Final answer:
The column of calcium chloride pellets is used for ion exchange in water softening processes to replace unwanted hard water ions with sodium ions.
Step-by-step explanation:
The purpose of a column filled with calcium chloride pellets in the context provided is for ion exchange. During the ion exchange process, hard water ions such as calcium (Ca2+) and magnesium (Mg2+) are replaced with more acceptable ions such as sodium (Na+). This is achieved as the hard water flows through a column containing a resin, which binds the unwanted ions and releases sodium ions into the water.