The balanced chemical equation for the reaction of hydrogen and oxygen to form water is:
\[ 2H_2 + O_2 \rightarrow 2H_2O \]
From this equation, we can see that 1 volume of \( O_2 \) produces 2 volumes of \( H_2O \). Thus, for every 1 cubic decimeter (dm³) of \( O_2 \), 2 cubic decimeters (dm³) of \( H_2O \) are produced.
If 3 dm³ of \( O_2 \) is used, we can calculate the volume of water produced:
\[ \text{Volume of } H_2O = 3 , \text{dm}^3 , O_2 \times \frac{2 , \text{dm}^3 , H_2O}{1 , \text{dm}^3 , O_2} = 6 , \text{dm}^3 , H_2O \]
Therefore, the volume of water produced is 6 dm³.