What mass of potassium chlorate (`KClO_3`) on heating gives 1.591 g of potassium chloride (KCl) and 0.772 litres of oxygen at NTP?

Options

A. 1.551g
B. 2.551g
C. 1.591g
D. None

Explanation

To solve the problem of determining the mass of potassium chlorate (KClO₃) that decomposes to produce 1.591 g of potassium chloride (KCl) and 0.772 liters of oxygen (O₂) at NTP, we can follow these steps:

### Step 1: Write the decomposition reaction of potassium chlorate
The decomposition of potassium chlorate can be represented by the following balanced chemical equation:
\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]

### Step 2: Determine the moles of potassium chloride produced
We know the mass of potassium chloride (KCl) produced is 1.591 g. To find the number of moles of KCl, we need to use its molar mass. The molar mass of KCl is approximately:
- K: 39.1 g/mol
- Cl: 35.5 g/mol
- Molar mass of KCl = 39.1 + 35.5 = 74.6 g/mol

Now, we calculate the number of moles of KCl:
\[ \text{Moles of KCl} = \frac{\text{mass of KCl}}{\text{molar mass of KCl}} = \frac{1.591 \text{ g}}{74.6 \text{ g/mol}} \approx 0.0213 \text{ moles} \]

### Step 3: Determine the moles of oxygen produced
Next, we need to calculate the number of moles of oxygen produced from the given volume at NTP. At NTP, 1 mole of gas occupies 22.4 liters. Therefore, we can calculate the moles of O₂:
\[ \text{Moles of O}_2 = \frac{\text{volume of O}_2}{22.4 \text{ L/mol}} = \frac{0.772 \text{ L}}{22.4 \text{ L/mol}} \approx 0.0345 \text{ moles} \]

### Step 4: Relate the moles of KCl and O₂ to KClO₃
From the balanced equation, we see that:
- 2 moles of KCl are produced for every 3 moles of O₂ produced.
- Therefore, the ratio of moles of KCl to O₂ is 2:3.

Using the moles of KCl calculated:
\[ \text{Moles of KClO}_3 = \text{Moles of KCl} = 0.0213 \text{ moles} \]

Using the stoichiometry from the balanced equation:
\[ \text{Moles of KClO}_3 = \frac{2}{2} \times \text{Moles of KCl} = 0.0213 \text{ moles} \]

### Step 5: Calculate the mass of potassium chlorate
Now, we can calculate the mass of KClO₃ using its molar mass. The molar mass of KClO₃ is:
- K: 39.1 g/mol
- Cl: 35.5 g/mol
- O: 16.0 g/mol × 3 = 48.0 g/mol
- Molar mass of KClO₃ = 39.1 + 35.5 + 48.0 = 122.6 g/mol

Now, we calculate the mass of KClO₃:
\[ \text{Mass of KClO}_3 = \text{Moles of KClO}_3 \times \text{Molar mass of KClO}_3 = 0.0213 \text{ moles} \times 122.6 \text{ g/mol} \approx 2.61 \text{ g} \]

### Conclusion
The mass of potassium chlorate (KClO₃) that decomposes to give 1.591 g of potassium chloride and 0.772 liters of oxygen at NTP is approximately **2.61 g**.