To determine which of the given samples could be the mineral hematite ([tex]$Fe_2O_3$[/tex]), we need to compare the given mass ratios to the theoretical mass ratio of iron (Fe) to oxygen (O) in [tex]$Fe_2O_3$[/tex].
### Step-by-Step Solution:
1. Calculate the Molar Masses:
- The molar mass of Iron (Fe): [tex]\( 55.845 \, \text{g/mol} \)[/tex]
- The molar mass of Oxygen (O): [tex]\( 16.00 \, \text{g/mol} \)[/tex]
2. Determine the Formula for Hematite:
Hematite has the chemical formula [tex]$Fe_2O_3$[/tex]. This means each molecule of [tex]$Fe_2O_3$[/tex] contains 2 atoms of Iron and 3 atoms of Oxygen.
3. Calculate the Mass of Iron in [tex]$Fe_2O_3$[/tex]:
[tex]\[
2 \times 55.845 \, \text{g/mol} = 111.69 \, \text{g/mol}
\][/tex]
4. Calculate the Mass of Oxygen in [tex]$Fe_2O_3$[/tex]:
[tex]\[
3 \times 16.00 \, \text{g/mol} = 48.00 \, \text{g/mol}
\][/tex]
5. Calculate the Theoretical Mass Ratio of Iron to Oxygen in [tex]$Fe_2O_3$[/tex]:
[tex]\[
\text{Mass Ratio of Fe to O} = \frac{111.69}{48.00} \approx 2.327
\][/tex]
6. Compare the Theoretical Mass Ratio to the Given Mass Ratios:
- Option A: [tex]$2.3: 1$[/tex]
- Option B: [tex]$3: 2 = 1.5: 1$[/tex]
- Option C: [tex]$2: 3 \approx 0.667: 1$[/tex]
- Option D: [tex]$3.5: 1$[/tex]
7. Find the Closest Match:
- The theoretical mass ratio, approximately 2.327:1, closely matches Option A ([tex]$2.3:1$[/tex]).
### Conclusion:
The sample with the mass ratio of [tex]$2.3:1$[/tex] (Option A) is the closest to the theoretical mass ratio of iron to oxygen in hematite ([tex]$Fe_2O_3$[/tex]). Therefore, Option A could be the mineral hematite.
So, Option A ([tex]$2.3: 1$[/tex]) is the correct answer.
