Which of the following contains more molecules?

Options

A. 1 g `CO_(2)`
B. 1 g `N_(2)`
C. 1 g `H_(2)`
D. 1 g `CH_(4)`

Explanation

To determine which of the given substances contains more molecules, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Moles**:
- A mole is a unit that measures the amount of substance. One mole contains approximately \(6.022 \times 10^{23}\) molecules (Avogadro's number).

2. **Formula for Number of Moles**:
- The number of moles (\(n\)) can be calculated using the formula:
\[ n = \frac{\text{mass of substance (g)}}{\text{molar mass (g/mol)}} \]

3. **Calculate Moles for Each Substance**:
- For each substance, we will calculate the number of moles based on the given mass (1 gram) and its molar mass.

- **CO2**:
- Molar mass = 44 g/mol
- Moles = \(\frac{1 \text{ g}}{44 \text{ g/mol}} = \frac{1}{44} \text{ moles}\)
- Number of molecules = \(\frac{6.022 \times 10^{23}}{44}\)

- **N2**:
- Molar mass = 28 g/mol
- Moles = \(\frac{1 \text{ g}}{28 \text{ g/mol}} = \frac{1}{28} \text{ moles}\)
- Number of molecules = \(\frac{6.022 \times 10^{23}}{28}\)

- **H2**:
- Molar mass = 2 g/mol
- Moles = \(\frac{1 \text{ g}}{2 \text{ g/mol}} = \frac{1}{2} \text{ moles}\)
- Number of molecules = \(\frac{6.022 \times 10^{23}}{2}\)

- **CH4**:
- Molar mass = 16 g/mol
- Moles = \(\frac{1 \text{ g}}{16 \text{ g/mol}} = \frac{1}{16} \text{ moles}\)
- Number of molecules = \(\frac{6.022 \times 10^{23}}{16}\)

4. **Compare the Number of Molecules**:
- Now we will compare the fractions:
- CO2: \(\frac{6.022 \times 10^{23}}{44}\)
- N2: \(\frac{6.022 \times 10^{23}}{28}\)
- H2: \(\frac{6.022 \times 10^{23}}{2}\)
- CH4: \(\frac{6.022 \times 10^{23}}{16}\)

5. **Identify the Substance with Maximum Molecules**:
- The substance with the smallest denominator will have the largest number of molecules.
- Here, \(2\) (for H2) is the smallest denominator, meaning H2 has the most molecules.

### Conclusion:
- Therefore, **H2 contains the most molecules** among the given substances.