What is the enthalpy change, ΔH, for this reaction? Show your work.
The Correct answer and Explanation is :
The correct answer is: (-393.5 \, \text{kJ/mol})
To calculate the enthalpy change (( \Delta H )) for a chemical reaction, you generally use the formula:
[
\Delta H = \sum H_{\text{products}} – \sum H_{\text{reactants}}
]
where ( H ) represents the standard enthalpy of formation of the substances involved in the reaction. The enthalpy of formation (( \Delta H_f^\circ )) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states.
Example Reaction:
Consider the reaction:
[
\text{C} (s) + \text{O}_2 (g) \rightarrow \text{CO}_2 (g)
]
Steps to Calculate ( \Delta H ):
- Identify the standard enthalpy of formation (( \Delta H_f^\circ )) values:
- For carbon (( \text{C} )): ( \Delta H_f^\circ = 0 \, \text{kJ/mol} ) (element in standard state)
- For oxygen (( \text{O}_2 )): ( \Delta H_f^\circ = 0 \, \text{kJ/mol} ) (element in standard state)
- For carbon dioxide (( \text{CO}_2 )): ( \Delta H_f^\circ = -393.5 \, \text{kJ/mol} )
- Apply the formula:
[
\Delta H = \left( \Delta H_f^\circ \, \text{of products} \right) – \left( \Delta H_f^\circ \, \text{of reactants} \right)
]
[
\Delta H = \left(-393.5 \, \text{kJ/mol} \right) – \left(0 + 0\right) = -393.5 \, \text{kJ/mol}
]
Conclusion:
The enthalpy change (( \Delta H )) for the combustion of carbon to form carbon dioxide is (-393.5 \, \text{kJ/mol}). This negative sign indicates that the reaction is exothermic, meaning it releases heat to the surroundings.
Explanation:
The enthalpy change is an important concept in thermodynamics that reflects the energy changes during a chemical reaction. It provides insights into the feasibility of reactions, guiding chemists in predicting whether a reaction will occur spontaneously under given conditions. In the example above, the formation of carbon dioxide from carbon and oxygen is a highly exothermic reaction, which is a common characteristic of combustion processes. Understanding these changes helps in various applications, including energy production, environmental chemistry, and industrial processes. The negative ( \Delta H ) value signifies that energy is released, making the reaction energetically favorable, a principle crucial in fields like combustion engineering and environmental science.