Answer
$35.4\text{ g/mol}$ The element is chlorine
Work Step by Step
Molar mass of $HXO_{3}$ = $1.123\text{ g}/0.0133\text{ mol}$ = $84.4\text{ g/mol}$
Value of Atomic mass of $HXO_{3}$ is equal to its molar mass, $84.4$.
The atomic mass of X can be taken by subtracting the atomic mass of $X$ and 3 $O$ from above value
Atomic mass of $X$ $= 84.4 - (16 \times 3 + 1) = 35.4$
Hence it can be determined that X is chlorine