Question at position 12 Calculate ΔS° for the reaction 4Cr(s) + 3O2(g) → 2Cr2O3(s) [table]
Substance | Cr(s) | O2(g) | Cr2O3(s) S°(J/K·mol) | 23.77 | 205.138 | 81.2
[/table] 147.7 J/(K mol)−147.7 J/(K mol)548.1 J/(K mol)−548.1 J/(K mol)310.1 J/(K mol)

Question

BlackTom AI · Accepted Answer

Entropy change ΔS° is calculated from the standard molar entropies of products minus reactants:
ΔS° = Σ S°(products) − Σ S°(reactants).

1) Relevant concepts:
- Standard entropy S° is an extensive property given per mole. For a reaction, multiply each S° by its stoichiometric coefficient and subtract reactants from products.
- The units are J·K−1 per mole of reaction (commonly written J/(K·mol)).

2) Step-by-step reasoning and calculations:
Products: 2 Cr2O3(s)
- S°(Cr2O3) = 81.2 J/(K·mol)
- Total S°(products) = 2 × 81.2 = 162.4 J/K

Reactants: 4 Cr(s) + 3 O2(g)
- S°(Cr) = 23.77 J/(K·mol) → 4 × 23.77 = 95.08 J/K
- S°(O2) = 205.138 J/(K·mol) → 3 × 205.138 = 615.414 J/K
- Total S°(reactants) = 95.08 + 615.414 = 710.494 J/K

3) Compute ΔS°:
ΔS° = 162.4 − 710.494 = −548.094 J/K

Rounding to the same precision as the given choices (one decimal) gives ΔS° = −548.1 J/(K·mol).

4) Why this is correct:
The large negative value arises because three moles of gaseous O2 (high entropy per mole) are consumed and converted into solid Cr2O3, greatly decreasing the total disorder; hence ΔS° is strongly negative.

5) Why the other options are incorrect:
- 147.7 J/(K·mol): This is neither the product nor reactant total; sign and magnitude do not match the computed difference.
- −147.7 J/(K·mol): Magnitude too small; incorrect subtraction.
- 548.1 J/(K·mol): Sign is positive but actual change is negative because entropy decreases.
- 310.1 J/(K·mol): Does not match the computed difference.

6) Conclusion:
The calculated standard entropy change is −548.1 J/(K·mol), which matches the provided correct answer: −548.1 J/(K mol).

Question at position 12 Calculate ΔS° for the reaction 4Cr(s) + 3O2(g) → 2Cr2O3(s) [table] Substance | Cr(s) | O2(g) | Cr2O3(s) S°(J/K·mol) | 23.77 | 205.138 | 81.2 [/table] 147.7 J/(K mol)−147.7 J/(K mol)548.1 J/(K mol)−548.1 J/(K mol)310.1 J/(K mol)单项选择题

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