Which has maximum number of molecules?

Options

A. 7 g `N_(2)`
B. 2g `H_(2)`
C. 16 g `NO_(2)`
D. 16 g `O_(2)`

Answer

To determine which substance has the maximum number of molecules, we need to calculate the number of moles for each substance given the mass and molar mass. The number of molecules can be found using Avogadro's number, which states that one mole of any substance contains approximately \(6.02 \times 10^{23}\) molecules.

### Step-by-Step Solution:

1. **Identify the substances and their given masses**:
- \(N_2\): 7 grams
- \(H_2\): 2 grams
- \(NO_2\): 16 grams
- \(O_2\): 16 grams

2. **Calculate the number of moles for each substance**:
- **For \(N_2\)**:
- Molar mass of \(N_2\) = 28 g/mol (14 g/mol for each nitrogen atom)
- Number of moles = \(\frac{\text{mass}}{\text{molar mass}} = \frac{7 \text{ g}}{28 \text{ g/mol}} = \frac{1}{4} \text{ moles}\)

- **For \(H_2\)**:
- Molar mass of \(H_2\) = 2 g/mol (1 g/mol for each hydrogen atom)
- Number of moles = \(\frac{2 \text{ g}}{2 \text{ g/mol}} = 1 \text{ mole}\)

- **For \(NO_2\)**:
- Molar mass of \(NO_2\) = 14 g/mol (for nitrogen) + 32 g/mol (for two oxygens) = 46 g/mol
- Number of moles = \(\frac{16 \text{ g}}{46 \text{ g/mol}} \approx 0.348 \text{ moles}\)

- **For \(O_2\)**:
- Molar mass of \(O_2\) = 32 g/mol (16 g/mol for each oxygen atom)
- Number of moles = \(\frac{16 \text{ g}}{32 \text{ g/mol}} = 0.5 \text{ moles}\)

3. **Compare the number of moles**:
- \(N_2\): \(\frac{1}{4} \approx 0.25\) moles
- \(H_2\): \(1\) mole
- \(NO_2\): \(\approx 0.348\) moles
- \(O_2\): \(0.5\) moles

4. **Determine which has the maximum number of moles**:
- The highest number of moles is for \(H_2\) with \(1\) mole.

5. **Calculate the number of molecules for \(H_2\)**:
- Number of molecules = \(1 \text{ mole} \times 6.02 \times 10^{23} \text{ molecules/mole} = 6.02 \times 10^{23} \text{ molecules}\)

### Conclusion:
The substance with the maximum number of molecules is \(H_2\) (hydrogen gas) with \(6.02 \times 10^{23}\) molecules.