When carbon dioxide is passed through lime water which is a diluted solution of Ca(OH) 2, it turns milky due to the formation of calcium carbonate which is CaCO3.

The reaction is like this:

Ca(OH) 2 + CO2 → CaCO3 + H2O

If you pay a little more attention, you will be able to observe that it is a neutralization reaction, where base is Ca(OH)2 and acid is H2CO3 and a salt CaCO3 and H2O are formed.

So, actually the above reaction is a short form of actual reaction.

Actually CO2 is no more CO2 after dissolving in water, it becomes H2CO3 via addition reaction as shown :

CO2+H2O→ H2CO3

Now, this CaCO3 is insoluble in water which is the reason behind the milkiness of solution.

However if excess carbon dioxide is passed, the milkiness disappears, think about it… milkiness was due to CaCO3 and now the milkiness is disappeared… this must mean that CaCO3 is no more left and git converted into something.

That something is actually calcium bicarbonate which is soluble in water and hence the solution becomes clear.

The reaction is as follows :

CO2+H2O→ H2CO3

CaCO3 + H2CO3 → Ca(HCO3)2

This is because…

Carbonate + carbonic acid gives 2 bicarbonates

CO3 2- + H2CO3 → 2 HCO3-

This is due to proton transfer.

So… H2CO3 gives H+(acting as acid) and CO3 2- accepts it(acting as a base).

This clearly means that, it is an acid base reaction in which no water is formed(coz its proton transfer)

Hope it helps.