The number of atoms present in 0.5 moles of nitrogen is same as the atoms in

Options

A. 12 g of C
B. 32 g of S
C. 8 g of oxygen
D. 24 g of Mg

Answer

To solve the question, we need to determine how many atoms are present in 0.5 moles of nitrogen and then find which of the given options has the same number of atoms.

### Step-by-Step Solution:

1. **Calculate the number of atoms in 0.5 moles of nitrogen (N2)**:
- The number of atoms in one mole of any substance is given by Avogadro's number, which is approximately \(6.022 \times 10^{23}\).
- Since nitrogen exists as a diatomic molecule (N2), each mole of nitrogen contains 2 moles of nitrogen atoms.
- Therefore, the number of nitrogen atoms in 0.5 moles of nitrogen is calculated as follows:
\[ \text{Number of atoms} = 0.5 \, \text{moles} \times 2 \, \text{(atoms/mole)} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]
\[ \text{Number of atoms} = 0.5 \times 2 \times 6.022 \times 10^{23} = 3.011 \times 10^{23} \, \text{atoms} \]

2. **Check the options to find an equivalent number of atoms**:
- **Option 1: 12 grams of carbon (C)**:
- The atomic weight of carbon is 12 g/mol.
- Moles of carbon in 12 grams = \( \frac{12 \, \text{g}}{12 \, \text{g/mol}} = 1 \, \text{mol} \).
- Number of atoms = \( 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms} \).

- **Option 2: 32 grams of sulfur (S)**:
- The atomic weight of sulfur is 32 g/mol.
- Moles of sulfur in 32 grams = \( \frac{32 \, \text{g}}{32 \, \text{g/mol}} = 1 \, \text{mol} \).
- Number of atoms = \( 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms} \).

- **Option 3: 8 grams of oxygen (O)**:
- The atomic weight of oxygen is 16 g/mol.
- Moles of oxygen in 8 grams = \( \frac{8 \, \text{g}}{16 \, \text{g/mol}} = 0.5 \, \text{mol} \).
- Number of atoms = \( 0.5 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 3.011 \times 10^{23} \, \text{atoms} \).

- **Option 4: 24 grams of magnesium (Mg)**:
- The atomic weight of magnesium is 24 g/mol.
- Moles of magnesium in 24 grams = \( \frac{24 \, \text{g}}{24 \, \text{g/mol}} = 1 \, \text{mol} \).
- Number of atoms = \( 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms} \).

3. **Conclusion**:
- The number of atoms in 0.5 moles of nitrogen (3.011 × 10^23 atoms) is equal to the number of atoms in 8 grams of oxygen (Option 3).

### Final Answer:
The number of atoms present in 0.5 moles of nitrogen is the same as the atoms in **8 grams of oxygen**.

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