Which of the following gives metal by electrolytic reduction conveniently and profitably?

Options

A. PbO
B. `Fe_2O_3`
C. `Cr_2O_3`
D. `Al_2O_3`

Answer

To determine which of the following compounds gives metal by electrolytic reduction conveniently and profitably, we will analyze each option provided:

1. **Identify the Compounds**: The options given are:
- PbO (Lead(II) oxide)
- Fe2O3 (Iron(III) oxide)
- Cr2O3 (Chromium(III) oxide)
- Al2O3 (Aluminum oxide)

2. **Understand Electrolytic Reduction**: Electrolytic reduction is a process where an electric current is used to drive a non-spontaneous reaction, typically to reduce metal ions to their elemental form.

3. **Evaluate Each Option**:
- **PbO**: The reduction of lead oxide can be done electrolytically, but lead is generally more expensive and less efficient in terms of energy consumption compared to aluminum.
- **Fe2O3**: Iron oxide can be reduced electrolytically, but the process is not as economically favorable as aluminum reduction due to higher energy costs and the complexity of the process.
- **Cr2O3**: Chromium oxide can also be reduced electrolytically, but like iron, it is costly and less efficient.
- **Al2O3**: Aluminum oxide is well-known for being reduced electrolytically in the Hall-Héroult process, which is both convenient and profitable. Aluminum is one of the most abundant and cheapest metals to produce through electrolysis.

4. **Conclusion**: Among the options, Al2O3 is the most convenient and profitable for electrolytic reduction due to its lower energy requirements and the abundance of aluminum.

5. **Final Answer**: The answer is **Al2O3 (Option D)**.