[home6442]

A tds meter is basically a conductivity meter which measures the amount of positively
charged ions dissolved  in the water.
These raise the level of conductivity and show up on the tds meter. Things like salt and so on.
Anything that has negatively charged ions will not show up on a tds meter but will
still be dissolved in the water. Sugar, alcohol and carbon dioxide and so on.

[dd]

Chlorine does not exist as a gas when it is dissolved in water.

As to the rest of the science I don't know.