Which of the following has greatest number of atoms?

Options

A. 1 g of butane `(C_(4)H_(10))`
B. 1 g of nitrogen `(N_(2))`
C. 1 g of silver (Ag)
D. 1 g of water `(H_(2)O)`

Explanation

To determine which of the given substances has the greatest number of atoms, we need to calculate the number of atoms in each substance based on the amount provided (in grams) and their molar masses. We will use the concept of moles and Avogadro's number to find the total number of atoms in each case.

### Step-by-Step Solution:

1. **Understand the Concept of Moles**:
- A mole is a unit that represents \(6.022 \times 10^{23}\) particles (Avogadro's number).
- To find the number of atoms in a substance, we first need to calculate the number of moles.

2. **Calculate Moles for Each Substance**:
- For each substance, use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

3. **Determine the Number of Atoms**:
- Once we have the number of moles, we can find the number of atoms by multiplying the number of moles by Avogadro's number and the number of atoms in each molecule.
- The formula is:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \times \text{Number of atoms per molecule} \]

4. **Calculate for Each Substance**:
- **Butane (C₄H₁₀)**:
- Molar mass = 58 g/mol
- Mass = 1 g
- Moles = \( \frac{1}{58} \)
- Number of atoms = \( \frac{1}{58} \times 6.022 \times 10^{23} \times 14 = 0.24 \, \text{Na} \)

- **Nitrogen (N₂)**:
- Molar mass = 28 g/mol
- Mass = 1 g
- Moles = \( \frac{1}{28} \)
- Number of atoms = \( \frac{1}{28} \times 6.022 \times 10^{23} \times 2 = 0.07 \, \text{Na} \)

- **Silver (Ag)**:
- Molar mass = 107.8 g/mol
- Mass = 1 g
- Moles = \( \frac{1}{107.8} \)
- Number of atoms = \( \frac{1}{107.8} \times 6.022 \times 10^{23} \times 1 = 0.008 \, \text{Na} \)

- **Water (H₂O)**:
- Molar mass = 18 g/mol
- Mass = 1 g
- Moles = \( \frac{1}{18} \)
- Number of atoms = \( \frac{1}{18} \times 6.022 \times 10^{23} \times 3 = 0.167 \, \text{Na} \)

5. **Compare the Results**:
- Butane: 0.24 Na
- Nitrogen: 0.07 Na
- Silver: 0.008 Na
- Water: 0.167 Na

6. **Conclusion**:
- The substance with the greatest number of atoms is **Butane (C₄H₁₀)** with 0.24 Na.