Which has maximum number of molecules?

Options

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

Explanation

To determine which option has the maximum number of molecules, we need to calculate the number of moles for each substance given and then convert that to the number of molecules using Avogadro's number (Na = 6.022 x 10²³ molecules/mol).

### Step-by-Step Solution:

1. **Calculate the number of moles of N2 (7 grams)**:
- Molecular mass of N2 = 2 × atomic weight of nitrogen (N) = 2 × 14 g/mol = 28 g/mol.
- Number of moles of N2 = Given mass / Molecular mass = 7 g / 28 g/mol = 1/4 mol.
- Number of molecules of N2 = (1/4 mol) × Na = (1/4) × 6.022 × 10²³ = 1.5055 × 10²³ molecules.

2. **Calculate the number of moles of H2 (2 grams)**:
- Molecular mass of H2 = 2 × atomic weight of hydrogen (H) = 2 × 1 g/mol = 2 g/mol.
- Number of moles of H2 = Given mass / Molecular mass = 2 g / 2 g/mol = 1 mol.
- Number of molecules of H2 = 1 mol × Na = 1 × 6.022 × 10²³ = 6.022 × 10²³ molecules.

3. **Calculate the number of moles of Na2 (16 grams)**:
- Molecular mass of Na2 = 2 × atomic weight of sodium (Na) = 2 × 23 g/mol = 46 g/mol.
- Number of moles of Na2 = Given mass / Molecular mass = 16 g / 46 g/mol = 8/23 mol.
- Number of molecules of Na2 = (8/23 mol) × Na = (8/23) × 6.022 × 10²³ = 2.094 × 10²³ molecules.

4. **Calculate the number of moles of O2 (16 grams)**:
- Molecular mass of O2 = 2 × atomic weight of oxygen (O) = 2 × 16 g/mol = 32 g/mol.
- Number of moles of O2 = Given mass / Molecular mass = 16 g / 32 g/mol = 1/2 mol.
- Number of molecules of O2 = (1/2 mol) × Na = (1/2) × 6.022 × 10²³ = 3.011 × 10²³ molecules.

5. **Compare the number of molecules**:
- N2: 1.5055 × 10²³ molecules
- H2: 6.022 × 10²³ molecules
- Na2: 2.094 × 10²³ molecules
- O2: 3.011 × 10²³ molecules

From the calculations, we can see that H2 has the maximum number of molecules.

### Conclusion:
The option with the maximum number of molecules is **2 grams of H2**.