A solid X held in a test tube received acetic acid addition. A colourless and odourless gas has evolved. The gas was passed through lime water which turned the water milky. It was concluded that:

When acetic acid reacted with X a colourless gas was given out. This gas turns lime water milky which suggests that it has carbon dioxide. Hence the gas released is carbon dioxide. So X should have been carbonate or bicarbonate. 

It was concluded that solid X is sodium bicarbonate and the gas evolved is ${\mathit{CO}}_2$ .

And the reaction occurs as follows:
${\mathit{CH}}_3\mathit{COOH}\left(\mathit{aq}\right)+{\mathit{NaHCO}}_3\left(\mathit{aq}\right)\to {\mathit{Na}(\mathit{CH}}_3\mathit{COO}\left)\right(\mathit{aq})+H_{2}O(\mathit{aq})+{\mathit{CO}}_2(g)\uparrow$