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Why do calcium ions tend to replace sodium ions in dilute hard water?

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chemical structure of cation exchanger — ion-exchange reaction Figure 1: Chemical structure of cation exchanger. The exchangeable ions are marked ⁺. The whole structure is permeated by solvent molecules, usually water (not shown).

In the context of ion-exchange reactions, the tendency for calcium ions to replace sodium ions in dilute hard water is driven by a phenomenon known as electroselectivity.1

When an ion-exchange resin is used for water softening, the process involves trading sodium ions for divalent calcium ions. Because calcium ions carry a higher charge than sodium ions, the equilibrium of the reaction is sensitive to the total concentration of the solution.21

In a dilute solution like hard water, the exchange is favored because one doubly-charged calcium ion can replace two singly-charged sodium ions. As the solution becomes more dilute, the likelihood of this replacement increases, effectively pulling the calcium ions out of the water and onto the resin. Conversely, this process is reversed during regeneration by using a highly concentrated solution of sodium chloride, which forces the sodium ions to displace the calcium ions from the resin.12