Barium. "Sulfate". K_(sp) = 1.5 x 10^(-9) => "Solubility" = sqrt(K_(sp) = sqrt(1.5 x 10^(-9) = 3.9 x 10^-5M. This means that there is very little chance Na^+ will react with SO_4^(2-) ion and very little chance that the GpIIA Ba^(+2) will react with the Cl^-. ion. Simply, there is no driving force for formation of product with Barium Sulfate + Sodium Chloride as reactants in the problem.
Theoretically, BaSO_4 + 2NaCl => Na_2SO_4 + BaCl_2 but neither sodium sulfate or barium chloride would form an insoluble precipitate (required) to be the driving force. Therefore, no reaction occurs.
