To determine the volume of nitrogen (N₂) that reacts with a given volume of oxygen (O₂) to produce nitrogen dioxide (NO₂), we can use the balanced chemical equation for the reaction:
\[ \text{N}_2 + 2\text{O}_2 \rightarrow 2\text{NO}_2 \]
According to the stoichiometry of the reaction:
- 1 volume of nitrogen (N₂) reacts with 2 volumes of oxygen (O₂).
From the equation, you can see that for every 1 volume of N₂, 2 volumes of O₂ are required.
Given that you have 33.9 liters of oxygen (O₂), you can set up the ratio to find the corresponding volume of nitrogen (N₂):
\[ \text{Volume of N}_2 = \frac{1 \text{ volume of N}_2}{2 \text{ volumes of O}_2} \times \text{Volume of O}_2 \]
Now plug in the value:
\[ \text{Volume of N}_2 = \frac{1}{2} \times 33.9 \text{ liters} \]
Calculating this gives:
\[ \text{Volume of N}_2 = 16.95 \text{ liters} \]
Therefore, 16.95 liters of nitrogen are required to react with 33.9 liters of oxygen to produce nitrogen dioxide.