Standard free energy of formation for `Al_(2)O_(3)` and `Cr_(2)O_(3)` at `1273 K` are `-827 kJ mol^(-1) (of O_(2))` and `-540 kJ mol^(-1) (of O_(2))`, respectively.
`Al` can reduce `Cr_(2)O_(3)` to `Cr` since, `Delta_(r) G^(Ө)` is negative.

Options

A. If both (A) and ( R) are correct and ( R) is the correct explanation of (A).
B. If both (A) and ( R) are correct, but ( R) is not the correct explanation of (A).
C. If (A) is correct, but ( R) is incorrect.
D. If (A) is incorrect, but ( R) is correct.

Answer

To determine whether aluminum can reduce chromium(III) oxide (Cr₂O₃) to chromium (Cr), we can analyze the standard free energy of formation values given for aluminum oxide (Al₂O₃) and chromium(III) oxide (Cr₂O₃) at 1273 K.

### Step-by-Step Solution:

1. **Identify the Standard Free Energy of Formation Values:**
- For Al₂O₃: ΔG_f° = -827 kJ/mol (of O₂)
- For Cr₂O₃: ΔG_f° = -540 kJ/mol (of O₂)

2. **Understand the Concept of Free Energy Change (ΔG):**
- The free energy change (ΔG) for a reaction indicates whether the reaction is spontaneous. A negative ΔG value suggests that the reaction can occur spontaneously.

3. **Determine the Relative Stability of the Oxides:**
- Since ΔG_f° for Al₂O₃ is more negative than that for Cr₂O₃, this indicates that Al₂O₃ is more stable than Cr₂O₃.

4. **Apply the Thermodynamic Principle:**
- According to thermodynamic principles, a more stable oxide (with a more negative ΔG) can reduce a less stable oxide. In this case, aluminum (from Al₂O₃) can reduce chromium(III) oxide (Cr₂O₃) to chromium (Cr).

5. **Conclusion:**
- Since the ΔG for the formation of Al₂O₃ is more negative than that for Cr₂O₃, aluminum can indeed reduce Cr₂O₃ to Cr. This process is known as the aluminothermic reaction.

### Final Statement:
Thus, aluminum can reduce chromium(III) oxide to chromium because the standard free energy change for the reaction is negative, confirming that the reaction is thermodynamically favorable.

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