Cations and anions of water-soluble salts cannot be removed from water using only mechanical filters (which rely on particle size) such as coffee filters.
In order to remove such ions, ion exchange resins can be used. These resins consist of an insoluble matrix, e.g. polystyrene that is crosslinked with divinylbenzene to vary the porosity of the resin. To convert the resin into an ion exchanger, the polymer structure is functionalized with many functional groups. Typical functional groups are
- sulfonate ($\ce{R-SO3-}$) for strong acid cation exchange resins,
- quarternary ammonium (e.g. $\ce{R-N(CH3)3+}$) for strong base anion exchange resins
- tertiary amine (e.g. $\ce{R-N(CH3)2}$) for weak base anion exchange resins
The counterion of new cation exchange resins used for water treatment is usually $\ce{H+}$ or $\ce{Na+}$ (other forms can be used for special applications, e.g. $\ce{Li+}$ in pressurized water reactors), i.e. $\ce{R-SO3- H+}$ or $\ce{R-SO3- Na+}$. These counterions can be replaced by another cation from the water. Thus, a cation exchange resin can remove various cations from the water and replace them with an equivalent amount of $\ce{H+}$ and $\ce{Na+}$, respectively, e.g.
$$\ce{2 (R-SO3- H+) + Ca^2+ <=> (2 R-SO3- Ca^2+) + 2 H+}$$
The counterion of new anion exchange resins is usually $\ce{OH-}$ or $\ce{Cl-}$. Thus, an anion exchange resin can remove various anions from the water and replace them with an equivalent amount of $\ce{OH-}$ and $\ce{Cl-}$, respectively.
In order to remove both kinds of ions, the water has to be passed through a cation exchanger and through an anion exchanger. Alternatively, a mixed-bed ion exchanger (which contains cation exchange resins and anion exchange resins) can be used. They are even more effective but cannot be easily regenerated.
Typical Brita water filter cartridges contain ion exchange resin beads to remove undesired ions and activated carbon to absorb other undesired compounds.