Question

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

• A. 12 g of C $\frac{12}{12}$
• B. 32 g of S $\frac{32}{32} \times$
• C. 8 g of oxygen $\frac{8}{16} \times$
• D. 24 g of Mg $\frac{24}{24}$

Answer 1

Answer: (C)

8 g of oxygen $\frac{8}{16} \times$

Answer 2

To determine the number of atoms, we use the concept of moles and Avogadro's number ($N_A$). One mole of any substance contains $N_A$ particles (atoms, molecules, ions, etc.). The number of moles of atoms can be calculated as:

$$\text{Number of moles of atoms} = \frac{\text{Given mass}}{\text{Molar mass of atom}}$$

The number of atoms is then:

$$\text{Number of atoms} = \text{Number of moles of atoms} \times N_A$$

First, let's find the number of atoms in "0.5 g atom of nitrogen". The term "g atom" is an older term for "gram atom", which is equivalent to "mole of atoms". So, "0.5 g atom of nitrogen" means 0.5 moles of nitrogen atoms. Number of nitrogen atoms = $0.5 \times N_A$ atoms.

Now, let's calculate the number of atoms for each given option:

1. 12 g of C (Carbon)
   Molar mass of Carbon (C) = 12 g/mol
   Number of moles of C atoms = $\frac{12 \text{ g}}{12 \text{ g/mol}} = 1 \text{ mole}$
   Number of C atoms = $1 \times N_A$ atoms

2. 32 g of S (Sulfur)
   Molar mass of Sulfur (S) = 32 g/mol
   Number of moles of S atoms = $\frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mole}$
   Number of S atoms = $1 \times N_A$ atoms

3. 8 g of oxygen
   Molar mass of Oxygen (O) atoms = 16 g/mol
   Number of moles of O atoms = $\frac{8 \text{ g}}{16 \text{ g/mol}} = 0.5 \text{ moles}$
   Number of O atoms = $0.5 \times N_A$ atoms

4. 24 g of Mg (Magnesium)
   Molar mass of Magnesium (Mg) = 24 g/mol
   Number of moles of Mg atoms = $\frac{24 \text{ g}}{24 \text{ g/mol}} = 1 \text{ mole}$
   Number of Mg atoms = $1 \times N_A$ atoms

Comparing the number of atoms:

• 0.5 g atom of nitrogen contains $0.5 \times N_A$ atoms.
• Option (1) contains $1 \times N_A$ atoms.
• Option (2) contains $1 \times N_A$ atoms.
• Option (3) contains $0.5 \times N_A$ atoms.
• Option (4) contains $1 \times N_A$ atoms.

Thus, 8 g of oxygen has the same number of atoms as 0.5 g atom of nitrogen.