In the given reaction cycle X, Y and Z respectively are

When calcium chloride reacts with sodium carbonate, a double replacement reaction takes place. The products of this reaction are calcium carbonate and sodium chloride.${CaCl}_{2} + {Na}_{2}{CO}_{3} \to \mathop{{CaCO}_{3}}_{\left(X\right)} + \mathop{2NaCl}_{\left(Y\right)}$

To Obtain Calcium chloride from Calcium carbonate we need to react calcium carbonate with Hydro chloric acid.

$\mathop{{CaCO}_{3}}_{\left(X\right)} + \mathop{2HCl}_{\left(Z\right)} \to {CaCl}_{2} + {CO}_{2}\left(g\right) + {H}_{2}O\left(l\right)$

$∴ ( X ) {CaCO}_{3}$

$( Y ) NaCl$

$( Z ) HCl$