To determine which reaction correctly shows the formation of \( NO_2 \) requiring 33.1 kJ/mol, we need to find the reaction where the energy (33.1 kJ/mol) is shown as a reactant.
Let's evaluate each option:
A. \( N(g) + 2O(g) \rightarrow NO_2(g) + 33.1 \text{kJ} \)
In this reaction, 33.1 kJ is shown as a product, indicating that energy is released during the reaction. This means it is an exothermic reaction, which is not what we are looking for.
B. \( \frac{1}{2} N_2(g) + O_2(g) + 33.1 \text{kJ} \rightarrow NO_2(g) \)
In this reaction, 33.1 kJ is shown as a reactant, indicating that energy is required for the formation of \( NO_2 \), which means it is an endothermic reaction. This matches the requirement of the formation of \( NO_2 \) requiring 33.1 kJ/mol.
C. \( \frac{1}{2} N_2(g) + O_2(g) \left. g(m) NO_2(g) + 33.1 \text{kJ} \right. \)
This reaction does not have a proper reaction arrow and is not correctly formatted, so it cannot be considered as the correct option regardless of the position of the energy term.
D. \( N(g) + O(g) + 33.1 \text{kJ} \rightarrow NO_2(g) \)
Although this reaction shows the energy as a reactant, it uses atomic nitrogen (\( N \)) and oxygen (\( O \)), which is not the standard form. Typically, we use molecular nitrogen (\( N_2 \)) and molecular oxygen (\( O_2 \)) in reactions involving the formation of compounds like \( NO_2 \).
Thus, the correct reaction should use molecular nitrogen and oxygen and show the energy as a reactant indicating an endothermic process.
Therefore, the correct answer is:
B. [tex]\( \frac{1}{2} N_2(g) + O_2(g) + 33.1 \text{kJ} \rightarrow NO_2(g) \)[/tex]
