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Ferrous hydroxide, Ferric hydroxide and Barium sulfate are insoluble or in other words they are not aqueous.
Ba(OH)2 is soluble and exists as Ba(2+) and 2 OH- ions. Ferrous sulfate reacts with the OH- ion and gives Ferrous hydroxide and a SO4(2-) ion. So if Ba(OH)2 and FeSO4 are mixed, the FeSO4 will react with the OH- ions to give Fe(OH)2, which is insoluble and a SO4(2-) ion that has to be accepted by the Ba(2+) ions resulting in Barium sulfate which is also insoluble.
I am not sure the two chemicals will react but if they do, both the resulting compounds of the reaction will be precipitated.
If a reaction does take place between the two, the balanced equation would be:
Ba(OH)2 (aq) + FeSO4 (aq) --> BaSO4 (s) + Fe (OH)2 (s)
Two soluble solutions reacting to form two insoluble precipitates.
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