Write the balanced chemical equation for the combustion of methane, CH4(g), to give carbon dioxide and water vapor. Explain why it is difficult to predict whether ΔS is positive or negative for this chemical reaction.
The correct answer and explanation is :
The balanced chemical equation for the combustion of methane is:
[
CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)
]
Explanation of Entropy Change (ΔS):
Entropy (( \Delta S )) is a measure of disorder or randomness in a system. Predicting whether ( \Delta S ) is positive or negative for the combustion of methane is challenging because of several competing factors:
- Number of Gas Molecules:
- Before the reaction: There are three gas molecules (1 (CH_4) + 2 (O_2)).
- After the reaction: There are three gas molecules (1 (CO_2) + 2 (H_2O)).
- Since the number of gas molecules remains the same, there is no obvious change in entropy due to molecular count.
- Complexity of Molecules:
- Methane ((CH_4)) and oxygen ((O_2)) are simple molecules.
- Carbon dioxide ((CO_2)) and water vapor ((H_2O)) are different in structure, with water molecules having hydrogen bonding.
- The structural changes can affect molecular motion and degrees of freedom, influencing entropy.
- Phase Changes and Hydrogen Bonding:
- If water is produced as gas, it retains higher entropy than liquid water.
- However, water molecules form hydrogen bonds, which limit their movement and reduce entropy compared to the freely moving oxygen molecules.
- Overall Effect:
- While oxygen molecules are highly disordered, water vapor may introduce some order due to intermolecular interactions.
- This makes it difficult to predict whether the overall ( \Delta S ) is positive or negative without experimental data.
Ultimately, while the total number of gas molecules stays the same, the nature of the molecules and intermolecular interactions make entropy change difficult to determine intuitively. Experimental values suggest that ( \Delta S ) is slightly negative due to the ordering effect of water vapor formation.
Here is the visual representation of the combustion of methane reaction. It illustrates the CH₄ and O₂ molecules on the reactant side and CO₂ and H₂O vapor molecules on the product side, with arrows showing the reaction direction in a combustion flame setting.