Which of the following has the maximum number of atoms?

Options

A. `24 g "of" C(12)`
B. `56 g "of" Fe(56)`
C. `27 "of" Al (27)`
D. `108 g "of" Ag(108)`

Explanation

To determine which of the given substances has the maximum number of atoms, we will calculate the number of atoms in each substance using the formula:

\[ \text{Number of atoms} = \left( \frac{\text{Given mass}}{\text{Molecular mass}} \right) \times N_A \]

where \( N_A \) is Avogadro's number, approximately \( 6.022 \times 10^{23} \) atoms/mol.

Let's analyze each option step by step:

### Step 1: Calculate the number of atoms in 24 grams of C-12
1. **Given mass** = 24 grams
2. **Molecular mass of C-12** = 12 g/mol

\[ \text{Number of moles of C-12} = \frac{24 \text{ g}}{12 \text{ g/mol}} = 2 \text{ moles} \]

\[ \text{Number of atoms} = 2 \times N_A = 2N_A \]

### Step 2: Calculate the number of atoms in 56 grams of Fe-56
1. **Given mass** = 56 grams
2. **Molecular mass of Fe-56** = 56 g/mol

\[ \text{Number of moles of Fe-56} = \frac{56 \text{ g}}{56 \text{ g/mol}} = 1 \text{ mole} \]

\[ \text{Number of atoms} = 1 \times N_A = N_A \]

### Step 3: Calculate the number of atoms in 27 grams of Al-27
1. **Given mass** = 27 grams
2. **Molecular mass of Al-27** = 27 g/mol

\[ \text{Number of moles of Al-27} = \frac{27 \text{ g}}{27 \text{ g/mol}} = 1 \text{ mole} \]

\[ \text{Number of atoms} = 1 \times N_A = N_A \]

### Step 4: Calculate the number of atoms in 108 grams of Ag-108
1. **Given mass** = 108 grams
2. **Molecular mass of Ag-108** = 108 g/mol

\[ \text{Number of moles of Ag-108} = \frac{108 \text{ g}}{108 \text{ g/mol}} = 1 \text{ mole} \]

\[ \text{Number of atoms} = 1 \times N_A = N_A \]

### Summary of Results
- **C-12**: \( 2N_A \)
- **Fe-56**: \( N_A \)
- **Al-27**: \( N_A \)
- **Ag-108**: \( N_A \)

### Conclusion
The maximum number of atoms is found in **24 grams of C-12**, which has \( 2N_A \) atoms.

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