A 1.0 L flask contains 2.0 g of `N_(2), 0.4 g H_(2)` and 9.0 of `O_(2)` at `27^(@)C`. What is the pressure in the flask?

Explanation

To find the pressure in the flask containing the gases \(N_2\), \(H_2\), and \(O_2\), we will use the ideal gas law and calculate the partial pressures of each gas. The total pressure in the flask will be the sum of these partial pressures.

### Step-by-Step Solution:

1. **Identify the given data:**
- Volume of the flask, \(V = 1.0 \, \text{L}\)
- Mass of \(N_2 = 2.0 \, \text{g}\)
- Mass of \(H_2 = 0.4 \, \text{g}\)
- Mass of \(O_2 = 9.0 \, \text{g}\)
- Temperature, \(T = 27^\circ C = 300 \, \text{K}\) (convert Celsius to Kelvin by adding 273)

2. **Calculate the number of moles for each gas:**
- For \(N_2\):
\[ n_{N_2} = \frac{\text{mass}}{\text{molar mass}} = \frac{2.0 \, \text{g}}{28.0 \, \text{g/mol}} = 0.0714 \, \text{mol} \]
- For \(H_2\):
\[ n_{H_2} = \frac{0.4 \, \text{g}}{2.0 \, \text{g/mol}} = 0.2 \, \text{mol} \]
- For \(O_2\):
\[ n_{O_2} = \frac{9.0 \, \text{g}}{32.0 \, \text{g/mol}} = 0.28125 \, \text{mol} \]

3. **Use the ideal gas law to calculate the partial pressure of each gas:**
The ideal gas law is given by:
\[ P = \frac{nRT}{V} \]
where \(R = 0.0821 \, \text{L atm/(K mol)}\).

- **Partial pressure of \(N_2\)**:
\[ P_{N_2} = \frac{(0.0714 \, \text{mol}) \times (0.0821 \, \text{L atm/(K mol)}) \times (300 \, \text{K})}{1.0 \, \text{L}} = 1.76 \, \text{atm} \]

- **Partial pressure of \(H_2\)**:
\[ P_{H_2} = \frac{(0.2 \, \text{mol}) \times (0.0821 \, \text{L atm/(K mol)}) \times (300 \, \text{K})}{1.0 \, \text{L}} = 4.93 \, \text{atm} \]

- **Partial pressure of \(O_2\)**:
\[ P_{O_2} = \frac{(0.28125 \, \text{mol}) \times (0.0821 \, \text{L atm/(K mol)}) \times (300 \, \text{K})}{1.0 \, \text{L}} = 6.93 \, \text{atm} \]

4. **Calculate the total pressure in the flask:**
\[ P_{\text{total}} = P_{N_2} + P_{H_2} + P_{O_2} = 1.76 \, \text{atm} + 4.93 \, \text{atm} + 6.93 \, \text{atm} = 13.62 \, \text{atm} \]

### Final Answer:
The pressure in the flask is \(13.62 \, \text{atm}\).