To determine which form of [tex]\( \text{NO}_2 \)[/tex] would make the reaction homogeneous, we need to understand the concept of a homogeneous reaction. A homogeneous reaction is one in which all reactants and products are in the same phase—usually all in the gas phase, liquid phase, or dissolved in a single solvent for liquid-phase reactions.
Given the reaction:
[tex]\[ 2 \text{SO}_2 (g) + \text{O}_2 (g) \rightarrow 2 \text{SO}_3 (g) \][/tex]
We can see that all the reactants and products in this reaction are in the gas phase [tex]\((g)\)[/tex]. To maintain a homogeneous reaction, the [tex]\( \text{NO}_2 \)[/tex] added should also be in the gas phase. Therefore, the form of [tex]\( \text{NO}_2 \)[/tex] that would make the reaction homogeneous is [tex]\( \text{NO}_2 (g) \)[/tex].
### Analysis of Other Forms:
- [tex]\( \text{NO}_2 (l) \)[/tex]: This indicates [tex]\( \text{NO}_2 \)[/tex] in liquid form. Since the rest of the reactants and products are gases, adding a liquid would create a heterogeneous reaction.
- [tex]\( \text{NO}_2 (s) \)[/tex]: This indicates [tex]\( \text{NO}_2 \)[/tex] in solid form. Adding a solid to a reaction where the other components are gases would also result in a heterogeneous reaction.
- [tex]\( \text{NO}_2 (aq) \)[/tex]: This indicates [tex]\( \text{NO}_2 \)[/tex] dissolved in water (aqueous). Again, since the rest of the species are gases, this would result in a heterogeneous reaction.
Thus, ensuring [tex]\( \text{NO}_2 \)[/tex] remains in the gas phase is essential for the reaction being homogeneous.
### Conclusion
[tex]\[
\boxed{\text{NO}_2(g)}
\][/tex]
is the correct form for [tex]\( \text{NO}_2 \)[/tex] to be added to maintain a homogeneous reaction.
