If I knew the concentration of a acid solution, what experiment coukd I do to find the concentration of a solution of Potassium carbonate?

2 H+ (acid) + CO3-- (Carbonate) = H2CO3 = H2O + CO2 (given off)

If you react any acid with carbonate, you'll get "carbonic acid" that decomposes to give water and carbon dioxide. If you can get the reaction to go to completion (to the right -- possibly by boiling off carbon dioxide or sequestering it in some other way), and if you know the concentration of acid, you can calculate the concentration of potassium carbonate.