Moles of `KClO_3` required for producing sufficient `O_2` to react with 1 mole of aluminium will be (Molar mass of `KClO_3` = 122.5)

Options

A. 2 mole
B. 1 mole
C. 1/2 mole
D. 3/2 mole

Answer

To solve the problem of how many moles of KClO₃ are required to produce sufficient O₂ to react with 1 mole of aluminum, we can follow these steps:

### Step 1: Write the decomposition reaction of KClO₃
The decomposition reaction of potassium chlorate (KClO₃) is:
\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]
This indicates that 2 moles of KClO₃ produce 3 moles of O₂.

### Step 2: Write the reaction of aluminum with oxygen
The reaction of aluminum with oxygen is:
\[ 4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3 \]
From this reaction, we can see that 4 moles of aluminum require 3 moles of O₂.

### Step 3: Calculate the moles of O₂ required for 1 mole of aluminum
From the second reaction, we can determine how much O₂ is needed for 1 mole of aluminum:
- If 4 moles of Al require 3 moles of O₂, then 1 mole of Al will require:
\[ \frac{3 \text{ moles O}_2}{4 \text{ moles Al}} = \frac{3}{4} \text{ moles O}_2 \]

### Step 4: Determine how many moles of KClO₃ are needed to produce the required O₂
From the first reaction, we know:
- 2 moles of KClO₃ produce 3 moles of O₂.
- Therefore, to find out how many moles of KClO₃ are needed to produce \(\frac{3}{4}\) moles of O₂, we can set up a proportion:
\[ \text{If } 3 \text{ moles O}_2 \text{ are produced by } 2 \text{ moles KClO}_3, \text{ then } 1 \text{ mole O}_2 \text{ is produced by } \frac{2}{3} \text{ moles KClO}_3 \]
Now, we need \(\frac{3}{4}\) moles of O₂:
\[ \frac{3}{4} \text{ moles O}_2 \text{ will be produced by } \left(\frac{2}{3} \times \frac{3}{4}\right) \text{ moles KClO}_3 \]

### Step 5: Calculate the moles of KClO₃ needed
Calculating the above expression:
\[ \frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{2}{4} = \frac{1}{2} \text{ moles KClO}_3 \]

### Final Answer
Thus, the moles of KClO₃ required to produce sufficient O₂ to react with 1 mole of aluminum is:
\[ \frac{1}{2} \text{ moles KClO}_3 \]

### Summary of Options
- Option 1: 2 moles (Incorrect)
- Option 2: 1 mole (Incorrect)
- Option 3: \(\frac{1}{2}\) mole (Correct)
- Option 4: \(\frac{3}{2}\) moles (Incorrect)

The correct answer is **Option 3: \(\frac{1}{2}\) moles of KClO₃**.