Calculate the mass of oxygen obtained by complete decomposition of 10kg of pure potassium chlorate (Atomic mass K=39,O=16 and Cl=35.5)

Options

A. 39.2kg
B. 392kg
C. 3.92kg
D. 3kg

Explanation

To calculate the mass of oxygen obtained by the complete decomposition of 10 kg of pure potassium chlorate (KClO3), we can follow these steps:

### Step 1: Write the balanced chemical equation for the decomposition of potassium chlorate.
The balanced equation for the decomposition of potassium chlorate is:
\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]

### Step 2: Calculate the molar mass of potassium chlorate (KClO3).
To find the molar mass, we add the atomic masses of all the atoms in the formula:
- Potassium (K): 39 g/mol
- Chlorine (Cl): 35.5 g/mol
- Oxygen (O): 16 g/mol × 3 = 48 g/mol

So, the molar mass of KClO3 is:
\[ 39 + 35.5 + 48 = 122.5 \text{ g/mol} \]

### Step 3: Convert the mass of potassium chlorate from kg to g.
Given that we have 10 kg of KClO3:
\[ 10 \text{ kg} = 10,000 \text{ g} \]

### Step 4: Calculate the number of moles of potassium chlorate.
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
We can calculate the moles of KClO3:
\[ \text{Number of moles of KClO}_3 = \frac{10,000 \text{ g}}{122.5 \text{ g/mol}} \approx 81.63 \text{ moles} \]

### Step 5: Use the stoichiometry of the reaction to find moles of oxygen produced.
From the balanced equation, we see that:
\[ 2 \text{ moles of KClO}_3 \rightarrow 3 \text{ moles of O}_2 \]
Thus, the mole ratio of KClO3 to O2 is 2:3. Therefore, we can set up the following proportion:
\[ \text{Moles of O}_2 = \left(81.63 \text{ moles KClO}_3\right) \times \frac{3 \text{ moles O}_2}{2 \text{ moles KClO}_3} \approx 122.45 \text{ moles O}_2 \]

### Step 6: Calculate the mass of oxygen produced.
Now, we can convert moles of O2 to grams using its molar mass (32 g/mol):
\[ \text{Mass of O}_2 = \text{Number of moles} \times \text{Molar mass} = 122.45 \text{ moles} \times 32 \text{ g/mol} \approx 3,911.2 \text{ g} \]

### Step 7: Convert the mass of oxygen from grams to kilograms.
\[ 3,911.2 \text{ g} = 3.9112 \text{ kg} \approx 3.92 \text{ kg} \]

### Final Answer:
The mass of oxygen obtained by the complete decomposition of 10 kg of pure potassium chlorate is approximately **3.92 kg**.

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