Here's how to balance the chemical equation for the reaction of nitrogen dioxide (NO2) with water (H2O) to produce nitric acid (HNO3) and nitrogen monoxide (NO):

1. Write the unbalanced equation:

NO₂ + H₂O → HNO₃ + NO

2. Balance the nitrogen atoms:

There are two nitrogen atoms on the left side and two on the right side, so nitrogen is already balanced.

3. Balance the hydrogen atoms:

There are two hydrogen atoms on the left side and one on the right side. To balance, add a coefficient of 2 in front of HNO₃:

NO₂ + H₂O → 2HNO₃ + NO

4. Balance the oxygen atoms:

There are three oxygen atoms on the left side and six on the right side. To balance, add a coefficient of 3 in front of NO₂:

3NO₂ + H₂O → 2HNO₃ + NO

5. Final balanced equation:

3NO₂ + H₂O → 2HNO₃ + NO

Explanation:

This reaction demonstrates the disproportionation of nitrogen dioxide. Nitrogen in NO₂ is in an oxidation state of +4. In the products, nitrogen is in an oxidation state of +5 in HNO₃ and +2 in NO.