What mass of potassium chlorate (`KClO_3`) on heating gives 1.751 g of potassium chloride (KCl) and 0.672 litres of oxygen at NTP?

Options

A. 2.711g
B. 4.211g
C. 1.458g
D. 0.5g

Explanation

To solve the problem of determining the mass of potassium chlorate (KClO₃) that decomposes to produce 1.751 g of potassium chloride (KCl) and 0.672 liters of oxygen (O₂) at normal temperature and pressure (NTP), we can follow these steps:

### Step 1: Write the balanced chemical equation for the decomposition of potassium chlorate.
The decomposition of potassium chlorate can be represented by the following balanced equation:

\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]

### Step 2: Determine the moles of KCl produced.
Given that the mass of KCl produced is 1.751 g, we can calculate the number of moles of KCl using its molar mass. The molar mass of KCl is approximately 74.55 g/mol.

\[ \text{Moles of KCl} = \frac{\text{Mass of KCl}}{\text{Molar mass of KCl}} = \frac{1.751 \, \text{g}}{74.55 \, \text{g/mol}} \approx 0.0235 \, \text{mol} \]

### Step 3: Use the stoichiometry of the reaction to find moles of O₂ produced.
From the balanced equation, we see that 2 moles of KCl are produced for every 3 moles of O₂ produced. Therefore, the moles of O₂ produced can be calculated as follows:

\[ \text{Moles of O}_2 = \frac{3}{2} \times \text{Moles of KCl} = \frac{3}{2} \times 0.0235 \, \text{mol} \approx 0.03525 \, \text{mol} \]

### Step 4: Calculate the volume of O₂ produced at NTP.
At NTP, 1 mole of gas occupies 22.4 liters. Thus, we can find the volume of O₂ produced:

\[ \text{Volume of O}_2 = \text{Moles of O}_2 \times 22.4 \, \text{L/mol} = 0.03525 \, \text{mol} \times 22.4 \, \text{L/mol} \approx 0.790 \, \text{L} \]

### Step 5: Calculate the mass of O₂ produced.
The molar mass of O₂ is approximately 32 g/mol. Therefore, the mass of O₂ produced is:

\[ \text{Mass of O}_2 = \text{Moles of O}_2 \times \text{Molar mass of O}_2 = 0.03525 \, \text{mol} \times 32 \, \text{g/mol} \approx 1.128 \, \text{g} \]

### Step 6: Calculate the total mass of KClO₃ decomposed.
The total mass of KClO₃ decomposed can be found by adding the mass of KCl produced and the mass of O₂ produced:

\[ \text{Mass of KClO}_3 = \text{Mass of KCl} + \text{Mass of O}_2 = 1.751 \, \text{g} + 1.128 \, \text{g} \approx 2.879 \, \text{g} \]

### Final Answer:
The mass of potassium chlorate (KClO₃) that decomposes to give the specified amounts of KCl and O₂ is approximately **2.879 g**.

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