Problem 87 - Chemistry A Molecular Approach

Question

Use standard enthalpies of formation to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for each reaction. a. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\) b. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\) c. \(3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)\) d. \(\mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Cr}(s)+3 \mathrm{CO}_{2}(g)\)

Step-by-Step Solution

Answer

To calculate the \(\Delta H_{\mathrm{rxn}}^{\circ}\) for each reaction, apply the formula \(\Delta H_{\mathrm{rxn}}^{\circ} = \sum \Delta H_{\mathrm{f,products}}^{\circ} - \sum \Delta H_{\mathrm{f,reactants}}^{\circ}\) using the standard enthalpies of formation for each substance in each reaction.

Step 1 - Understanding Enthalpy Change of Reaction

The enthalpy change of a reaction, denoted as \(\Delta H_{\mathrm{rxn}}^{\circ}\), is calculated using the formula: \(\Delta H_{\mathrm{rxn}}^{\circ} = \sum \Delta H_{\mathrm{f,products}}^{\circ} - \sum \Delta H_{\mathrm{f,reactants}}^{\circ}\). This means that you subtract the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products.

Step 2 - Applying the Calculation to Reaction (a)

For reaction a: \(\mathrm{C}_{2} \mathrm{H}_{4}(g) + \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\), calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) using known values of standard enthalpies of formation (these values would typically be provided in a table or need to be looked up). The calculation is \(\Delta H_{\mathrm{rxn}}^{\circ} = \Delta H_{\mathrm{f,C}_{2}\mathrm{H}_{6}(g)}^{\circ} - (\Delta H_{\mathrm{f,C}_{2}\mathrm{H}_{4}(g)}^{\circ} + \Delta H_{\mathrm{f,H}_{2}(g)}^{\circ})\).

Step 3 - Applying the Calculation to Reaction (b)

For reaction b: \(\mathrm{CO}(g) + \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g) + \mathrm{CO}_{2}(g)\), calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) using \(\Delta H_{\mathrm{rxn}}^{\circ} = (\Delta H_{\mathrm{f,H}_{2}(g)}^{\circ} + \Delta H_{\mathrm{f,CO}_{2}(g)}^{\circ}) - (\Delta H_{\mathrm{f,CO}(g)}^{\circ} + \Delta H_{\mathrm{f,H}_{2}O(g)}^{\circ})\).

Step 4 - Applying the Calculation to Reaction (c)

For reaction c: \(3 \mathrm{NO}_{2}(g) + \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(aq) + \mathrm{NO}(g)\), calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) using \(\Delta H_{\mathrm{rxn}}^{\circ} = (2 \Delta H_{\mathrm{f,HNO}_{3}(aq)}^{\circ} + \Delta H_{\mathrm{f,NO}(g)}^{\circ}) - (3 \Delta H_{\mathrm{f,NO}_{2}(g)}^{\circ} + \Delta H_{\mathrm{f,H}_{2}O(l)}^{\circ})\).

Step 5 - Applying the Calculation to Reaction (d)

For reaction d: \(\mathrm{Cr}_{2} \mathrm{O}_{3}(s) + 3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Cr}(s) + 3 \mathrm{CO}_{2}(g)\), calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) using \(\Delta H_{\mathrm{rxn}}^{\circ} = (2 \Delta H_{\mathrm{f,Cr}(s)}^{\circ} + 3 \Delta H_{\mathrm{f,CO}_{2}(g)}^{\circ}) - (\Delta H_{\mathrm{f,Cr}_{2}\mathrm{O}_{3}(s)}^{\circ} + 3 \Delta H_{\mathrm{f,CO}(g)}^{\circ})\).

Key Concepts

Standard Enthalpies of Formation

When dealing with thermochemistry, we frequently use the concept of standard enthalpies of formation, ewline denoted as ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline standard enthalpy of formation of any substance is the heat change that occurs when one mole of a substance is formed from its elements in their standard states. To apply these values in calculations, we use tables listing the enthalpies for various substances under standard conditions, typically at 1 bar pressure and a reference temperature of 298.15 K (25°C). For example, the ewline standard enthalpy of formation of liquid water ( ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline liquid) is -285.8 kJ/mol, suggestive of the fact that energy is released when gaseous hydrogen and oxygen combine to form liquid water. Having a grasp of standard enthalpies of formation is critical for accurate enthalpy calculations in chemical reactions.

Thermochemistry

Thermochemistry is the branch of chemistry that studies the energy and heat involved with chemical reactions and physical transformations. The key concept here is enthalpy ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ( ), a measure of the total heat content of a system. In a chemical reaction, enthalpy change (ewline) can be positive or negative, indicating endothermic or exothermic reactions, respectively. Thermochemical equations often include enthalpy changes to reflect the heat transfer during the reaction, which is vital for understanding reaction energetics and designing processes that comply with energy requirements and conservation.

Chemical Reactions

Chemical reactions are processes where reactants transform into products through the breaking and forming of chemical bonds. These reactions involve energy changes, often observed as heat or light. The type of reaction—whether it's a combination, decomposition, single-replacement, double-replacement, or combustion—can greatly influence the amount and direction of energy transfer. By applying the laws of thermodynamics and the concept of enthalpy of formation, we can predict the feasibility and spontaneity of reactions. Recognizing how these reactions absorb or release heat is crucial for not only chemistry but also for applications across materials science, biology, environmental science, and engineering.

Enthalpy Calculations

Calculating the enthalpy change ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline (ewline) of a reaction involves utilizing the standard enthalpies of formation for both reactants and products as mentioned in the original exercise. This method, known as Hess's Law, allows us to determine the overall enthalpy change without needing to know the entire reaction pathway. It is an invaluable tool for chemists, allowing the calculation of the energy changes associated with reactions, which is fundamental when designing chemical processes and understanding reaction mechanisms.