When carbon dioxide is passed intro lime water for a short period of time, the lime water turns milky. This is due to formation of insoluble calcium carbonate.

\(\rm Ca(OH)_{2}\) + \(\rm CO_{2}\) → \(\rm CaCO_{3} \)(milky) + \(\rm H_{2}O\)

If \(\rm CO_{2}\) is passed in lime water continuously for a long period of time, the formed milky colored insoluble calcium carbonate disappears slowly due to the formation of soluble calcium bicarbonate \(\rm [Ca(HCO_{3})_{2}] \).

\(\rm CaCO_{3} \) + \(\rm CO_{2}\) + \(\rm H_{2}O\) → \(\rm Ca(HCO_{3})_{2} \)