Which of the following contain highest number of atoms ?

Options

A. `1.0` g of water
B. `1.0` g of silver
C. `1.0` g of nitrogen
D. `1.0` g of propane `C_(3)H_(8)`

Answer

To determine which of the given substances contains the highest number of atoms, we will calculate the total number of atoms in each of the four substances based on the provided weights.

### Step-by-Step Solution:

1. **Calculate the number of atoms in 1 gram of water (H₂O)**:
- **Molecular weight of water (H₂O)**:
- Hydrogen (H) = 1 g/mol × 2 = 2 g/mol
- Oxygen (O) = 16 g/mol
- Total = 2 + 16 = 18 g/mol
- **Moles of water in 1 gram**:
\[ \text{Moles of H₂O} = \frac{1 \text{ g}}{18 \text{ g/mol}} = \frac{1}{18} \text{ moles} \]
- **Number of molecules in 1 gram of water**:
\[ \text{Number of molecules} = \frac{1}{18} \times 6.022 \times 10^{23} \approx 0.3346 \times 10^{23} \text{ molecules} \]
- **Total number of atoms in water**:
- Each molecule of water has 3 atoms (2 H + 1 O).
\[ \text{Total atoms} = 0.3346 \times 10^{23} \times 3 \approx 1.0038 \times 10^{23} \text{ atoms} \]

2. **Calculate the number of atoms in 1 gram of silver (Ag)**:
- **Atomic weight of silver (Ag)**: 108 g/mol
- **Moles of silver in 1 gram**:
\[ \text{Moles of Ag} = \frac{1 \text{ g}}{108 \text{ g/mol}} = \frac{1}{108} \text{ moles} \]
- **Number of atoms in 1 gram of silver**:
\[ \text{Number of atoms} = \frac{1}{108} \times 6.022 \times 10^{23} \approx 0.0557 \times 10^{23} \text{ atoms} \]

3. **Calculate the number of atoms in 1 gram of nitrogen (N₂)**:
- **Molecular weight of nitrogen (N₂)**:
- Nitrogen (N) = 14 g/mol × 2 = 28 g/mol
- **Moles of nitrogen in 1 gram**:
\[ \text{Moles of N₂} = \frac{1 \text{ g}}{28 \text{ g/mol}} = \frac{1}{28} \text{ moles} \]
- **Number of molecules in 1 gram of nitrogen**:
\[ \text{Number of molecules} = \frac{1}{28} \times 6.022 \times 10^{23} \approx 0.2143 \times 10^{23} \text{ molecules} \]
- **Total number of atoms in nitrogen**:
- Each molecule of nitrogen has 2 atoms.
\[ \text{Total atoms} = 0.2143 \times 10^{23} \times 2 \approx 0.4286 \times 10^{23} \text{ atoms} \]

4. **Calculate the number of atoms in 1 gram of propane (C₃H₈)**:
- **Molecular weight of propane (C₃H₈)**:
- Carbon (C) = 12 g/mol × 3 = 36 g/mol
- Hydrogen (H) = 1 g/mol × 8 = 8 g/mol
- Total = 36 + 8 = 44 g/mol
- **Moles of propane in 1 gram**:
\[ \text{Moles of C₃H₈} = \frac{1 \text{ g}}{44 \text{ g/mol}} = \frac{1}{44} \text{ moles} \]
- **Number of molecules in 1 gram of propane**:
\[ \text{Number of molecules} = \frac{1}{44} \times 6.022 \times 10^{23} \approx 0.1364 \times 10^{23} \text{ molecules} \]
- **Total number of atoms in propane**:
- Each molecule of propane has 11 atoms (3 C + 8 H).
\[ \text{Total atoms} = 0.1364 \times 10^{23} \times 11 \approx 1.5004 \times 10^{23} \text{ atoms} \]

### Summary of Total Atoms:
- Water: \( \approx 1.0038 \times 10^{23} \) atoms
- Silver: \( \approx 0.0557 \times 10^{23} \) atoms
- Nitrogen: \( \approx 0.4286 \times 10^{23} \) atoms
- Propane: \( \approx 1.5004 \times 10^{23} \) atoms

### Conclusion:
The substance with the highest number of atoms is **1 gram of propane (C₃H₈)**.

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