A mixture of `N_2` and Ar gases in a cylinder contains 7g of `N_2` & 8 g of Ar. If the total pressure of the mixture of the gases in the cylinder is 27bar, the partial pressure of `N_2` is:

Options

A. 9bar
B. 12bar
C. 15bar
D. 18bar

Answer

To find the partial pressure of \( N_2 \) in a mixture of \( N_2 \) and \( Ar \) gases, we can follow these steps:

### Step 1: Calculate the number of moles of \( N_2 \) and \( Ar \)

1. **Given data:**
- Mass of \( N_2 = 7 \, g \)
- Mass of \( Ar = 8 \, g \)
- Molar mass of \( N_2 = 28 \, g/mol \) (since \( N \) has an atomic mass of 14)
- Molar mass of \( Ar = 40 \, g/mol \)

2. **Calculate moles of \( N_2 \):**
\[ \text{Moles of } N_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{7 \, g}{28 \, g/mol} = 0.25 \, mol \]

3. **Calculate moles of \( Ar \):**
\[ \text{Moles of } Ar = \frac{8 \, g}{40 \, g/mol} = 0.2 \, mol \]

### Step 2: Calculate the total number of moles in the mixture

4. **Total moles:**
\[ \text{Total moles} = \text{Moles of } N_2 + \text{Moles of } Ar = 0.25 \, mol + 0.2 \, mol = 0.45 \, mol \]

### Step 3: Calculate the mole fraction of \( N_2 \)

5. **Mole fraction of \( N_2 \):**
\[ \text{Mole fraction of } N_2 = \frac{\text{Moles of } N_2}{\text{Total moles}} = \frac{0.25 \, mol}{0.45 \, mol} = \frac{5}{9} \]

### Step 4: Calculate the partial pressure of \( N_2 \)

6. **Using Dalton's Law of Partial Pressures:**
\[ \text{Partial pressure of } N_2 = \text{Total pressure} \times \text{Mole fraction of } N_2 \]
\[ \text{Partial pressure of } N_2 = 27 \, bar \times \frac{5}{9} = 15 \, bar \]

### Conclusion

The partial pressure of \( N_2 \) is \( 15 \, bar \).

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