Verified Answer :
- Identify the standard enthalpies of formation: \(\Delta H_f^\circ(SO_2) = -296.8 \text{ kJ/mol}\), while \(\Delta H_f^\circ(S) = 0 \text{ kJ/mol}\) and \(\Delta H_f^\circ(O_2) = 0 \text{ kJ/mol}\) for elements in their standard states.
- Use the formula \(\Delta H_{rxn}^\circ = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants})\) to relate these values to the reaction.
- Calculate the enthalpy change: \(\Delta H_{rxn}^\circ = -296.8 - (0 + 0) = -296.8 \text{ kJ/mol}\).
- The final result for the reaction enthalpy is \(\boxed{-296.8 \text{ kJ/mol}}\).
Explanation
- Problem Analysis and Data Overview
The reaction between sulfur and oxygen to form sulfur dioxide is represented by the chemical equation:
\[S(s) + O_2(g) \rightarrow SO_2(g)\]
The standard enthalpy of formation, \(\Delta H_f^\circ\), represents the enthalpy change when one mole of a substance is formed from its constituent elements in their standard states. For sulfur in its solid state \(S(s)\) and oxygen in its gaseous diatomic state \(O_2(g)\), the standard enthalpy of formation is defined as \(0 \text{ kJ/mol}\). The provided standard enthalpy of formation for sulfur dioxide, \(SO_2(g)\), is \(-296.8 \text{ kJ/mol}\). Our objective is to determine the standard enthalpy change of the reaction, denoted by \(\Delta H_{rxn}^\circ\).
- Formulating the Reaction Enthalpy Calculation
The standard enthalpy change of a reaction is calculated by taking the sum of the standard enthalpies of formation of the products and subtracting the sum of the standard enthalpies of formation of the reactants, weighted by their stoichiometric coefficients from the balanced chemical equation. The formula is expressed as:
\[\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ(\text{products}) - \sum n_r \Delta H_f^\circ(\text{reactants})\]
In our equation \(1 S(s) + 1 O_2(g) \rightarrow 1 SO_2(g)\), the product is \(SO_2\) and the reactants are \(S\) and \(O_2\). All stoichiometric coefficients are \(1\). Thus, the formula becomes:
\[\Delta H_{rxn}^\circ = [1 \cdot \Delta H_f^\circ(SO_2)] - [1 \cdot \Delta H_f^\circ(S) + 1 \cdot \Delta H_f^\circ(O_2)]\]
- Calculating the Enthalpy Change
We substitute the known standard enthalpy values into the formula:
\[\Delta H_f^\circ(SO_2) = -296.8 \text{ kJ/mol}\]
\[\Delta H_f^\circ(S) = 0 \text{ kJ/mol}\]
\[\Delta H_f^\circ(O_2) = 0 \text{ kJ/mol}\]
Substituting these into the expression:
\[\Delta H_{rxn}^\circ = [1 \cdot (-296.8 \text{ kJ/mol})] - [1 \cdot 0 \text{ kJ/mol} + 1 \cdot 0 \text{ kJ/mol}]\]
\[\Delta H_{rxn}^\circ = -296.8 \text{ kJ/mol} - 0 \text{ kJ/mol}\]
\[\Delta H_{rxn}^\circ = -296.8 \text{ kJ/mol}\]
- Conclusion
The standard enthalpy change for the reaction \(S(s) + O_2(g) \rightarrow SO_2(g)\) is calculated to be \(-296.8 \text{ kJ/mol}\). This negative value indicates that the reaction is exothermic, meaning it releases energy to the surroundings. The final answer is \(\boxed{-296.8 \text{ kJ/mol}}\).
Examples
Standard enthalpies of formation are essential in fields like chemical engineering and environmental science to predict whether reactions will release or absorb heat. For example, when calculating the heat produced by industrial boilers burning sulfur-containing fuels, engineers use these values to estimate fuel efficiency and the total thermal output of the system. By understanding the energy dynamics, they can design more efficient and safer industrial processes.