A student monitors the progress of the reaction between a solid Group 2 metal carbonate, ${XCO}_3$, and excess hydrochloric acid by measuring the loss in mass of the reaction vessel over time:

$${XCO}_3(s)+2HCl(aq)\to {XCl}_2(aq)+H_{2}O(l)+{CO}_2(g)$$

The initial mass of the beaker containing the excess hydrochloric acid is 150.00 g. A 1.69 g sample of ${XCO}_3$ is added to the beaker.

Once the reaction is complete and the mass recorded on the balance remains constant, the final mass of the beaker and its contents is 150.81 g.

What is the relative atomic mass ($A_r$) of the metal $X$?

(Assume $A_r$: $C=12.0$, $O=16.0$)