1 mol of `KCIO_(3)` is thermally decomposed and excess of aluminium is burnt in the gaseous product. How many moles of `Al_(2)O_(3)` are formed?

Options

A. 1
B. 2
C. 1.5
D. 3

Answer

To solve the problem step by step, we will analyze the thermal decomposition of potassium chlorate (KClO3) and the subsequent reaction with aluminum (Al).

### Step 1: Write the decomposition reaction of KClO3
The thermal decomposition of potassium chlorate (KClO3) can be represented as follows:

\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]

From this reaction, we can see that 2 moles of KClO3 produce 3 moles of oxygen gas (O2).

### Step 2: Determine the amount of O2 produced from 1 mole of KClO3
Since the decomposition of 2 moles of KClO3 produces 3 moles of O2, we can find out how much O2 is produced from 1 mole of KClO3:

\[ \text{From 1 mole of KClO}_3: \]
\[ \frac{3 \text{ moles O}_2}{2 \text{ moles KClO}_3} = 1.5 \text{ moles O}_2 \]

So, 1 mole of KClO3 produces 1.5 moles of O2.

### Step 3: Write the reaction of aluminum with oxygen
When aluminum reacts with oxygen, it forms aluminum oxide (Al2O3). The balanced chemical equation for this reaction is:

\[ 4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3 \]

### Step 4: Determine how many moles of Al2O3 are produced from the available O2
From the balanced equation, we can see that 3 moles of O2 produce 2 moles of Al2O3. To find out how many moles of Al2O3 can be produced from 1.5 moles of O2, we set up a proportion:

\[ \text{From 3 moles O}_2: 2 \text{ moles Al}_2\text{O}_3 \]
\[ \text{From 1.5 moles O}_2: x \text{ moles Al}_2\text{O}_3 \]

Using the ratio:

\[ \frac{2 \text{ moles Al}_2\text{O}_3}{3 \text{ moles O}_2} = \frac{x \text{ moles Al}_2\text{O}_3}{1.5 \text{ moles O}_2} \]

Cross-multiplying gives:

\[ 2 \times 1.5 = 3x \]
\[ 3 = 3x \]
\[ x = 1 \]

### Conclusion
Therefore, from the thermal decomposition of 1 mole of KClO3 and the reaction of the produced O2 with excess aluminum, **1 mole of Al2O3** is formed.

### Final Answer
**1 mole of Al2O3 is formed.**

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