Select the correct statements.
I. 50 g of Al contains more atoms than 50 g of Fe.
II. 32.5 g of Mg have the same number of moles of atoms as 40.5 g of Al.
III. 20 g of water contains more number of moles of water molecules as compared to 22 g of carbon dioxide.
IV. The ratio by mass of elements (Al : F) in aluminium fluoride is 9:19.
(Given : Atomic mass of H=1 u, Mg= 24 u, O = 16 u, C = 12 u, F = 19 u, Al = 27 u and Fe = 56 u)

Options

A. I and III only
B. I and IV only
C. II and III only
D. I, III and IV only

Answer

To solve the question, we need to evaluate each statement one by one based on the given data and chemical principles.

### Statement I: 50 g of Al contains more atoms than 50 g of Fe.
1. **Calculate the number of moles of Al:**
- Molar mass of Al = 27 g/mol
- Number of moles of Al = Mass / Molar mass = 50 g / 27 g/mol ≈ 1.85 moles
2. **Calculate the number of moles of Fe:**
- Molar mass of Fe = 56 g/mol
- Number of moles of Fe = Mass / Molar mass = 50 g / 56 g/mol ≈ 0.89 moles
3. **Compare the number of atoms:**
- Number of atoms in Al = 1.85 moles × Avogadro's number (N_A)
- Number of atoms in Fe = 0.89 moles × Avogadro's number (N_A)
- Since 1.85 > 0.89, 50 g of Al contains more atoms than 50 g of Fe.

**Conclusion:** Statement I is **True**.

### Statement II: 32.5 g of Mg have the same number of moles of atoms as 40.5 g of Al.
1. **Calculate the number of moles of Mg:**
- Molar mass of Mg = 24 g/mol
- Number of moles of Mg = 32.5 g / 24 g/mol ≈ 1.35 moles
2. **Calculate the number of moles of Al:**
- Molar mass of Al = 27 g/mol
- Number of moles of Al = 40.5 g / 27 g/mol ≈ 1.5 moles
3. **Compare the number of moles:**
- 1.35 moles (Mg) ≠ 1.5 moles (Al)

**Conclusion:** Statement II is **False**.

### Statement III: 20 g of water contains more number of moles of water molecules as compared to 22 g of carbon dioxide.
1. **Calculate the number of moles of water (H₂O):**
- Molar mass of water = 18 g/mol
- Number of moles of water = 20 g / 18 g/mol ≈ 1.11 moles
2. **Calculate the number of moles of carbon dioxide (CO₂):**
- Molar mass of CO₂ = 44 g/mol
- Number of moles of CO₂ = 22 g / 44 g/mol = 0.5 moles
3. **Compare the number of moles:**
- 1.11 moles (H₂O) > 0.5 moles (CO₂)

**Conclusion:** Statement III is **True**.

### Statement IV: The ratio by mass of elements (Al : F) in aluminium fluoride is 9:19.
1. **Determine the molar mass of AlF₃:**
- Molar mass of Al = 27 g/mol
- Molar mass of F = 19 g/mol
- Molar mass of AlF₃ = 27 g + (3 × 19 g) = 27 g + 57 g = 84 g
2. **Calculate the ratio by mass of Al to F:**
- Mass of Al in AlF₃ = 27 g
- Mass of F in AlF₃ = 57 g
- Ratio by mass = Al : F = 27 g : 57 g = 27 : 57 = 9 : 19

**Conclusion:** Statement IV is **True**.

### Final Evaluation:
- **True Statements:** I, III, IV
- **False Statement:** II

### Summary of Correct Statements:
The correct statements are I, III, and IV.

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