions only require one exchange site, while divalent ions need two exchange sites. When two available exchange sites are close together, this favors divalent ions—since charge attraction dissipates rapidly with distance. This is why high capacity resins favor divalent ions. When the solution concentration is high, the sheer number of ions present in the solution prevents the two charges of a divalent ion from remaining next to each other. The two charges necessary for exchange of a divalent ion are therefore forced farther apart—making the exchange more difficult—and the exchange for monovalent ions becomes easier by comparison.
In water softening, selectivity reversal doesn’t occur. However, the reduction in selectivity is enough to make regeneration go efficiently. The resin still favors calcium over sodium, even when the brine concentration is very high—but to a much lesser degree (see Figure 3).
Figure 3 here. Divalent to monovalent apparent selectivity slide here.
Now, let’s explore the consequences of concentration on the softening efficiency. In the service exchange, the process is most efficient when the solution concentration is low and becomes much less efficient as salinity (TDS) increases. For brackish waters, softening is considerably less efficient than for fresh waters. When the water is as salty as seawater, the softening process becomes so inefficient it’s practically worthless.
During regeneration, the higher the brine concentration, the more efficient the exchange becomes. This is one reason why most systems use 10-to-15 percent brine concentration. As this concentration increases, efficiency of hardness removal increases. However, other factors comes into play such as contact time and ionic activity, which is referred to as the “activity coefficient.” Every ion needs several water molecules around it to actually be an ion. Activity coefficients reflect the percentage of a salt that actually ionizes. The coefficients for salts always decrease as solution concentrations increase. Saturated brine actually has fewer available ions than more dilute solutions. The optimum brine concentration is somewhere around 12-to-13 percent, where the reduction in contact time and activity coefficient offsets the benefits of higher concentration.
Hopefully, this article helps more than it confuses. For those of you who’ve never had a basic chemistry course, this may be a stretch to swallow in a single reading. Just remember—low concentrations always favor divalent ions such as hardness, while high concentrations favor monovalent ions such as sodium. Softeners work efficiently because the service exchange occurs at a low TDS while regeneration occurs at much higher TDS levels. If you enjoyed this article, please see next month’s issue for more details and a discussion of the mathematical relationships involved in water softening.
About the author
Peter Meyers is technical manager for ResinTech Inc., a resin manufacturer and distributor in Cherry Hill, N.J. He has nearly 30 years industry experience covering a wide range of applications from demineralizers, polishers and softeners to industrial process design. A member of the WC&P Technical Review Committee, he attended the University of California-Santa Barbara and holds an associates degree from Mt. San Antonio College in Walnut, Calif. Meyers can be reached at (856) 354-1152, (856) 354-6165 (fax) or email: firstname.lastname@example.org