J.R. S. answered 01/04/18
Tutor
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Ph.D. in Biochemistry--University Professor--Chemistry Tutor
The key to knowing this is to know, or look up, solubilities of different salt, compounds, etc. So, taking your examples, BaCO3 is certainly insoluble in water, but what Ba salt is soluble? Well, Ba(NO3)2 , i.e. barium nitrate is a soluble salt. You'd either have to know this or look it up. Now, how do you make barium nitrate from barium carbonate?
BaCO3 + 2HNO3 ==> Ba(NO3)2 + H2O + CO2. Get it?
Now for calcium oxalate, since acetic acid is a WEAK acid, it will increase the solubility of calcium oxalate only slightly, since calcium acetate is soluble. But a strong acid would be better. So, for example, CaC2O4 (calcium oxalate) would be more soluble in, say, HNO3 because calcium nitrate is soluble and HNO3 is a strong acid. I hope this "sort of" makes sense.