`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 among the given gases (H₂, O₂, N₂, and CO₂), we need to calculate the concentration of each gas in the 500 ml bulb. The concentration is given by the formula:

\[ \text{Concentration (C)} = \frac{\text{Number of moles (n)}}{\text{Volume (V)}} \]

Where the volume should be in liters.

### Step-by-step Solution:

1. **Calculate the number of moles for each gas:**
- **For H₂:**
- Molecular weight of H₂ = 2 g/mol (since H = 1 g/mol and there are 2 H atoms)
- Moles of H₂ = \(\frac{4 \text{ g}}{2 \text{ g/mol}} = 2 \text{ moles}\)

- **For O₂:**
- Molecular weight of O₂ = 32 g/mol (since O = 16 g/mol and there are 2 O atoms)
- Moles of O₂ = \(\frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mole}\)

- **For N₂:**
- Molecular weight of N₂ = 28 g/mol (since N = 14 g/mol and there are 2 N atoms)
- Moles of N₂ = \(\frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ moles}\)

- **For CO₂:**
- Molecular weight of CO₂ = 44 g/mol (C = 12 g/mol and O = 16 g/mol, thus 12 + 2(16) = 44)
- Moles of CO₂ = \(\frac{11 \text{ g}}{44 \text{ g/mol}} = 0.25 \text{ moles}\)

2. **Convert the volume from ml to liters:**
- Volume = 500 ml = 0.5 L

3. **Calculate the concentration for each gas:**
- **For H₂:**
\[ C_{H_2} = \frac{2 \text{ moles}}{0.5 \text{ L}} = 4 \text{ moles/L} \]

- **For O₂:**
\[ C_{O_2} = \frac{1 \text{ mole}}{0.5 \text{ L}} = 2 \text{ moles/L} \]

- **For N₂:**
\[ C_{N_2} = \frac{0.5 \text{ moles}}{0.5 \text{ L}} = 1 \text{ mole/L} \]

- **For CO₂:**
\[ C_{CO_2} = \frac{0.25 \text{ moles}}{0.5 \text{ L}} = 0.5 \text{ moles/L} \]

4. **Compare the concentrations:**
- \(C_{H_2} = 4 \text{ moles/L}\)
- \(C_{O_2} = 2 \text{ moles/L}\)
- \(C_{N_2} = 1 \text{ mole/L}\)
- \(C_{CO_2} = 0.5 \text{ moles/L}\)

5. **Determine the maximum active mass:**
- The gas with the highest concentration (active mass) is H₂ with 4 moles/L.

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