Is carbonic acid (H2CO3) soluble?

Here is the reaction:
CaCO3(s) + 2HCl(aq) --> CaCl2(aq) + H2CO3(?)
I am trying to figure out if it forms a precipitate or is aqueous.. I actually did this experiment today and it fizzed so I'm assuming that H+ gas forms, does that mean that it is soluble? thanks!

Answer:
the gas that forms is actually CO2.
the reaction is
CaCO3(s) + 2HCl(aq) --> CaCl2(aq) + CO2(g) + H2O(l)
Carbonic acid is unstable and decomposes to CO2 and H2O like titanium007 said. The foaming is evolution of CO2.
Your equation is not completely right. The end products are CaCl2 and CO2. Carbon dioxide then reacts with water which is present to form carbonic acid, H2CO3. Excess CO2 escapes as you saw.
in an acid-base reaction where the base is a carbonate (CO3 or bicarbonate HCO3) three products will form: water, carbon dioxide and a salt. the carbon dioxide is what you obsered with the fizzing. CaCl2 you have correctly identified as the salt. And yes, carbonic acid is soluble. it's dissolved in soda, hence the carbonation when you open the bottle and releases the pressure.

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