What mass of potassium chlorate `(KClO_3)` on heating gives 1.971 g of potassium chloride (KCl) and 0.772 litres of oxygen at NTP?

Explanation

To determine the mass of potassium chlorate (KClO₃) that decomposes to produce 1.971 g of potassium chloride (KCl) and 0.772 liters of oxygen (O₂) at NTP, we can follow these steps:

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

### Step 2: Calculate the number of moles of oxygen produced.
At NTP (Normal Temperature and Pressure), 1 mole of gas occupies 22.4 liters. We can calculate the number of moles of oxygen produced from the given volume of 0.772 liters:
\[ \text{Number of moles of } O_2 = \frac{0.772 \text{ L}}{22.4 \text{ L/mol}} = 0.0345 \text{ moles} \]

### Step 3: Relate the moles of oxygen to the moles of KClO₃.
From the balanced equation, we see that 3 moles of O₂ are produced from 2 moles of KClO₃. Therefore, we can set up a ratio:
\[ \frac{2 \text{ moles KClO}_3}{3 \text{ moles } O_2} = \frac{x \text{ moles KClO}_3}{0.0345 \text{ moles } O_2} \]
Solving for \(x\):
\[ x = \frac{2}{3} \times 0.0345 = 0.0230 \text{ moles of KClO}_3 \]

### Step 4: Calculate the mass of KClO₃.
The molar mass of KClO₃ is calculated as follows:
- K: 39.1 g/mol
- Cl: 35.5 g/mol
- O: 16.0 g/mol × 3 = 48.0 g/mol

Thus, the molar mass of KClO₃ is:
\[ 39.1 + 35.5 + 48.0 = 122.6 \text{ g/mol} \]

Now, we can calculate the mass of KClO₃:
\[ \text{Mass of KClO}_3 = \text{Number of moles} \times \text{Molar mass} = 0.0230 \text{ moles} \times 122.6 \text{ g/mol} = 2.83 \text{ g} \]

### Step 5: Calculate the total mass of KClO₃.
We also need to add the mass of KCl produced to find the total mass of KClO₃ that decomposed:
\[ \text{Mass of KCl} = 1.971 \text{ g} \]
\[ \text{Mass of O}_2 = \text{Number of moles} \times \text{Molar mass of O}_2 = 0.0345 \text{ moles} \times 32 \text{ g/mol} = 1.104 \text{ g} \]

### Step 6: Total mass of KClO₃.
Now we can find the total mass of KClO₃:
\[ \text{Total mass of KClO}_3 = \text{Mass of KCl} + \text{Mass of O}_2 = 1.971 \text{ g} + 1.104 \text{ g} = 3.075 \text{ g} \]

### Final Answer:
The mass of potassium chlorate (KClO₃) that decomposes to give the specified amounts of KCl and O₂ is approximately **3.075 g**.

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