Predict the sign of the entropy change of the system for each of the following reactions: (d) Al₂O₃(s) + 3 H₂(g) → 2 Al(s) + 3 H₂O(g)

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1. Identify the states of matter for each reactant and product in the reaction: Al_2O_3(s) is a solid, H_2(g) is a gas, Al(s) is a solid, and H_2O(g) is a gas.
2. Consider the number of moles of gas on each side of the reaction. On the reactant side, there are 3 moles of H_2(g). On the product side, there are 3 moles of H_2O(g).
3. Since the number of moles of gas is the same on both sides of the reaction, the change in entropy due to the number of gas molecules is likely minimal.
4. Examine the change in the state of matter: Al_2O_3(s) is converted to Al(s) and H_2(g) is converted to H_2O(g). The conversion of solid to solid and gas to gas suggests no significant change in entropy due to phase change.
5. Predict the sign of the entropy change: Since there is no significant change in the number of gas molecules or phase, the entropy change of the system is likely to be small, possibly slightly positive or negative, but not significantly different from zero.

Key Concepts

Entropy (S)

Entropy is a measure of the disorder or randomness in a system. In chemical reactions, changes in entropy can indicate whether the products are more or less disordered than the reactants. A positive change in entropy suggests an increase in disorder, while a negative change indicates a decrease.

Phase Changes and Entropy

The phase of a substance significantly affects its entropy. Gases generally have higher entropy than solids due to their greater freedom of movement and higher disorder. In the given reaction, the conversion of solid aluminum oxide and gaseous hydrogen into solid aluminum and gaseous water must be analyzed in terms of phase changes to predict the overall entropy change.

Stoichiometry and Reaction Direction

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. Understanding the stoichiometry of the reaction helps in predicting the number of moles of gaseous products and reactants, which is crucial for determining the overall change in entropy. In this reaction, the balance of gaseous and solid components will influence the sign of the entropy change.