Soda is an aquious solution of carbonic acid. So in order to make a tablet to make soda you need a tablet of carbonic acid. It is possible to make carbonic acid in solid form. The problem is that carbonic acid is very unstable and will easily react to form carbon dioxide and water. So if you make carbonic acid you need to keep it in conditions where this reaction will not take place. For solid carbonic acid this requires you to cool it down to negative 80 degrees. At this temperature water is not liquid and you can not mix the carbonic acid tablets with the water. In fact carbonic acid is not even stable in aquious solution. In order to keep soda stable you need to keep it under pressure so that the carbon dioxide will react with the water to form carbonic acid at the same rate as the carbonic acid turns back into carbon dioxide.
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