Problem 22 - Chemistry: An Atoms-Focused Approach

Question

Using data in Appendix \(4,\) calculate \(\Delta H^{\circ}\) for the reaction $$\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{NO}_{2}(g)$$

Step-by-Step Solution

Answer

Answer: The standard enthalpy change for the given reaction is -199.52 kJ/mol.

Step 1: Find the standard enthalpy of formation values for each compound

Refer to Appendix 4 to find the standard enthalpy of formation values for each compound in the given reaction. You should find the following values: - \(\Delta H^{\circ}_{\mathrm{O}_{3}} = 142.33\,\text{kJ/mol}\) - \(\Delta H^{\circ}_{\mathrm{O}_{2}} = 0\,\text{kJ/mol}\) - \(\Delta H^{\circ}_{\mathrm{NO}} = 90.37\,\text{kJ/mol}\) - \(\Delta H^{\circ}_{\mathrm{NO}_{2}} = 33.18\,\text{kJ/mol}\)

Step 2: Calculate the enthalpy change for the reaction

Plug the values found in Step 1 into the equation: $$\Delta H^{\circ} = \sum \Delta H^{\circ}_{\text{products}} - \sum \Delta H^{\circ}_{\text{reactants}}$$ $$\Delta H^{\circ} = (\Delta H^{\circ}_{\mathrm{O}_{2}} + \Delta H^{\circ}_{\mathrm{NO}_{2}}) - (\Delta H^{\circ}_{\mathrm{O}_{3}} + \Delta H^{\circ}_{\mathrm{NO}})$$ Substitute the values: $$\Delta H^{\circ} = (0\,\text{kJ/mol} + 33.18\,\text{kJ/mol}) - (142.33\,\text{kJ/mol} + 90.37\,\text{kJ/mol})$$

Step 3: Calculate the result

Now, perform the calculation to find the standard enthalpy change for the reaction: $$\Delta H^{\circ} = 33.18\,\text{kJ/mol} - 232.70\,\text{kJ/mol} = -199.52\,\text{kJ/mol}$$ So, the standard enthalpy change for the given reaction is \(\Delta H^{\circ} = -199.52\,\text{kJ/mol}\).

Key Concepts

Standard Enthalpy of Formation

Understanding standard enthalpy of formation is key in chemical thermodynamics. It refers to the energy change when one mole of a compound forms from its elements under standard conditions, which are

• Pressure: 1 atmosphere
• Temperature: 25°C (298 K)

This concept is crucial as it provides a baseline for calculating enthalpy changes in reactions.
When elements form a compound, energy is either absorbed or released. For instance, the formation enthalpy of the diatomic molecule the diatomic molecule diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen, diatomic oxygen ( diatomic oxygen ( diatomic oxygen ( diatomic oxygen ( diatomic oxygen ( diatomic oxygen ( diatomic oxygen ( diatomic oxygen ( diatomic oxygen and gas and gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas nitric oxide ( gas nitric oxide ( gas nitric oxide ( gas nitric oxide ( gas nitric oxide (NO) are 0 kJ/mol and 90.37 kJ/mol respectively. Recognizing these values helps visualize how compounds derive energy during formation. It bolsters our understanding of why reactions either release or absorb heat.

Chemical Thermodynamics

Chemical thermodynamics explores energy transformations in chemical processes. It helps predict if reactions occur and how much energy they require or release.
Key components include:

• Enthalpy (Enthalpy Enthalpy enthalpy (\(H\)): which indicates heat content.
• Entropy (Entropy Entropy entropy entropy(\(S\)): which measures system disorder.
• Gibbs Free Energy (Gibbs Free Energy (Gibbs Free Energy (Gibbs Free Energy (Gibbs Free Energy (Gibbs Free Energy (Gibbs Free Energy Gibbs Free Energy Gibbs Free Energy (\(G\)): providing insight into spontaneity.

Understanding these concepts and their interplay is critical in determining reaction feasibility.
Applying these principles helps solve practical problems such as calculating reaction enthalpy changes using known formation data or predicting if processes are endothermic or exothermic.

Hess's Law

Hess's Law is an essential principle in chemistry stating that total enthalpy change is the same, regardless of how a reaction proceeds. It highlights that enthalpy is a state function, path-independent.
To calculate enthalpy change, you can use the formula:\[\Delta H^{\circ} = \sum \Delta H^{\circ}_{\mathrm{products}} - \sum \Delta H^{\circ}_{\mathrm{reactants}} \]This enables calculations by summing known formation enthalpies, reaffirming the concept that a reaction's overall energy change remains consistent, irrespective of multiple pathways.A practical example involves calculating the standard enthalpy change for ozone (standard enthalpy change for ozone (standard enthalpy change for ozone (\(\mathrm{O}_3\)). This showcases real-world implications, such as environmental effects in atmospheric reactions. Ultimately, Hess's Law forms the backbone of enthalpy calculations and enhances understanding of complex thermodynamic relationships.