Problem 21 - General Chemistry

Question

Is the following reaction the appropriate one to use in determining the enthalpy of formation of methane, \(\mathrm{CH}_{4}(g) ?\) Why or why not? $$ \mathrm{C}(g)+4 \mathrm{H}(g) \longrightarrow \mathrm{CH}_{4}(g) $$

Step-by-Step Solution

Answer

No, the reaction involves gaseous atoms, not stable forms of elements.

Step 1: Understanding the Enthalpy of Formation

The enthalpy of formation of a compound is the change in enthalpy when one mole of the compound is formed from its elements in their most stable forms under standard conditions. For methane \( \mathrm{CH}_4(g) \), this involves the elements carbon and hydrogen in their stable forms.

Step 2: Elements in Stable Form

The stable form of carbon under standard conditions is solid graphite \( \mathrm{C(s)} \), and the stable form of hydrogen is diatomic gas \( \mathrm{H_2(g)} \). Any reaction used to determine the enthalpy of formation must start from these forms.

Step 3: Evaluating the Given Reaction

The given reaction, \( \mathrm{C}(g) + 4 \mathrm{H}(g) \rightarrow \mathrm{CH}_4(g) \), involves gaseous carbon and hydrogen atoms, \( \mathrm{C}(g) \) and \( \mathrm{H}(g) \), which are not the stable forms of these elements under standard conditions.

Step 4: Conclusion on the Appropriateness of the Reaction

Since the reaction uses carbon and hydrogen in the gaseous atomic forms rather than graphite and \( \mathrm{H_2} \), it is not appropriate for determining the enthalpy of formation of \( \mathrm{CH}_4(g) \). The enthalpy of formation must start from the most stable forms of the elements.

Key Concepts

Methane

Methane, with the chemical formula \(\mathrm{CH}_4(g)\), is a simple hydrocarbon and one of the most common compounds on Earth. It is composed of one carbon atom bonded to four hydrogen atoms. Understanding the formation of methane is crucial in thermodynamics, especially when it comes to its enthalpy of formation.

• Methane is often produced naturally in environments such as wetlands, where organic material breaks down anaerobically.
• It is a significant component of natural gas and is used widely as a fuel due to its clean combustion.
• In the atmosphere, methane acts as a potent greenhouse gas, having a considerable impact on climate change.

During the formation of methane, the carbon atom typically comes from its elemental form, usually graphite. Understanding the enthalpy of formation for methane helps in assessing energy changes associated with chemical reactions. This information is essential in various industrial processes, where methane is a common reactant or product.

Stable Forms of Elements

Every element can exist in various forms, but in thermodynamics, the stable forms under standard conditions are essential when calculating the enthalpy of formation. These are the forms that elements naturally assume under standard pressure and temperature.
For the elements involved in methane's formation:

• Carbon: The most stable form is graphite, represented as \(\mathrm{C(s)}\). This allotrope of carbon is thermodynamically favored over diamond under normal conditions. Graphite's layered structure accounts for its stability and conductive properties.
• Hydrogen: Exists as a diatomic molecule, \(\mathrm{H_2(g)}\), under standard conditions. The \(\mathrm{H-H}\) bond is stable and requires significant energy to break.

Reactions calculating the enthalpy of formation must begin with these stable forms. Using other forms, like atomic carbon \(\mathrm{C(g)}\) or atomic hydrogen \(\mathrm{H(g)}\), would not reflect the true enthalpy of formation due to added energy involved in converting these unstable forms into their stable states.

Standard Conditions

Standard conditions are a set of standardized reference points used in chemistry to ensure consistency. They are crucial for determining various thermodynamic quantities, including the enthalpy of formation.

• These conditions typically refer to a pressure of 1 atmosphere (atm).
• The standard temperature usually considered is 298 K (25°C).
• Solutions are generally assumed to have a concentration of 1 M.

When discussing enthalpy changes, the term 'standard' implies these specific conditions. Deviations from these conditions can lead to different energetic outcomes. Therefore, reactions used for calculating enthalpy changes must reflect these standard conditions to be accurate and comparable across different studies. In the context of enthalpy of formation for methane, starting with the most stable forms of carbon and hydrogen ensures that the measurements align with these standardized parameters.