Carbon reacts with oxygen to produce carbon dioxide ($CO_2(g), \Delta H_{f }=-393.5 kJ / mol$) according to the equation below.
$C(s)+2 O_2(g) \rightarrow CO_2(g)$
What is the enthalpy change of the reaction?
Use $\Delta H_{r \times n}=\sum\left(\Delta H_{t, \text { products }}\right)-\sum\left(\Delta H_{t, \text { reactants }}\right)$.
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 state is zero.
Apply 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 ) to find the enthalpy change.
The enthalpy change of the reaction is − 393.5 kJ .
Explanation
Problem Analysis and Given Data We are given the reaction: C ( s ) + O 2 ( g ) i g h t ha r p oo n u pC 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, Δ H r x n , using the formula: Δ H r x n = ∑ ( Δ H f , products ) − ∑ ( Δ H f , reactants )
Enthalpy of Formation of Elements The enthalpy of formation of an element in its standard state is zero. Therefore, the enthalpy of formation of C ( s ) is 0 and the enthalpy of formation of O 2 ( g ) is 0. That is, Δ H f ( C ( s )) = 0 and Δ H f ( O 2 ( g )) = 0 .
Applying the Formula Now, we can apply the formula for the enthalpy change of the reaction: Δ H r x n = Δ H f ( C O 2 ( g )) − [ Δ H f ( C ( s )) + Δ H f ( O 2 ( g ))] Substituting the given values, we have: Δ H r x n = − 393.5 kJ/mol − [ 0 + 0 ] = − 393.5 kJ/mol
Final Answer Therefore, the enthalpy change of the reaction is − 393.5 kJ/mol .
Examples
Enthalpy change is crucial in various real-world applications. For instance, in designing efficient combustion engines, understanding the enthalpy change helps optimize fuel mixtures for maximum energy output. Similarly, in industrial chemistry, knowing the enthalpy change of a reaction allows chemists to determine the heat required or released during a chemical process, which is essential for safety and efficiency. In everyday life, the enthalpy change is relevant in understanding the energy content of foods; it helps nutritionists calculate the caloric value of different food items, aiding in dietary planning and weight management.
