When aluminium oxide `(Al_(2)O_(3))` is electrolysed for the production of aluminium metal. For a given quantity of electricty, the number of moles of aluminium obtained if the volume of `O_(2)` gas obtained is 201.6 litre measured at NTP, is

Options

A. 3
B. 9
C. 12
D. 6

Answer

To solve the problem of determining the number of moles of aluminium obtained from the electrolysis of aluminium oxide `(Al_(2)O_(3))`, given that the volume of `O_(2)` gas produced is 201.6 liters at NTP, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Reaction**:
The electrolysis of aluminium oxide can be represented by the following reaction:
\[ 2 Al_2O_3 \rightarrow 4 Al + 3 O_2 \]
From this reaction, we can see that 2 moles of aluminium oxide produce 3 moles of oxygen gas.

2. **Calculate Moles of Oxygen**:
At Normal Temperature and Pressure (NTP), 1 mole of gas occupies 22.4 liters. Therefore, we can calculate the number of moles of oxygen produced from the volume given:
\[ \text{Moles of } O_2 = \frac{\text{Volume of } O_2}{\text{Molar volume at NTP}} = \frac{201.6 \text{ L}}{22.4 \text{ L/mol}} = 9 \text{ moles} \]

3. **Relate Moles of Oxygen to Moles of Aluminium**:
From the balanced equation, we see that 3 moles of `O_2` produce 4 moles of `Al`. Therefore, we can set up a proportion to find the moles of aluminium produced:
\[ \frac{4 \text{ moles of } Al}{3 \text{ moles of } O_2} = \frac{x \text{ moles of } Al}{9 \text{ moles of } O_2} \]
Cross-multiplying gives:
\[ 3x = 36 \implies x = \frac{36}{3} = 12 \text{ moles of } Al \]

4. **Conclusion**:
The number of moles of aluminium obtained from the electrolysis of aluminium oxide when 201.6 liters of `O_2` is produced is **12 moles**.

### Final Answer:
The number of moles of aluminium obtained is **12 moles**.

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