A $55\mathrm{.}0$ mL sample of a $0\mathrm{.}122$ M potassium sulfate solution is mixed with $35\mathrm{.}0$ mL of a

$0\mathrm{.}135$ M lead$($II$)$ acetate solution and this precipitation reaction occurs:

K$2$SO$4($aq$)+$ Pb$($C$2$H$3$O$2)2($aq$)2$ KC$2$H$3$O$2($aq$)+$ PbSO$4($s$)$

The solid PbSO$4$ is collected, dried, and found to have a mass of $1\mathrm{.}01$ g$.$ Determine the

limiting reactant, the theoretical yield, and the percent yield.