What mass of potassium chlorate `(KClO_3)` on heating gives 1.791 g of potassium chloride (KCl) and 0.772 litres of oxygen at NTP?

Explanation

To solve the problem, we need to determine the mass of potassium chlorate (KClO₃) that decomposes to produce a given mass of potassium chloride (KCl) and a certain volume of oxygen gas (O₂) at normal temperature and pressure (NTP).

### Step-by-Step Solution:

1. **Write the Decomposition Reaction**:
The decomposition of potassium chlorate can be represented as:
\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]

2. **Determine Moles of Oxygen Produced**:
At NTP, 1 mole of gas occupies 22.4 liters. We need to find the number of moles of oxygen produced from the given volume (0.772 liters).
\[ \text{Moles of } O_2 = \frac{0.772 \text{ L}}{22.4 \text{ L/mol}} \approx 0.0345 \text{ moles} \]

3. **Relate Moles of KClO₃ to Moles of O₂**:
From the balanced equation, 2 moles of KClO₃ produce 3 moles of O₂. Therefore, we can set up a ratio to find the moles of KClO₃ that correspond to the moles of O₂ produced:
\[ \text{Moles of KClO}_3 = \frac{2}{3} \times \text{Moles of } O_2 = \frac{2}{3} \times 0.0345 \approx 0.0230 \text{ moles} \]

4. **Calculate the Mass of KClO₃**:
The molar mass of KClO₃ can be calculated as follows:
- K: 39.1 g/mol
- Cl: 35.5 g/mol
- O: 16.0 g/mol × 3 = 48.0 g/mol
\[ \text{Molar mass of KClO}_3 = 39.1 + 35.5 + 48.0 = 122.6 \text{ g/mol} \]
Now, we can calculate the mass of KClO₃:
\[ \text{Mass of KClO}_3 = \text{Moles} \times \text{Molar Mass} = 0.0230 \text{ moles} \times 122.6 \text{ g/mol} \approx 2.83 \text{ grams} \]

5. **Final Calculation**:
We need to ensure that we also consider the mass of KCl produced. The mass of KCl is given as 1.791 grams. The total mass of KClO₃ decomposed is the sum of the mass of KCl produced and the mass of oxygen produced.

First, calculate the mass of oxygen produced:
\[ \text{Moles of } O_2 = 0.0345 \text{ moles} \Rightarrow \text{Mass of } O_2 = 0.0345 \times 32 \text{ g/mol} \approx 1.104 \text{ grams} \]

Now, add the masses:
\[ \text{Total mass of KClO}_3 = \text{Mass of KCl} + \text{Mass of } O_2 = 1.791 \text{ g} + 1.104 \text{ g} \approx 2.895 \text{ grams} \]

### Conclusion:
The mass of potassium chlorate (KClO₃) that decomposes to give the specified amounts of KCl and O₂ is approximately **2.895 grams**.