When NaOH reacts with CO2, it forms Na2CO3 and H2O as you can see the below equation. In this below equation, Sodium Carbonate having a Carbon dioxide which is passed through the Lime water (CaO + H2O + CO2 present in Sodium) to form in the product side CaCO3 with a formation of Caustic soda (NaOH).

Na2CO3 + CaO + H2O → CaCO3 + 2NaOH

Sodium carbonate react with calcium oxide and water to produce calcium carbonate and sodium hydroxide.

Chemical Equation:
The balanced chemical equation for the reaction between carbon dioxide gas (CO2) and lime water (Ca(OH)2) is as follows:

CO2 + Ca(OH)2 → CaCO3 + H2O

Explanation:
When carbon dioxide gas is passed through lime water, a chemical reaction occurs. Lime water is a solution of calcium hydroxide (Ca(OH)2) in water. Carbon dioxide gas reacts with calcium hydroxide to form calcium carbonate (CaCO3) and water (H2O).

Step-by-Step Explanation:
1. The reactants in this reaction are carbon dioxide gas (CO2) and calcium hydroxide (Ca(OH)2), while the products are calcium carbonate (CaCO3) and water (H2O).
2. The first step is to balance the number of atoms on each side of the equation.
3. Start by balancing the carbon atoms. There is only one carbon atom on the left side and one on the right side, so the equation is already balanced in terms of carbon.
4. Next, balance the hydrogen atoms. There are two hydrogen atoms in calcium hydroxide on the left side, and two hydrogen atoms in water on the right side. The equation is balanced in terms of hydrogen atoms.
5. Finally, balance the oxygen atoms. There are two oxygen atoms in carbon dioxide on the left side, two oxygen atoms in calcium hydroxide, and three oxygen atoms in calcium carbonate on the right side. To balance the oxygen atoms, we need to put a coefficient of 3 in front of the calcium hydroxide:
CO2 + 3Ca(OH)2 → CaCO3 + H2O
6. Now, the equation is balanced in terms of atoms on both sides.
7. The balanced equation shows that one molecule of carbon dioxide reacts with three molecules of calcium hydroxide to form one molecule of calcium carbonate and one molecule of water.
8. This reaction is commonly used to test for the presence of carbon dioxide gas. When carbon dioxide is passed through lime water, the solution turns milky due to the formation of calcium carbonate, which is insoluble and appears as a precipitate.
9. Lime water is often used as a laboratory reagent to identify the presence of carbon dioxide gas in chemical reactions or as a simple way to test for the gas in everyday situations.