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First, we need to identify the reactants involved in the reactions. The reactants are NOâ‚‚ and NO, as well as water (Hâ‚‚O).

When nitrogen dioxide (NO₂) reacts with water, it forms nitrous acid (HNO₂) and nitric acid (HNO₃). The chemical reaction is as follows: \[ \mathrm{NO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{H}\mathrm{NO}_{2} + \mathrm{H}\mathrm{NO}_{3} \] Now, we need to check if the equation is balanced. On the left-hand side, we have 1 nitrogen atom, 2 oxygen atoms, and 2 hydrogen atoms. On the right-hand side, we also have 1 nitrogen atom, 2 oxygen atoms, and 2 hydrogen atoms. Since the number of atoms on both sides of the equation is equal, the equation is balanced.

When nitric oxide (NO) reacts with water, it forms nitrous acid (HNOâ‚‚). The chemical reaction is as follows: \[ \mathrm{NO} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{H}\mathrm{NO}_{2} \] Now, we need to check if the equation is balanced. On the left-hand side, we have 1 nitrogen atom, 1 oxygen atom, and 2 hydrogen atoms. On the right-hand side, we have 1 nitrogen atom, 2 oxygen atoms, and 2 hydrogen atoms. The number of oxygen atoms is not equal on both sides, so we need to further investigate the possible products of this reaction or alternative reactants.

NO can also react with oxygen (O₂) before it reacts with water to form HNO₂ and HNO₃. The overall process can be divided into two steps: Step 1: NO reacts with O₂ to form NO₂: \[ 2 \mathrm{NO} + \mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2} \] Step 2: NO₂ reacts with H₂O to form HNO₂ and HNO₃: \[ \mathrm{NO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{H}\mathrm{NO}_{2} + \mathrm{H}\mathrm{NO}_{3} \] By combining the two steps, we have the following: \[ 2 \mathrm{NO} + \mathrm{O}_{2} + 2 \mathrm{H}_{2}\mathrm{O} \rightarrow 2 \mathrm{H}\mathrm{NO}_{2} + 2 \mathrm{H}\mathrm{NO}_{3} \] Now, we check if the equation is balanced. On the left-hand side, we have 2 nitrogen atoms, 4 oxygen atoms, and 4 hydrogen atoms. On the right-hand side, we also have 2 nitrogen atoms, 4 oxygen atoms, and 4 hydrogen atoms. Thus, the equation is balanced.

We found the corresponding balanced chemical equations for NO and NOâ‚‚ when reacting with water: For NO: \[ 2 \mathrm{NO} + \mathrm{O}_{2} + 2 \mathrm{H}_{2}\mathrm{O} \rightarrow 2 \mathrm{H}\mathrm{NO}_{2} + 2 \mathrm{H}\mathrm{NO}_{3} \] For NOâ‚‚: \[ \mathrm{NO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{H}\mathrm{NO}_{2} + \mathrm{H}\mathrm{NO}_{3} \]