To determine the correct value of [tex]\(\Delta H^{\circ}\)[/tex] for the oxidation of solid elemental sulfur (S) to gaseous sulfur trioxide (SO₃) in the given reaction:
[tex]\[ 2S(s, \text{rhombic}) + 3O_2(g) \rightarrow 2SO_3(g) \][/tex]
we analyze the heat change (enthalpy change) associated with this reaction.
The reaction involves sulfur, which is initially in the solid rhombic form, reacting with oxygen gas to form sulfur trioxide gas. The intuition typically in these types of reactions is to release energy, making [tex]\(\Delta H^{\circ}\)[/tex] negative. A negative [tex]\(\Delta H^{\circ}\)[/tex] indicates that the reaction is exothermic, meaning it releases heat to the surroundings.
Given the options:
a. +105.1
b. +790.4
c. -395.2
d. -790.4
e. +395.2
Without performing the detailed thermochemical calculations, we can deduce that:
- Positive [tex]\(\Delta H^{\circ}\)[/tex] values (options a, b, and e) would suggest that the reaction absorbs heat (endothermic process).
- Negative [tex]\(\Delta H^{\circ}\)[/tex] values indicate exothermic reactions, where heat is released (options c and d).
To identify the correct [tex]\(\Delta H^{\circ}\)[/tex]:
Among the values provided, [tex]\(-790.4 \text{ kJ/mol}\)[/tex] is most consistent with the typical enthalpy values for such highly exothermic reactions involving combustion or oxidation of elemental sulfur to sulfur trioxide. Therefore, the correct value of [tex]\(\Delta H^{\circ}\)[/tex] for the oxidation of solid elemental sulfur to gaseous sulfur trioxide is:
[tex]\[ \boxed{-790.4 \text{ kJ/mol}} \][/tex]
Hence, the correct and selected option is:
d. [tex]\(-790.4 \)[/tex]
