Carbon reacts with oxygen to produce carbon dioxide ([tex]CO_2(g), \Delta H_{f }=-393.5 kJ / mol$[/tex]) according to the equation below.
[tex]C(s)+2 O_2(g) \rightarrow CO_2(g)$[/tex]
What is the enthalpy change of the reaction?
Use [tex]\Delta H_{\text {rxn }}=\sum(\Delta H_{\text {f, products }})-\sum(\Delta H_{\text {f, reactants }})$[/tex].
A. -393.5 kJ
B. -196.8 kJ
C. 196.8 kJ
D. 393.5 kJ
Answer (1)
The problem provides the enthalpy of formation for carbon dioxide and asks for the enthalpy change of the reaction.
Recall that the enthalpy of formation of elements in their standard states is zero.
Apply the formula: Δ H rxn = ∑ Δ H f, products − ∑ Δ H f, reactants .
Calculate the enthalpy change: − 393.5 kJ
Explanation
Understanding the Problem We are given the reaction: C ( s ) + O 2 ( g ) → C O 2 ( g ) . We are also given that the enthalpy of formation of C O 2 ( g ) is Δ H f = − 393.5 kJ/mol . We need to find the enthalpy change of the reaction using the formula Δ H rxn = ∑ Δ H f, products − ∑ Δ H f, reactants .
Enthalpy of Formation of Elements The enthalpy of formation of elements in their standard states is zero. Therefore, Δ H f ( C ( s )) = 0 and Δ H f ( O 2 ( g )) = 0 .
Applying the Formula Now, we apply the formula for the enthalpy change of the reaction: Δ H rxn = ∑ Δ H f, products − ∑ Δ H f, reactants In this case, we have: Δ H rxn = Δ H f ( C O 2 ( g )) − [ Δ H f ( C ( s )) + Δ H f ( O 2 ( g ))]
Calculating the Enthalpy Change Substitute the given values: Δ H rxn = − 393.5 kJ/mol − [ 0 + 0 ] Δ H rxn = − 393.5 kJ/mol
Final Answer Therefore, the enthalpy change of the reaction is − 393.5 kJ/mol .
Examples
Understanding enthalpy changes is crucial in many real-world applications. For instance, in designing engines, knowing the enthalpy change of combustion reactions helps engineers calculate the energy output and efficiency. Similarly, in chemical industries, it's essential for optimizing reaction conditions to maximize product yield and minimize energy consumption. Enthalpy changes also play a vital role in understanding climate change, as they help quantify the energy absorbed or released by various chemical processes in the atmosphere.
