When dilute hydrochloric acid reacts with calcium carbonate, the gas evolved is passed through limewater. On passing the gas in excess, the milkiness disappears due to the formation of:

The correct answer is Calcium hydrogen carbonate.

Let's understand the step-by-step chemical reactions that take place during this process:

Step 1: Reaction of dilute hydrochloric acid with calcium carbonate
When dilute hydrochloric acid reacts with calcium carbonate, it produces calcium chloride, water, and carbon dioxide gas. The chemical equation for this reaction is:
${\mathrm{CaCO}}_3\left(s\right)+2\mathrm{HCl}\left(\mathrm{aq}\right)\to {\mathrm{CaCl}}_2\left(\mathrm{aq}\right)+H_{2}O\left(l\right)+{\mathrm{CO}}_2\left(g\right)$
Thus, the evolved gas is carbon dioxide (CO₂).

Step 2: Passing the evolved gas through limewater (limited amount)
Limewater is an aqueous solution of calcium hydroxide. When carbon dioxide gas is passed through limewater, it reacts to form water-insoluble calcium carbonate. The suspension of these fine calcium carbonate particles makes the solution look cloudy or milky:
$\mathrm{Ca}{\left(\mathrm{OH}\right)}_2\left(\mathrm{aq}\right)+{\mathrm{CO}}_2\left(g\right)\to {\mathrm{CaCO}}_3\left(s\right)+H_{2}O\left(l\right)$

Step 3: Passing the gas in excess
If we continue to pass carbon dioxide gas in excess through the milky solution, the insoluble calcium carbonate reacts further with the excess carbon dioxide and water to form calcium hydrogen carbonate. Calcium hydrogen carbonate is soluble in water, which causes the precipitate to dissolve and the milkiness to disappear:
${\mathrm{CaCO}}_3\left(s\right)+H_{2}O\left(l\right)+{\mathrm{CO}}_2\left(g\right)\to \mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}_2\left(\mathrm{aq}\right)$
Since calcium hydrogen carbonate, Ca(HCO₃)₂, is highly soluble in water, the solution becomes clear again.