#Barium. "Sulfate". K_(sp) = 1.5 x 10^(-9)# => #"Solubility" = sqrt(K_(sp)# = #sqrt(1.5 x 10^(-9)# = #3.9 x 10^-5#M. 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.
