Which of the following contains the greatest number of atoms?

Options

A. 1.0g of butane `(C_(4)H_(10))`
B. 1.0 g of nitrogen `(N_(2))`
C. `1.0g` of silver (Ag)
D. `1.0g` of water `(H_(2)O)`

Answer

To determine which of the given options contains the greatest number of atoms, we will calculate the number of atoms in each substance based on the provided mass (1.0 gram) and their respective molecular weights.

### Step 1: Calculate the number of moles for each substance.

1. **Butane (C₄H₁₀)**:
- Molecular weight = (4 × 12) + (10 × 1) = 48 + 10 = 58 g/mol
- Moles of butane = mass / molecular weight = 1.0 g / 58 g/mol = 0.01724 mol
- Total atoms in butane = 0.01724 mol × 14 atoms/mol = 0.2414 mol of atoms

2. **Nitrogen (N₂)**:
- Molecular weight = 2 × 14 = 28 g/mol
- Moles of nitrogen = mass / molecular weight = 1.0 g / 28 g/mol = 0.03571 mol
- Total atoms in nitrogen = 0.03571 mol × 2 atoms/mol = 0.07142 mol of atoms

3. **Silver (Ag)**:
- Atomic weight = 107.87 g/mol
- Moles of silver = mass / atomic weight = 1.0 g / 107.87 g/mol = 0.00925 mol
- Total atoms in silver = 0.00925 mol × 1 atom/mol = 0.00925 mol of atoms

4. **Water (H₂O)**:
- Molecular weight = (2 × 1) + (16) = 2 + 16 = 18 g/mol
- Moles of water = mass / molecular weight = 1.0 g / 18 g/mol = 0.05556 mol
- Total atoms in water = 0.05556 mol × 3 atoms/mol = 0.16667 mol of atoms

### Step 2: Compare the total number of atoms in each substance.

- Butane: 0.2414 mol of atoms
- Nitrogen: 0.07142 mol of atoms
- Silver: 0.00925 mol of atoms
- Water: 0.16667 mol of atoms

### Conclusion:
The substance with the greatest number of atoms is **Butane (C₄H₁₀)** with approximately 0.2414 mol of atoms.