Use data from Appendix IIB to calculate ΔS°_rxn for each of the reactions. In each case, try to rationalize the sign of ΔS°_rxn. b. Cr₂O₃(s) + 3 CO(g) → 2 Cr(s) + 3 CO₂(g)

Verified step by step guidance

1. Identify the standard entropy values (S°) for each reactant and product from Appendix IIB.
2. Write the balanced chemical equation: Cr2O3(s) + 3 CO(g) → 2 Cr(s) + 3 CO2(g).
3. Calculate the total standard entropy of the reactants: S°(reactants) = S°(Cr2O3) + 3 * S°(CO).
4. Calculate the total standard entropy of the products: S°(products) = 2 * S°(Cr) + 3 * S°(CO2).
5. Determine the change in standard entropy for the reaction: ΔS°rxn = S°(products) - S°(reactants).

Key Concepts

Standard Entropy (ΔS°)

Standard entropy (ΔS°) is a measure of the disorder or randomness in a system at standard conditions (1 bar, 25°C). It quantifies the amount of energy that is unavailable to do work due to the dispersal of energy among the available microstates of a system. Higher entropy values indicate greater disorder, while lower values suggest more order.

Entropy Change in Reactions

The change in entropy (ΔS°rxn) for a chemical reaction is calculated by subtracting the total standard entropies of the reactants from those of the products. A positive ΔS°rxn indicates an increase in disorder, often associated with the production of gas from solids or liquids, while a negative ΔS°rxn suggests a decrease in disorder, typically when gases are converted to solids or liquids.

Rationalizing the Sign of ΔS°rxn

Rationalizing the sign of ΔS°rxn involves analyzing the physical states and the number of moles of reactants and products. For example, in the reaction given, the conversion of solid Cr2O3 and gaseous CO to solid Cr and gaseous CO2 results in a net increase in the number of gas molecules, which typically leads to a positive ΔS°rxn, indicating increased disorder in the system.