The product formed is XCl, which tells us that element X combines with chlorine in a 1:1 ratio. This means X has a valency of +1 and forms a monovalent chloride.
Examining the options:
K (potassium): Group 1 element with a valency of +1. It forms KCl. The equation becomes \(2\text{K} + 2\text{HCl} \rightarrow 2\text{KCl} + \text{H}_2\), which balances correctly.
Mg (magnesium): Group 2 element with a valency of +2. It forms MgCl2, not MgCl. Does not match.
Ca (calcium): Group 2 element with a valency of +2. It forms CaCl2, not CaCl. Does not match.
Ba (barium): Group 2 element with a valency of +2. It forms BaCl2, not BaCl. Does not match.
Only potassium (K) has a valency of +1 and forms a chloride with the formula XCl, making it the correct identity of X.