Yes, you saturate the water, so what I do is keep a large container with "saturated" water. It only takes a tablespoon every 6 months to saturate gallons of water, and I leave two inches of this water in the container when I add more water. Pouring it into a glass will not "saturate" the water.
If you are going to drink it without saturation, I have heard that you can add citric acid (lemon or lime) to it and it produces the acid that you want to absorb.