Step1. Write the balanced chemical equation
#"Na"_2"S" + "2AgNO"_3 → "2NaNO"_3 + "Ag"_2"S"#
Step 2. Calculate the moles of #"AgNO"_3#
#"Moles of AgNO"_3 = "0.030 00" color(red)(cancel(color(black)("L AgNO"_3))) × "0.513 mol AgNO"_3/(1 color(red)(cancel(color(black)("L AgNO"_3)))) = "0.015 39 mol AgNO"_3#
Step 3. Calculate the moles of #"Na"_2"S"#
#"Moles of Na"_2"S" = "0.015 39" color(red)(cancel(color(black)("mol AgNO"_3))) × ("1 mol Na"_2"S")/(2 color(red)(cancel(color(black)("mol AgNO"_3)))) = "0.007 695 mol Na"_2"S"#
Step 4. Calculate the volume of #"Na"_2"S"#
#"Vol. of Na"_2"S" = "0.007 695" color(red)(cancel(color(black)("mol Na"_2"S"))) ×("1 L Na"_2"S")/(0.230 color(red)(cancel(color(black)("mol Na"_2"S")))) = "0.0335 L Na"_2"S" = "33.5 mL Na"_2"S"#