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11 grade chemistry others

Which one of the following represents one mole of the substance? (A) 16 g of {{N}_{2}} (B) 5.6d{{m}^{3}} of {{H}_{2}} at STP (C) 11.2 d{{m}^{3}}of C{{l}_{2}} at STP (D) 4 g of Helium

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1 Year agoGrade
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1 Answer

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1 Year ago

To determine which option represents one mole of a substance, we need to use the concepts of molar mass and gas volume at standard temperature and pressure (STP).

1. **Molar Mass**:
- For \( \text{N}_2 \) (Nitrogen): The molar mass of nitrogen is approximately 14 g/mol, so \( \text{N}_2 \) (which has 2 nitrogen atoms) has a molar mass of \( 14 \, \text{g/mol} \times 2 = 28 \, \text{g/mol} \).
- For \( \text{H}_2 \) (Hydrogen): The molar mass of hydrogen is approximately 1 g/mol, so \( \text{H}_2 \) has a molar mass of \( 1 \, \text{g/mol} \times 2 = 2 \, \text{g/mol} \).
- For \( \text{Cl}_2 \) (Chlorine): The molar mass of chlorine is approximately 35.5 g/mol, so \( \text{Cl}_2 \) has a molar mass of \( 35.5 \, \text{g/mol} \times 2 = 71 \, \text{g/mol} \).
- For Helium (He): The molar mass of helium is approximately 4 g/mol.

2. **Volume of Gases at STP**:
- At STP (Standard Temperature and Pressure), one mole of any ideal gas occupies a volume of \( 22.4 \, \text{L} \) or \( 22.4 \, \text{dm}^3 \).

### Evaluation of Each Option:

(A) **16 g of \( \text{N}_2 \)**:
- Moles of \( \text{N}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{16 \, \text{g}}{28 \, \text{g/mol}} \approx 0.57 \, \text{moles} \).
- This is not one mole.

(B) **5.6 dm³ of \( \text{H}_2 \) at STP**:
- Moles of \( \text{H}_2 = \frac{\text{volume}}{22.4 \, \text{dm}^3/mol} = \frac{5.6 \, \text{dm}^3}{22.4 \, \text{dm}^3/mol} = 0.25 \, \text{moles} \).
- This is not one mole.

(C) **11.2 dm³ of \( \text{Cl}_2 \) at STP**:
- Moles of \( \text{Cl}_2 = \frac{11.2 \, \text{dm}^3}{22.4 \, \text{dm}^3/mol} = 0.5 \, \text{moles} \).
- This is not one mole.

(D) **4 g of Helium (He)**:
- Moles of He = \( \frac{4 \, \text{g}}{4 \, \text{g/mol}} = 1 \, \text{mole} \).
- This is one mole.

### Conclusion:
The correct answer is **(D) 4 g of Helium**, as it represents one mole of the substance.