Problem 83 - Chemistry The Science in Context

Question

For which of the following reactions does \(\Delta H_{\mathrm{rxn}}^{\circ}\) represent an enthalpy of formation? a. \(C(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)\) b. \(\mathrm{CO}_{2}(g)+\mathrm{C}(s) \rightarrow 2 \mathrm{CO}(g)\) c. \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)\) d. \(2 \mathrm{H}_{2}(g)+\mathrm{C}(s) \rightarrow \mathrm{CH}_{4}(g)\)

Step-by-Step Solution

Answer

Answer: Reactions (a) and (d) represent enthalpies of formation for CO₂ and CH₄, respectively.

Step 1: Analyze the reactions

We will go through each of the reactions and check if it represents an enthalpy of formation.

Step 2: Reaction a

\(C(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)\): In this reaction, one mole of carbon dioxide (CO\(_2\)) is formed from its constituent elements, carbon (C) and oxygen (O\(_2\)), both in their standard states (solid carbon and gaseous oxygen). Thus, this reaction represents the enthalpy of formation for CO\(_2\).

Step 3: Reaction b

\(\mathrm{CO}_{2}(g)+\mathrm{C}(s) \rightarrow 2 \mathrm{CO}(g)\): In this reaction, one mole of CO is formed from CO\(_2\) and C. This does not represent an enthalpy of formation, as CO is not being formed directly from its constituent elements (C and O\(_2\)).

Step 4: Reaction c

\(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{H}_{2}\mathrm{O}(g)+\mathrm{CO}(g)\): This reaction involves the formation of two compounds - water (H\(_2\)O) and carbon monoxide (CO) - from two other compounds - carbon dioxide (CO\(_2\)) and hydrogen gas (H\(_2\)). This reaction does not represent the enthalpy of formation for either H\(_2\)O or CO, as neither is being formed directly from their constituent elements.

Step 5: Reaction d

\(2 \mathrm{H}_{2}(g)+\mathrm{C}(s) \rightarrow \mathrm{CH}_{4}(g)\): In this reaction, one mole of methane (CH\(_4\)) is formed from its constituent elements - hydrogen (H\(_2\)) and carbon (C) - both in their standard states (gaseous hydrogen and solid carbon). Thus, this reaction represents the enthalpy of formation for CH\(_4\).

Step 6: Conclusion

From the given reactions, we can conclude that reactions (a) and (d) represent enthalpies of formation, as they involve the formation of one mole of CO\(_2\) (carbon dioxide) and CH\(_4\) (methane), respectively, from their constituent elements in their standard states.

Key Concepts

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the energy and heat associated with chemical reactions and physical transformations. A fundamental aspect of thermochemistry is the study of enthalpy changes during chemical processes. Enthalpy, denoted as H, is a measure of total heat content in a thermodynamic system at constant pressure. The change in enthalpy, \(\Delta H\), helps us understand how much energy is absorbed or released in a reaction.

When a substance is formed from its most basic elements in their standard states, the enthalpy change of the reaction is known as the enthalpy of formation, \(\Delta H_f^\circ\). For instance, the formation of one mole of carbon dioxide (CO2) from elemental carbon and oxygen gas involves an enthalpy change that coincides with its standard enthalpy of formation.

Standard Enthalpy Change

The standard enthalpy change, \(\Delta H^\circ\), is the change in enthalpy for a process where the reactants and products are in their standard states. The \(\circ\) symbol represents standard conditions, typically 298 K and 1 atmosphere of pressure. For example, the standard enthalpy of formation is a specific type of standard enthalpy change pertaining to the formation of one mole of a compound from its constituent elements in their standard states.

Reaction (d) in the exercise brings attention to the fact that the standard enthalpy of formation must be carefully delineated from other types of enthalpy changes, as it relates specifically to the creation of a compound from its elemental forms under standard conditions. Hence, the reaction must be between the most stable forms of those elements at standard conditions to qualify.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products and can be represented by chemical equations. Every chemical reaction is associated with an energy change, typically in the form of heat. This energy change is a reflection of the difference in bond energies between reactants and products.

It's important to distinguish different types of chemical reactions. For instance, synthesis reactions involve combining elements or simpler compounds to form a more complex compound, like the formation of CO2 from C and O2 in reaction (a). On the other hand, reaction (b) is a decomposition reaction, where a complex molecule breaks down into simpler substances, such as CO2 decomposing into CO and C, which does not correspond to an enthalpy of formation.

Standard States

The standard state of a substance is its thermodynamically most stable physical form at 1 atmosphere of pressure and a specified temperature, usually taken as 25°C (298 K). For example, oxygen exists as a diatomic gas (O2), and carbon is in the form of graphite at these conditions, and they represent the standard states of those elements.

In thermochemistry, it is crucial to account for reactants and products being in their standard states when calculating or referring to standard enthalpy changes. This ensures consistency and comparability in thermodynamic data. The reactions presented in the exercise highlight how only those reactions that involve elements in their standard states leading to the formation of a single product can be classified as enthalpy of formation, emphasizing the relevance of standard states in thermochemical measurements and calculations.