To determine the enthalpy change (ΔH[tex]\(_{rxn}\)[/tex]) for the reaction:
[tex]\[ S(s) + O_2(g) \rightarrow SO_2(g) \][/tex]
we use the formula for the enthalpy change of a reaction, which is given by:
[tex]\[ \Delta H_{rxn} = \sum (\Delta H_{f, \text{products}}) - \sum (\Delta H_{f, \text{reactants}}) \][/tex]
Here,
- [tex]\(\Delta H_{f, \text{products}}\)[/tex] is the enthalpy of formation of the product(s)
- [tex]\(\Delta H_{f, \text{reactants}}\)[/tex] is the enthalpy of formation of the reactant(s)
Let's list the enthalpy of formation values:
- Enthalpy of formation for sulfur dioxide (SO[tex]\(_2\)[/tex]): [tex]\(\Delta H_f = -296.8 \ \text{kJ/mol}\)[/tex]
- Enthalpy of formation for elemental sulfur (S): [tex]\(\Delta H_f = 0 \ \text{kJ/mol}\)[/tex] (by definition, the enthalpy of formation of an element in its standard state is zero)
- Enthalpy of formation for elemental oxygen (O[tex]\(_2\)[/tex]): [tex]\(\Delta H_f = 0 \ \text{kJ/mol}\)[/tex] (similarly, the enthalpy of formation of an element in its standard state is zero)
Applying these values in the formula, we have:
[tex]\[
\Delta H_{rxn} = \left( \Delta H_{f, SO_2} \right) - \left( \Delta H_{f, S} + \Delta H_{f, O_2} \right)
\][/tex]
Substitute the known values:
[tex]\[
\Delta H_{rxn} = (-296.8) \ \text{kJ/mol} - (0 \ \text{kJ/mol} + 0 \ \text{kJ/mol})
\][/tex]
[tex]\[
\Delta H_{rxn} = -296.8 \ \text{kJ/mol}
\][/tex]
Hence, the enthalpy change for the reaction is [tex]\(-296.8 \ \text{kJ/mol}\)[/tex].
So, the correct answer is:
[tex]\[
-296.8 \ \text{kJ}
\][/tex]
