Why doesn't barium nitrate react with sulfuric acid?

Barium nitrate, #"Ba"("NO"_3)_2#, will react with sulfuric acid, #"H"_2"SO"_4#, to produce barium sulfate, #"BaSO"_4#, and aqueous nitric acid, #"HNO"_3#.

Barium sulfate is insoluble in water and will precipitate out of solution.

The balanced chemical equation for this double replacement reaction looks like this

#"Ba"("NO"_3)_text(2(aq]) + "H"_2"SO"_text(4(aq]) -> "BaSO"_text(4(s]) darr + 2"HNO"_text(3(aq])#

The complete ionic equation for this reaction looks like this

#"Ba"_text((aq])^(2+) + 2"NO"_text(3(aq])^(-) + 2"H"_text((aq])^(+) + "SO"_text(4(aq])^(2-) -> "BaSO"_text(4(s]) darr + 2"H"_text((aq])^(+) + 2"NO"_text(3(aq])^(-)#

To get the net ionic equation, eliminate spectator ions, i.e. the ions that are present on both sides of the equation

#"Ba"_text((aq])^(2+) + color(red)(cancel(color(black)(2"NO"_text(3(aq])^(-)))) + color(red)(cancel(color(black)(2"H"_text((aq])^(+)))) + "SO"_text(4(aq])^(2-) -> "BaSO"_text(4(s]) darr + color(red)(cancel(color(black)(2"H"_text((aq])^(+)))) + color(red)(cancel(color(black)(2"NO"_text(3(aq])^(-))))#

This will give you

#"Ba"_text((aq])^(2+) + "SO"_text(4(aq])^(2-) -> "BaSO"_text(4(s]) darr#

Barium sulftate is a white insoluble solid that precipitates out of solution.