Calculate the ∆H_rxn for
S (s) + $\frac32$ O₂ (g) → SO₃ (g) ΔH_rxn = ?
Given the following set of reactions:
$\frac12$ S (s) + $\frac12$ O₂ (g) → $\frac12$ SO₂ (g) ΔH° = −296.8 kJ
2 SO₃ (g) → 2 SO₂ (g) + O₂ (g) ΔH° = 198.4 kJ

• A. -494.4 kJ
• B. -692.8 kJ
• C. 494.4 kJ
• D. -346.4 kJ

Answer: (B)

Verified step by step guidance

1. Identify the target reaction: S (s) + \frac{3}{2} O_2 (g) \rightarrow SO_3 (g). We need to find the \Delta H_{rxn} for this reaction.
2. Examine the given reactions and their enthalpy changes: \frac{1}{2} S (s) + \frac{1}{2} O_2 (g) \rightarrow \frac{1}{2} SO_2 (g) with \Delta H^\circ = -296.8 \text{ kJ}, and 2 SO_3 (g) \rightarrow 2 SO_2 (g) + O_2 (g) with \Delta H^\circ = 198.4 \text{ kJ}.
3. Use Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for each step. We need to manipulate the given reactions to match the target reaction.
4. Reverse the second reaction to get: 2 SO_2 (g) + O_2 (g) \rightarrow 2 SO_3 (g). This changes the sign of \Delta H^\circ to -198.4 \text{ kJ}.
5. Add the modified reactions: \frac{1}{2} S (s) + \frac{1}{2} O_2 (g) \rightarrow \frac{1}{2} SO_2 (g) and 2 SO_2 (g) + O_2 (g) \rightarrow 2 SO_3 (g). Adjust stoichiometry and sum the enthalpy changes to find \Delta H_{rxn} for the target reaction.