Salt is actually two types of atoms bound together, and they have a loose bond – once salt gets into water, it dissolves. This means the atoms float around by themselves. However, some other molecules can form from the leftovers, molecules which do not have a loose bond. These include the other minerals, which bind with parts of the dissolved salt, and drop to the bottom as solid materials, which are easily filtered out.
Now, a water softener uses some other smart tricks to remove the salt, but this is the basic version – salt dissolves, other materials form from the leftovers. We can use the same principle to clean water of lots of other unwanted things, and I recall a science project we had in high school where we went to a sewage plant and collected some, well, sewage water, and had to clean it using, basically, filtering and this method. My group’s water ended up crystal clear – but quite toxic, as we hadn’t figured out how to get the pH value down to normal levels.
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