Question
Directions: Solve the problem shown below. Any data, calculations, or models you use to support your thinking should be explained. Use the periodic table in your analysis. Problem: A scientist is studying rust. Rust forms according to the following chemical equations. 푆푡푒푝 1: 4퐹푒 + 3푂 2 + 6퐻 2 푂 → 4퐹푒(푂퐻) 3푆푡푒푝 2: 2퐹푒(푂퐻) 3 → 퐹푒 2 푂 3 · 3퐻 2 푂 The scientist measures the following masses after the reaction is complete: Substance Mass (g) Fe(OH)3 641.25 Fe2 O3 798.5 H2 O 216.192 The scientist wrote down that 5 moles of one of the substances was found but forgot to write down which substance it was. Help the scientist: which substance was it? Justify your answer.
Answers
Answered by
GPT-4o mini
To determine which substance corresponds to the 5 moles referenced by the scientist, we will need to calculate the number of moles for each of the three substances involved based on the provided masses and then identify which one equals 5 moles.
1. **Identify the molar masses**:
- **Fe(OH)₃ (Iron(III) hydroxide)**:
- Molar mass:
- Fe: 55.85 g/mol
- O: 16.00 g/mol
- H: 1.01 g/mol
- Calculation:
\[
\text{Molar mass of Fe(OH)₃} = 55.85 + 3 \times (16.00 + 1.01) = 55.85 + 3 \times 17.01 = 55.85 + 51.03 = 106.88 \, \text{g/mol}
\]
- **Fe₂O₃ (Iron(III) oxide)**:
- Molar mass:
- Fe: 55.85 g/mol
- O: 16.00 g/mol
- Calculation:
\[
\text{Molar mass of Fe₂O₃} = 2 \times 55.85 + 3 \times 16.00 = 111.70 + 48.00 = 159.70 \, \text{g/mol}
\]
- **H₂O (Water)**:
- Molar mass:
- H: 1.01 g/mol
- O: 16.00 g/mol
- Calculation:
\[
\text{Molar mass of H₂O} = 2 \times 1.01 + 16.00 = 2.02 + 16.00 = 18.02 \, \text{g/mol}
\]
2. **Calculate the number of moles for each substance**:
- **For Fe(OH)₃**:
\[
n = \frac{\text{mass}}{\text{molar mass}} = \frac{641.25 \, \text{g}}{106.88 \, \text{g/mol}} \approx 5.99 \, \text{mol}
\]
- **For Fe₂O₃**:
\[
n = \frac{798.5 \, \text{g}}{159.70 \, \text{g/mol}} \approx 4.99 \, \text{mol}
\]
- **For H₂O**:
\[
n = \frac{216.192 \, \text{g}}{18.02 \, \text{g/mol}} \approx 12.00 \, \text{mol}
\]
3. **Identify the substance with 5 moles**:
- **Fe(OH)₃**: Approximately 5.99 moles
- **Fe₂O₃**: Approximately 4.99 moles (this is very close to 5 moles)
- **H₂O**: Approximately 12.00 moles
**Conclusion**: The substance that corresponds to the 5 moles mentioned by the scientist is **Fe₂O₃ (Iron(III) oxide)**, as its calculated moles are approximately 4.99, which is very close to 5 moles. This calculation was derived by using the measured mass for Fe₂O₃ and its molar mass based on the periodic table.
1. **Identify the molar masses**:
- **Fe(OH)₃ (Iron(III) hydroxide)**:
- Molar mass:
- Fe: 55.85 g/mol
- O: 16.00 g/mol
- H: 1.01 g/mol
- Calculation:
\[
\text{Molar mass of Fe(OH)₃} = 55.85 + 3 \times (16.00 + 1.01) = 55.85 + 3 \times 17.01 = 55.85 + 51.03 = 106.88 \, \text{g/mol}
\]
- **Fe₂O₃ (Iron(III) oxide)**:
- Molar mass:
- Fe: 55.85 g/mol
- O: 16.00 g/mol
- Calculation:
\[
\text{Molar mass of Fe₂O₃} = 2 \times 55.85 + 3 \times 16.00 = 111.70 + 48.00 = 159.70 \, \text{g/mol}
\]
- **H₂O (Water)**:
- Molar mass:
- H: 1.01 g/mol
- O: 16.00 g/mol
- Calculation:
\[
\text{Molar mass of H₂O} = 2 \times 1.01 + 16.00 = 2.02 + 16.00 = 18.02 \, \text{g/mol}
\]
2. **Calculate the number of moles for each substance**:
- **For Fe(OH)₃**:
\[
n = \frac{\text{mass}}{\text{molar mass}} = \frac{641.25 \, \text{g}}{106.88 \, \text{g/mol}} \approx 5.99 \, \text{mol}
\]
- **For Fe₂O₃**:
\[
n = \frac{798.5 \, \text{g}}{159.70 \, \text{g/mol}} \approx 4.99 \, \text{mol}
\]
- **For H₂O**:
\[
n = \frac{216.192 \, \text{g}}{18.02 \, \text{g/mol}} \approx 12.00 \, \text{mol}
\]
3. **Identify the substance with 5 moles**:
- **Fe(OH)₃**: Approximately 5.99 moles
- **Fe₂O₃**: Approximately 4.99 moles (this is very close to 5 moles)
- **H₂O**: Approximately 12.00 moles
**Conclusion**: The substance that corresponds to the 5 moles mentioned by the scientist is **Fe₂O₃ (Iron(III) oxide)**, as its calculated moles are approximately 4.99, which is very close to 5 moles. This calculation was derived by using the measured mass for Fe₂O₃ and its molar mass based on the periodic table.