Sulfur reacts with oxygen to form sulfur dioxide ($SO_2(g), \Delta H_{f}=-296.8 \text{ kJ/mol}$) according to the equation below:
$S(s)+O_2(g) \rightarrow SO_2(g)$
What is the enthalpy change for the reaction?
Use $\Delta H_{\text{rxn}} = \sum(\Delta H_{\text{f,products}}) - \sum(\Delta H_{\text{f,reactants}})$
A. -593.6 kJ
B. -296.8 kJ
C. 296.8 kJ
D. 593.6 kJ
Answer (1)
The enthalpy change for the reaction is calculated using the formula Δ H r x n = ∑ Δ H f ( p ro d u c t s ) − ∑ Δ H f ( re a c t an t s ) .
The enthalpy of formation of elements in their standard state is 0.
Substituting the given values, Δ H r x n = − 296.8 k J / m o l − [ 0 + 0 ] .
The enthalpy change for the reaction is − 296.8 k J .
Explanation
Problem Analysis We are given the reaction: S ( s ) + O 2 ( g ) i g h t ha r p oo n u pS O 2 ( g ) . We are also given that the enthalpy of formation of S O 2 ( g ) is Δ H f ( S O 2 ( g )) = − 296.8 m o l k J . We need to find the enthalpy change for the reaction.
Enthalpy Change Formula The enthalpy change for a reaction can be calculated using the formula: Δ H r x n = ∑ Δ H f ( p ro d u c t s ) − ∑ Δ H f ( re a c t an t s ) In this case, the products consist of S O 2 ( g ) and the reactants consist of S ( s ) and O 2 ( g ) .
Enthalpy of Formation of Elements The enthalpy of formation of an element in its standard state is 0. Therefore, Δ H f ( S ( s )) = 0 m o l k J and Δ H f ( O 2 ( g )) = 0 m o l k J .
Calculation Now, we can substitute the given values into the formula: Δ H r x n = Δ H f ( S O 2 ( g )) − [ Δ H f ( S ( s )) + Δ H f ( O 2 ( g ))] Δ H r x n = − 296.8 m o l k J − [ 0 m o l k J + 0 m o l k J ] Δ H r x n = − 296.8 m o l k J
Final Answer Therefore, the enthalpy change for the reaction is − 296.8 k J .
Examples
Enthalpy changes are crucial in various real-world applications, such as designing chemical reactors, understanding combustion processes, and developing new materials. For instance, when designing a power plant that burns coal, knowing the enthalpy change of the combustion reaction helps engineers calculate the amount of energy released and design the plant for optimal efficiency. Similarly, in the development of new drugs, understanding the enthalpy changes of reactions can help scientists optimize the synthesis process and improve the yield of the desired product. Enthalpy changes also play a vital role in understanding climate change, as they help scientists model the energy balance of the Earth's atmosphere and predict the effects of greenhouse gas emissions.
