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What is the balanced chemical equation for the reaction that occurs between carbon dioxide and water?

Answer
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Hint: In a chemical reaction when the number of the atoms involved in the reactants side is equal to the number of atoms in the products side then this chemical reaction is known as balanced chemical reaction. In other words, the reaction which follows the law of conservation of mass is called a balanced equation.

Complete Step By Step Answer:
Carbon dioxide is slightly soluble in water. They combine with water and form a weak acid known as Carbonic acid $ {H_2}C{O_3} $ . The small value of $ {K_a} $ shows that most of the $ C{O_2} $ molecules stay as $ C{O_2} $ molecules, only few react with the water.
In this question we have to first write the skeletal equation of the reaction and then we will balance. As we know, a balanced chemical equation is the equation in which the number of atoms in the reactant side is equal to the number of atoms in the product side.
So, the skeletal equation of the reaction is:
 $ C{O_2}(g) + {H_2}O(aq) \rightarrow {H_2}C{O_3}(aq) $
As we can see in this skeletal equation the number of atoms present in the reactant side is equal to the number of atoms present in the product side. So, the balanced equation for this reaction is same to skeletal equation, i.e.
 $ C{O_2}(g) + {H_2}O(aq) \rightarrow {H_2}C{O_3}(aq) $
This is the required answer.

Note:
As water is given proton so it is a weak acid, $ C{O_2} $ will accept it. On the other hand, the carbonic acid is even though weak but stronger than water thus the molecule is more like an adduct. Skeletal equations are those in which the number of atoms of reactants is not necessarily equal to the number of products. It just shows how the molecules react.