Which one of the following statements is true?

Options

A. Mass of 0.5 mole of `N_2` gas `gt` Mass of 0.5 mole of N atoms
B. Mass of 0.5 mole of `N_2` gas = Mass of 0.5 mole of N atoms
C. Mass of 0.5 mole of `N_2` gas `lt` Mass of 0.5 mole of N atoms
D. Mass of 0.5 mole of `N_2` gas = Mass of 0.5 mole of `O_(2)` gas

Explanation

To determine which of the statements is true, we need to analyze each statement based on the mass of nitrogen (N) and nitrogen gas (N2) as well as oxygen gas (O2).

### Step-by-Step Solution:

1. **Calculate the mass of 0.5 moles of N2 gas:**
- The molar mass of nitrogen (N) is approximately 14 g/mol.
- Therefore, the molar mass of nitrogen gas (N2) is:
\[ \text{Molar mass of N2} = 2 \times 14 \, \text{g/mol} = 28 \, \text{g/mol} \]
- For 0.5 moles of N2 gas:
\[ \text{Mass of 0.5 moles of N2} = 0.5 \times 28 \, \text{g} = 14 \, \text{g} \]

2. **Calculate the mass of 0.5 moles of N atoms:**
- The molar mass of a single nitrogen atom (N) is 14 g/mol.
- For 0.5 moles of N atoms:
\[ \text{Mass of 0.5 moles of N} = 0.5 \times 14 \, \text{g} = 7 \, \text{g} \]

3. **Evaluate the first statement:**
- The first statement claims that the mass of 0.5 mole of N2 gas is greater than the mass of 0.5 mole of N atoms.
- We found that:
- Mass of 0.5 moles of N2 = 14 g
- Mass of 0.5 moles of N = 7 g
- Since 14 g > 7 g, this statement is **true**.

4. **Evaluate the second statement:**
- The second statement claims that the mass of both the atoms is equal.
- We calculated:
- Mass of 0.5 moles of N = 7 g
- Mass of 0.5 moles of N2 = 14 g
- Since 7 g ≠ 14 g, this statement is **false**.

5. **Evaluate the third statement:**
- The third statement claims that the mass of 0.5 mole of N2 gas is less than the mass of 0.5 mole of N atoms.
- We already established that 14 g > 7 g, so this statement is **false**.

6. **Evaluate the fourth statement:**
- The fourth statement claims that the mass of 0.5 mole of N2 gas is equal to the mass of 0.5 mole of O2 gas.
- The molar mass of oxygen (O) is approximately 16 g/mol, thus:
\[ \text{Molar mass of O2} = 2 \times 16 \, \text{g/mol} = 32 \, \text{g/mol} \]
- For 0.5 moles of O2 gas:
\[ \text{Mass of 0.5 moles of O2} = 0.5 \times 32 \, \text{g} = 16 \, \text{g} \]
- Since 14 g (N2) ≠ 16 g (O2), this statement is **false**.

### Conclusion:
The only true statement is the first one: **The mass of 0.5 mole of N2 gas is greater than the mass of 0.5 mole of N atom.**