Which of the following contains maximum number of molecules?

Question

Accepted Answer

To determine which option contains the maximum number of molecules, we need to calculate the number of moles for each substance, as the number of molecules is directly proportional to the number of moles. The number of moles is calculated using the formula:

$$ \text{Number of moles} = \frac{\text{Mass of the substance (g)}}{\text{Molar mass of the substance (g/mol)}} $$

Once we have the number of moles, we can determine the number of molecules using Avogadro's number, which is $6.022 \times 10^{23}$ molecules per mole.

Let's calculate the number of moles for each option:

1. **$1~g~CO_{2}$:**
   - Molar mass of $CO_{2} = 12 + 2 \times 16 = 44 \, \text{g/mol}$
   - Number of moles = $\frac{1}{44} \approx 0.0227 \, \text{moles}$

2. **$1~g~N_{2}$:**
   - Molar mass of $N_{2} = 2 \times 14 = 28 \, \text{g/mol}$
   - Number of moles = $\frac{1}{28} \approx 0.0357 \, \text{moles}$

3. **$1~g~H_{2}$:**
   - Molar mass of $H_{2} = 2 \times 1 = 2 \, \text{g/mol}$
   - Number of moles = $\frac{1}{2} = 0.5 \, \text{moles}$

4. **$1~g~CH_{4}$:**
   - Molar mass of $CH_{4} = 12 + 4 \times 1 = 16 \, \text{g/mol}$
   - Number of moles = $\frac{1}{16} = 0.0625 \, \text{moles}$

Now, comparing the number of moles:

- $CO_{2}$ has approximately 0.0227 moles.
- $N_{2}$ has approximately 0.0357 moles.
- $H_{2}$ has 0.5 moles.
- $CH_{4}$ has 0.0625 moles.

Option 3, $1~g~H_{2}$, has the highest number of moles (0.5 moles), which means it contains the maximum number of molecules. This is because hydrogen gas ($H_{2}$) has the smallest molar mass among the given options, allowing more moles to be present in 1 gram compared to the other substances.

Therefore, Option 3 is correct because it results in the highest number of molecules due to the highest number of moles. The other options have fewer moles and thus fewer molecules, making them incorrect in this context.