Predict the sign of the entropy change of the system for each of the following reactions: (c) 3 C₂H₂(g) → C₆H₆(g)

Verified step by step guidance

1. Identify the states of matter for the reactants and products. In this reaction, both the reactants and the product are gases.
2. Count the number of moles of gas on each side of the reaction. For the reactants, there are 3 moles of C_2H_2(g), and for the product, there is 1 mole of C_6H_6(g).
3. Compare the number of moles of gas on the reactant side to the product side. A decrease in the number of moles of gas generally indicates a decrease in entropy.
4. Consider the molecular complexity. Although C_6H_6 is more complex than C_2H_2, the significant reduction in the number of gas molecules is the dominant factor affecting entropy.
5. Conclude that the entropy change (ΔS) for the system is likely negative because the reaction results in fewer moles of gas, indicating a decrease in disorder.

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. Understanding entropy is crucial for predicting the spontaneity of reactions and the direction of energy flow.

Molecular Complexity

Molecular complexity refers to the number of atoms and the structural arrangement within a molecule. In the given reaction, three molecules of ethyne (C2H2) combine to form one molecule of benzene (C6H6). This change in the number of molecules can significantly affect the entropy of the system, as fewer molecules typically lead to lower entropy.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the direction of chemical reactions and phase changes. It combines enthalpy and entropy into a single value, allowing for the assessment of spontaneity. A reaction is spontaneous if the change in Gibbs Free Energy is negative, which is influenced by both enthalpy and entropy changes.