To solve the problem step by step, we will follow these calculations:
### Step 1: Determine the mass loss during the reaction
The initial mass of the sample is given as 2.0 g, and the mass of the residue after heating is 1.96 g.
**Calculation:**
\[
\text{Mass loss} = \text{Initial mass} - \text{Residue mass} = 2.0 \, \text{g} - 1.96 \, \text{g} = 0.04 \, \text{g}
\]
### Step 2: Write the balanced chemical equation
The reaction responsible for the loss of weight is:
\[
\text{Fe}_2\text{O}_3(s) \rightarrow \text{Fe}_3\text{O}_4(s) + \text{O}_2(g)
\]
Balancing this equation, we find that:
\[
4 \text{Fe}_2\text{O}_3 \rightarrow 6 \text{Fe}_3\text{O}_4 + 3 \text{O}_2
\]
### Step 3: Calculate the molar mass of Fe2O3
Using the atomic masses provided:
- Fe = 56 g/mol
- O = 16 g/mol
**Calculation:**
\[
\text{Molar mass of Fe}_2\text{O}_3 = (2 \times 56) + (3 \times 16) = 112 + 48 = 160 \, \text{g/mol}
\]
### Step 4: Determine the amount of Fe2O3 that corresponds to the mass loss
From the balanced equation, we see that 1 mole of Fe2O3 produces 0.5 moles of O2. The molar mass of O2 is:
\[
\text{Molar mass of O}_2 = 2 \times 16 = 32 \, \text{g/mol}
\]
**Calculation:**
The mass loss (0.04 g) corresponds to the oxygen produced. We need to find out how much Fe2O3 corresponds to this loss.
Using the ratio:
\[
\text{Mass of O}_2 \text{ produced from 1 mole of Fe}_2\text{O}_3 = 32 \, \text{g}
\]
\[
\text{Mass of Fe}_2\text{O}_3 \text{ that produces 0.04 g of O}_2 = \left(\frac{160 \, \text{g}}{32 \, \text{g}}\right) \times 0.04 \, \text{g} = 0.2 \, \text{g}
\]
### Step 5: Calculate the mass of SiO2 in the original sample
Since the original sample is a mixture of SiO2 and Fe2O3, we can find the mass of SiO2 by subtracting the mass of Fe2O3 from the total mass of the sample.
**Calculation:**
Let \( x \) be the mass of Fe2O3 in the original sample:
\[
x = 0.2 \, \text{g} \text{ (mass of Fe}_2\text{O}_3\text{)}
\]
\[
\text{Mass of SiO}_2 = \text{Total mass} - \text{Mass of Fe}_2\text{O}_3 = 2.0 \, \text{g} - 0.2 \, \text{g} = 1.8 \, \text{g}
\]
### Step 6: Calculate the percentage by mass of SiO2
**Calculation:**
\[
\text{Percentage of SiO}_2 = \left(\frac{\text{Mass of SiO}_2}{\text{Total mass}} \times 100\right) = \left(\frac{1.8 \, \text{g}}{2.0 \, \text{g}} \times 100\right) = 90\%
\]
### Final Answer:
The percentage by mass of SiO2 in the original sample is **90%**.
