If 1 mole of `H_(2)`, 2 moles of `O_(2)` and 3 moles of `N_(2)` are mixed in a vessel and total pressure was found to be 12 atm then the partial pressure exerted by `N_(2)` in the vessel will be

Options

A. 2 atm
B. 4 atm
C. 6 atm
D. 12 atm

Answer

To find the partial pressure exerted by \( N_2 \) in the vessel, we can use Dalton's Law of Partial Pressures. According to this law, the partial pressure of a gas in a mixture is given by the formula:

\[ P_i = X_i \times P_{total} \]

where:
- \( P_i \) is the partial pressure of the gas,
- \( X_i \) is the mole fraction of the gas,
- \( P_{total} \) is the total pressure of the gas mixture.

### Step-by-Step Solution:

1. **Calculate the total number of moles of gas in the mixture:**
- Moles of \( H_2 = 1 \)
- Moles of \( O_2 = 2 \)
- Moles of \( N_2 = 3 \)
- Total moles = \( 1 + 2 + 3 = 6 \) moles.

2. **Calculate the mole fraction of \( N_2 \):**
- The mole fraction \( X_{N_2} \) is calculated as:
\[ X_{N_2} = \frac{\text{Moles of } N_2}{\text{Total moles}} = \frac{3}{6} = 0.5 \]

3. **Use the total pressure to find the partial pressure of \( N_2 \):**
- Given that the total pressure \( P_{total} = 12 \) atm,
- The partial pressure \( P_{N_2} \) can be calculated as:
\[ P_{N_2} = X_{N_2} \times P_{total} = 0.5 \times 12 \text{ atm} = 6 \text{ atm} \]

### Final Answer:
The partial pressure exerted by \( N_2 \) in the vessel is **6 atm**.