To determine the enthalpy change for the reaction, we will use the given equation and the provided values.
[tex]\[
S(s) + O_2(g) \rightarrow SO_2(g)
\][/tex]
We know the formula to calculate the enthalpy change for the reaction:
[tex]\[
\Delta H_{rxn} = \sum\left(\Delta H_{f, \text{products}}\right) - \sum\left(\Delta H_{f, \text{reactants}}\right)
\][/tex]
Step-by-Step Breakdown:
1. Identify the ΔH_f values:
- For the product [tex]\(SO_2(g)\)[/tex], the enthalpy of formation [tex]\(\Delta H_f = -296.8 \text{ kJ/mol}\)[/tex] as given.
- For the reactants, sulfur (S(s)) and oxygen (O_2(g)) are in their standard states. The enthalpies of formation for elements in their standard states are zero:
[tex]\[
\Delta H_f(S(s)) = 0 \text{ kJ/mol}
\][/tex]
[tex]\[
\Delta H_f(O_2(g)) = 0 \text{ kJ/mol}
\][/tex]
2. Calculate the sum of the enthalpies of formation for the products:
[tex]\[
\sum\left(\Delta H_{f, \text{products}}\right) = \Delta H_f(SO_2(g)) = -296.8 \text{ kJ/mol}
\][/tex]
3. Calculate the sum of the enthalpies of formation for the reactants:
[tex]\[
\sum\left(\Delta H_{f, \text{reactants}}\right) = \Delta H_f(S(s)) + \Delta H_f(O_2(g)) = 0 + 0 = 0 \text{ kJ/mol}
\][/tex]
4. Plug these values into the enthalpy change formula:
[tex]\[
\Delta H_{rxn} = \sum\left(\Delta H_{f, \text{products}}\right) - \sum\left(\Delta H_{f, \text{reactants}}\right)
\][/tex]
[tex]\[
\Delta H_{rxn} = -296.8 \text{ kJ/mol} - 0 \text{ kJ/mol}
\][/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]\[
\boxed{-296.8 \text{ kJ}}
\][/tex]
