To determine which reaction shows that the formation of [tex]$CO_2$[/tex] releases [tex]$393.5 \, \text{kJ/mol}$[/tex], we need to understand the concept of exothermic reactions. In an exothermic reaction, energy is released as a product. Thus, when energy (in the form of kJ) appears on the product side of the reaction equation, it indicates that the reaction releases energy.
Let's analyze each option:
Option A: [tex]$C (s) + O_2(g) + 393.5 \, \text{kJ} \rightarrow CO_2(g)$[/tex]
- In this equation, [tex]$393.5 \, \text{kJ}$[/tex] is shown on the reactant side. This implies that energy is absorbed to form [tex]$CO_2$[/tex], which would indicate an endothermic reaction. Therefore, this does not correctly represent the release of energy.
Option B: [tex]$C (s) + O_2(g) \rightarrow CO_2(g) + 393.5 \, \text{kJ}$[/tex]
- Here, [tex]$393.5 \, \text{kJ}$[/tex] is shown on the product side. This means that [tex]$393.5 \, \text{kJ}$[/tex] of energy is released when [tex]$CO_2$[/tex] is formed. This aligns with the requirement that the formation of [tex]$CO_2$[/tex] releases energy. Thus, this option correctly represents the release of [tex]$393.5 \, \text{kJ}$[/tex] of energy.
Option C: [tex]$C (s) + O (g) \rightarrow CO_2(g) + 393.5 \, \text{kJ}$[/tex]
- Similarly to Option B, this equation has [tex]$393.5 \, \text{kJ}$[/tex] on the product side, indicating that energy is released. However, the reactants include [tex]$O (g)$[/tex] (atomic oxygen), not [tex]$O_2 (g)$[/tex] (molecular oxygen). The formation of [tex]$CO_2$[/tex] typically involves [tex]$O_2 (g)$[/tex], not atomic oxygen, making this chemical equation less accurate for the given context.
Option D: [tex]$C (s) + 2 O (g) + 393.5 \, \text{kJ} \rightarrow CO_2(g)$[/tex]
- In this reaction, [tex]$393.5 \, \text{kJ}$[/tex] is on the reactant side, which implies energy absorption (endothermic reaction). Additionally, the reactants include [tex]$2 O (g)$[/tex] (atomic oxygen), which is an inaccurate representation for the context of forming [tex]$CO_2$[/tex] usually involving [tex]$O_2 (g)$[/tex].
Given the analysis above, the correct reaction that shows the formation of [tex]$CO_2$[/tex] releases [tex]$393.5 \, \text{kJ/mol}$[/tex] is:
B. [tex]$C (s) + O_2(g) \rightarrow CO_2(g) + 393.5 \, \text{kJ}$[/tex]
Hence, the correct option is 2 (Option B).
