What mass of potassium chlorate `(KClO_3)` on heating gives 1.691 g of potassium chloride (KCl) and 0.772 litres of oxygen at NTP?

Options

A. 1.56g
B. 2.65g
C. 22.5g
D. 4.57g

Explanation

To find the mass of potassium chlorate (KClO₃) that decomposes to give 1.691 g of potassium chloride (KCl) and 0.772 liters of oxygen at NTP, we can follow these steps:

### Step 1: Write the balanced chemical equation for the decomposition of potassium chlorate.

The decomposition reaction of potassium chlorate is:
\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]

### Step 2: Determine the moles of oxygen produced.

At NTP (Normal Temperature and Pressure), 1 mole of gas occupies 22.4 liters. Therefore, we can calculate the number of moles of oxygen produced from the volume given (0.772 liters):

\[ \text{Moles of } O_2 = \frac{0.772 \text{ L}}{22.4 \text{ L/mol}} = 0.0345 \text{ moles} \]

### Step 3: Relate moles of oxygen to moles of KClO₃.

From the balanced equation, we see that 3 moles of O₂ are produced from 2 moles of KClO₃. Therefore, we can find the moles of KClO₃ that decomposed to produce 0.0345 moles of O₂:

\[ \text{Moles of } KClO_3 = \frac{2}{3} \times \text{Moles of } O_2 = \frac{2}{3} \times 0.0345 \approx 0.0230 \text{ moles} \]

### Step 4: Calculate the mass of KCl produced.

We know that the mass of KCl produced is given as 1.691 g. To find the moles of KCl produced, we use the molar mass of KCl (approximately 74.55 g/mol):

\[ \text{Moles of } KCl = \frac{1.691 \text{ g}}{74.55 \text{ g/mol}} \approx 0.0227 \text{ moles} \]

### Step 5: Verify the stoichiometric relationship.

From the balanced equation, 2 moles of KCl are produced for every 2 moles of KClO₃ decomposed. Thus, the moles of KCl produced should equal the moles of KClO₃ decomposed:

\[ \text{Moles of } KCl = \text{Moles of } KClO_3 \approx 0.0227 \text{ moles} \]

This is consistent with our earlier calculation.

### Step 6: Calculate the mass of KClO₃.

Now, we can calculate the mass of KClO₃ using its molar mass (approximately 122.55 g/mol):

\[ \text{Mass of } KClO_3 = \text{Moles of } KClO_3 \times \text{Molar mass of } KClO_3 \]
\[ \text{Mass of } KClO_3 = 0.0230 \text{ moles} \times 122.55 \text{ g/mol} \approx 2.82 \text{ g} \]

### Step 7: Final Calculation of Total Mass.

The total mass of KClO₃ that decomposed can be calculated as the sum of the mass of KCl produced and the mass of oxygen produced.

First, calculate the mass of oxygen produced:

\[ \text{Mass of } O_2 = \text{Moles of } O_2 \times \text{Molar mass of } O_2 \]
\[ \text{Mass of } O_2 = 0.0345 \text{ moles} \times 32 \text{ g/mol} \approx 1.10 \text{ g} \]

Now, add the mass of KCl and the mass of O₂:

\[ \text{Total mass of } KClO_3 = \text{Mass of } KCl + \text{Mass of } O_2 = 1.691 \text{ g} + 1.10 \text{ g} \approx 2.79 \text{ g} \]

### Conclusion

The mass of potassium chlorate (KClO₃) that decomposes to give the specified amounts of KCl and O₂ is approximately **2.79 g**.

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