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Given the mass ratios of iron to oxygen, which of the following samples could be the mineral hematite, [tex]Fe_2O_3[/tex]?

A. [tex]2.3:1[/tex]
B. [tex]3:2[/tex]
C. [tex]2:3[/tex]
D. [tex]3.5:1[/tex]


Sagot :

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.