To solve the problem step-by-step, we can follow these calculations:
### Step 1: Write the decomposition reaction
The decomposition of potassium chlorate (KClO3) upon heating can be represented as:
\[ 2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2 \]
### Step 2: Calculate moles of \( O_2 \) produced
Given that 2.50 g of \( O_2 \) is produced, we can find the number of moles of \( O_2 \) using its molar mass (32 g/mol):
\[
\text{Moles of } O_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{2.50 \, \text{g}}{32 \, \text{g/mol}} = 0.078125 \, \text{mol}
\]
### Step 3: Relate moles of \( O_2 \) to moles of \( KClO_3 \)
From the balanced equation, we see that 3 moles of \( O_2 \) are produced from 2 moles of \( KClO_3 \). Therefore, we can set up a ratio:
\[
\frac{2 \, \text{mol KClO}_3}{3 \, \text{mol } O_2} \Rightarrow \text{Moles of } KClO_3 = \frac{2}{3} \times 0.078125 \, \text{mol} = 0.0520833 \, \text{mol}
\]
### Step 4: Calculate the mass of \( KClO_3 \)
To find the mass of \( KClO_3 \), we multiply the number of moles by its molar mass (122.5 g/mol):
\[
\text{Mass of } KClO_3 = 0.0520833 \, \text{mol} \times 122.5 \, \text{g/mol} = 6.375 \, \text{g}
\]
### Step 5: Calculate the mass of \( KCl \) in the mixture
The total mass of the mixture is given as 7 g. Therefore, the mass of \( KCl \) can be calculated as:
\[
\text{Mass of } KCl = \text{Total mass} - \text{Mass of } KClO_3 = 7 \, \text{g} - 6.375 \, \text{g} = 0.625 \, \text{g}
\]
### Step 6: Calculate the mass fraction of \( KCl \)
The mass fraction of \( KCl \) in the original mixture is calculated as:
\[
\text{Mass fraction of } KCl = \frac{\text{Mass of } KCl}{\text{Total mass of mixture}} = \frac{0.625 \, \text{g}}{7 \, \text{g}} \approx 0.0893
\]
### Final Answer
The mass fraction of \( KCl \) in the original mixture is approximately **0.0893**.
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