To determine in which form [tex]$NO_2$[/tex] should be added as a homogeneous catalyst for the reaction
[tex]\[ 2 \, SO_2(g) + O_2(g) \rightarrow 2 \, SO_3(g), \][/tex]
we need to understand the concept of a homogeneous catalyst. A homogeneous catalyst is a catalyst that is in the same phase as the reactants in the reaction.
1. First, identify the phases of the reactants in the given reaction. Both [tex]$SO_2$[/tex] and [tex]$O_2$[/tex] are in the gas phase, as indicated by the notation [tex]\((g)\)[/tex].
2. Since the reactants are in the gas phase, the homogeneous catalyst must also be in the gas phase to ensure it is uniformly distributed throughout the reaction mixture and interacts effectively with the reactants.
3. Now, consider the different forms of [tex]$NO_2$[/tex] provided:
- [tex]$NO_2(g)$[/tex]: Gas phase
- [tex]$NO_2( )$[/tex]: This option lacks specific phase information, and is therefore uncertain.
- [tex]$NO_2(s)$[/tex]: Solid phase
- [tex]$NO_2(aq)$[/tex]: Aqueous phase
4. Among these forms, only [tex]$NO_2(g)$[/tex] matches the phase of the reactants, which are also gases. Therefore, for [tex]$NO_2$[/tex] to act as a homogeneous catalyst, it should also be in the gas phase.
Hence, the correct form for [tex]$NO_2$[/tex] to be a homogeneous catalyst in this reaction is:
[tex]\[ NO_2(g) \][/tex]
