If 5 moles of BaCl _ 2 is mixed with 2 moles of Na _ 3 PO _ 4 , the...

The balanced chemical equation for the reaction between ${BaCl}_{2}$ and ${Na}_{3}{PO}_{4}$ is:

$3{BaCl}_{2} + 2{Na}_{3}{PO}_{4} \to {Ba}_{3} ( {PO}_{4}{)}_{2} + 6NaCl$

$5$ moles of barium chloride will require $\dfrac{5 \times 2}{3} = 3 . 3$ moles of sodium phosphate.

Here, sodium phosphate is the limiting reagent.
$2$ moles of sodium phosphate produce $1$ mole of barium phosphate.

Thus,$2$ moles of sodium phosphate will produce$1$ mole of barium phosphate.

Hence, the maximum no. of moles of ${Ba}_{3} ( {PO}_{4}{)}_{2}$that can be formed is one mole.