If 0.5 mole of ${\mathrm{BaCl}}_2$ is mixed with 0.2 mole of ${\mathrm{Na}}_3{\mathrm{PO}}_4,$the maximum number of moles of ${\mathrm{Ba}}_3{\left({\mathrm{PO}}_4\right)}_2 \mathrm{formed} \mathrm{are}$

$3 {\mathrm{BaCl}}_2+2{\mathrm{Na}}_3{\mathrm{PO}}_4\to {\mathrm{Ba}}_3{\left({\mathrm{PO}}_4\right)}_2+6{\mathrm{NaCl}}_{\left(\mathrm{ar}\right)}$

3 mole          2 mol                 1 mole

0.2 mole ${\mathrm{Na}}_3{\mathrm{PO}}_4=0.3 \mathrm{mole} {\mathrm{BaCl}}_2$

So, here limiting reagent ${\mathrm{Na}}_3{\mathrm{PO}}_4$

0.2 mole ${\mathrm{Na}}_3{\mathrm{PO}}_4=0.1 \mathrm{mole} \mathrm{Barium} \mathrm{Phosphate}$