What mass of potassium chlorate `(KClO_3)` on heating gives 1.591 g of potassium chloride (KCl) and 0.672 litres of oxygen at NTP?

Options

A. 4.58g
B. 2.55g
C. `8.11`g
D. `9.13`g

Explanation

To find the mass of potassium chlorate (KClO₃) that decomposes to give 1.591 g of potassium chloride (KCl) and 0.672 liters of oxygen (O₂) at NTP, we can follow these steps:

### Step 1: Write the balanced equation for the decomposition of potassium chlorate (KClO₃).
The balanced chemical equation for the decomposition of potassium chlorate is:
\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]

### Step 2: Determine the moles of KCl produced.
We know the mass of KCl produced is 1.591 g. To find the number of moles of KCl, we use the molar mass of KCl. The molar mass of KCl is:
- K (Potassium) = 39.1 g/mol
- Cl (Chlorine) = 35.5 g/mol
- Total = 39.1 + 35.5 = 74.6 g/mol

Now, calculate the moles of KCl:
\[ \text{Moles of KCl} = \frac{\text{mass}}{\text{molar mass}} = \frac{1.591 \text{ g}}{74.6 \text{ g/mol}} \approx 0.0214 \text{ moles} \]

### Step 3: Use the stoichiometry of the reaction to find moles of O₂ produced.
From the balanced equation, 2 moles of KCl are produced for every 3 moles of O₂. Therefore, the moles of O₂ produced can be calculated as follows:
\[ \text{Moles of O}_2 = \text{Moles of KCl} \times \frac{3 \text{ moles O}_2}{2 \text{ moles KCl}} = 0.0214 \times \frac{3}{2} \approx 0.0321 \text{ moles} \]

### Step 4: Calculate the volume of O₂ produced at NTP.
At NTP, 1 mole of gas occupies 22.4 liters. Therefore, the volume of O₂ produced can be calculated as:
\[ \text{Volume of O}_2 = \text{Moles of O}_2 \times 22.4 \text{ L/mol} = 0.0321 \times 22.4 \approx 0.72 \text{ L} \]

### Step 5: Calculate the mass of O₂ produced.
The molar mass of O₂ is 32 g/mol. Therefore, the mass of O₂ produced is:
\[ \text{Mass of O}_2 = \text{Moles of O}_2 \times \text{Molar mass of O}_2 = 0.0321 \text{ moles} \times 32 \text{ g/mol} \approx 1.03 \text{ g} \]

### Step 6: Calculate the total mass of KClO₃ decomposed.
From the balanced equation, we see that 2 moles of KClO₃ produce 2 moles of KCl and 3 moles of O₂. Therefore, the total mass of KClO₃ can be calculated as:
\[ \text{Mass of KClO}_3 = \text{Mass of KCl} + \text{Mass of O}_2 = 1.591 \text{ g} + 1.03 \text{ g} \approx 2.621 \text{ g} \]

### Step 7: Calculate the mass of KClO₃.
Now, we need to find the mass of KClO₃ that corresponds to the moles we calculated. The molar mass of KClO₃ is:
- K (Potassium) = 39.1 g/mol
- Cl (Chlorine) = 35.5 g/mol
- O (Oxygen) = 16 g/mol × 3 = 48 g/mol
- Total = 39.1 + 35.5 + 48 = 122.6 g/mol

Now, we can calculate the mass of KClO₃:
\[ \text{Mass of KClO}_3 = \text{Moles of KClO}_3 \times \text{Molar mass of KClO}_3 \]
Since 2 moles of KClO₃ produce 2 moles of KCl, we can find the moles of KClO₃:
\[ \text{Moles of KClO}_3 = \text{Moles of KCl} = 0.0214 \text{ moles} \]
Now, calculate the mass:
\[ \text{Mass of KClO}_3 = 0.0214 \text{ moles} \times 122.6 \text{ g/mol} \approx 2.621 \text{ g} \]

### Final Answer:
The mass of potassium chlorate (KClO₃) that decomposes to give the specified amounts of KCl and O₂ is approximately **2.621 g**.

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