This is a less than problem.

We start with the balanced equation:

#"Ba"("NO"_3)_2 + "Na"_2"SO"_4 → "BaSO"_4 + "2NaNO"_3#

**Find the limiting reactant**

**(a)** Calculate the initial moles of each reactant

#"Initial moles of Ba"("NO"_3)_2 = 0.200 color(red)(cancel(color(black)("L"))) × ("0.35 mol Ba"("NO"_3)_2)/(1 color(red)(cancel(color(black)("L")))) = "0.0700 mol Ba"("NO"_3)_2#

#"Initial moles of Na"_2"SO"_4 = 0.300 color(red)(cancel(color(black)("L"))) × ("0.2 mol Na"_2"SO"_4)/(1 color(red)(cancel(color(black)("L")))) = "0.060 mol Na"_2"SO"_4#

**(b)** Calculate the moles of #"NaNO"_3# from each reactant.

**From #"Ba"("NO"_3)_2#**:

#"Moles of NaNO"_3 = 0.0700 color(red)(cancel(color(black)("mol Ba"("NO"_3)_2))) × "2 mol NaNO"_3/(1 color(red)(cancel(color(black)("mol Ba"("NO"_3)_2)))) = "0.140 mol NaNO"_3#

**From #"Na"_2"SO"_4#:**

#"Moles of NaNO"_3 = 0.060 color(red)(cancel(color(black)("mol Na"_2"SO"_4))) × "2 mol NaNO"_3/(1 color(red)(cancel(color(black)("mol Na"_2"SO"_4)))) = "0.12 mol NaNO"_3#

#"Na"_2"SO"_4# is the limiting reactant, because it gives the fewest moles of #"NaNO"_3#.

**Calculate the normality of the #"NaNO"_3#**

At this point we have 0.12 mol #"NaNO"_3# in 0.5 L of solution.

If we add another 2 L of water, we have 2.5 L of solution.

#"Molarity" = "moles"/"litres" = "0.12 mol"/"2.5 L" = "0.048 mol/L"#

Since #"1 mol NaNO"_3 = "1 eq NaNO"_3#,

#"Normality = 0.05 eq/L"#