Solid Na$_2$SO$_4$ is slowly added to a solution which is 0.020 M in Ba(NO$_3$)$_2$ and 0.020 M in Pb(NO$_3$)$_2$. Assume no increase in volume. Preferential precipitation takes place. What is the concentration of Ba$^{2+}$ when PbSO$_4$ starts to precipitate? $K_{sp}(\text{BaSO}_4) = 1.0 \times 10^{-10}$ and $K_{sp}(\text{PbSO}_4) = 1.6 \times 10^{-8}$