A 10 L flask contains 0.2 mole of `CH_4` and 0.3 mole of hydrogen at `25^@` C ansd which makes non- reacting gaseous mixture. Then, the total pressure inside the flask is

Options

A. `1.22 atm`
B. 0.5 atm
C. 0.61 atm
D. 2.20 atm

Answer

To find the total pressure inside the flask containing a mixture of gases, we can use the Ideal Gas Law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature (in Kelvin)

### Step-by-Step Solution:

1. **Determine the total number of moles of gas:**
- We have 0.2 moles of \( CH_4 \) and 0.3 moles of hydrogen.
- Total moles \( n = 0.2 + 0.3 = 0.5 \) moles.

2. **Convert the temperature from Celsius to Kelvin:**
- The temperature is given as \( 25^\circ C \).
- To convert to Kelvin, use the formula:
\[ T(K) = T(°C) + 273.15 \]
- Thus, \( T = 25 + 273.15 = 298.15 \, K \) (approximately 298 K for calculations).

3. **Identify the volume of the flask:**
- The volume \( V \) is given as 10 L.

4. **Use the ideal gas constant:**
- The value of \( R \) is given as \( 0.0821 \, L·atm/(K·mol) \).

5. **Substitute the values into the Ideal Gas Law equation:**
- Rearranging the equation for pressure \( P \):
\[ P = \frac{nRT}{V} \]
- Substitute the known values:
\[ P = \frac{(0.5 \, \text{mol}) \times (0.0821 \, L·atm/(K·mol)) \times (298 \, K)}{10 \, L} \]

6. **Calculate the pressure:**
- Performing the calculation:
\[ P = \frac{(0.5) \times (0.0821) \times (298)}{10} \]
\[ P = \frac{12.295}{10} \]
\[ P = 1.2295 \, atm \]
- Rounding to three significant figures, we get \( P \approx 1.23 \, atm \).

### Final Answer:
The total pressure inside the flask is approximately **1.23 atm**.