`4 g H_2, 32 g O_2 ,14 g N_2 and 11_g CO_2` are taken in a bulb of 500 ml. Which one of these has maximum active mass ?

Options

A. `H_2`
B. `O_2`
C. `N_2`
D. `CO_2`

Answer

To determine which gas has the maximum active mass in the given scenario, we will calculate the number of moles for each gas and then identify which one has the highest value. Active mass is directly related to the number of moles, as it is defined as molarity (moles per unit volume).

### Step-by-Step Solution:

1. **Identify the Given Masses and Molar Masses:**
- Hydrogen (H₂): Given mass = 4 g, Molar mass = 2 g/mol
- Oxygen (O₂): Given mass = 32 g, Molar mass = 32 g/mol
- Nitrogen (N₂): Given mass = 14 g, Molar mass = 28 g/mol
- Carbon Dioxide (CO₂): Given mass = 11 g, Molar mass = 44 g/mol

2. **Calculate the Number of Moles for Each Gas:**
- For Hydrogen (H₂):
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{4 \text{ g}}{2 \text{ g/mol}} = 2 \text{ moles} \]

- For Oxygen (O₂):
\[ \text{Number of moles} = \frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mole} \]

- For Nitrogen (N₂):
\[ \text{Number of moles} = \frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ moles} \]

- For Carbon Dioxide (CO₂):
\[ \text{Number of moles} = \frac{11 \text{ g}}{44 \text{ g/mol}} = 0.25 \text{ moles} \]

3. **Compare the Number of Moles:**
- Hydrogen: 2 moles
- Oxygen: 1 mole
- Nitrogen: 0.5 moles
- Carbon Dioxide: 0.25 moles

4. **Identify the Gas with Maximum Active Mass:**
- The gas with the highest number of moles is Hydrogen (H₂) with 2 moles.

### Conclusion:
The gas with the maximum active mass is **Hydrogen (H₂)**.