A 10 L flask contains 0.2 mole of `CH_4` and 0.3 mole of hydrogen at `25^@` C and 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 non-reacting gaseous mixture of methane (CH₄) and hydrogen (H₂), we can use the ideal gas law and the concept of partial pressures. Here’s how to solve the problem step by step:

### Step 1: Identify the Given Data
- Volume of the flask (V) = 10 L
- Moles of methane (n₁) = 0.2 moles
- Moles of hydrogen (n₂) = 0.3 moles
- Temperature (T) = 25°C = 25 + 273 = 298 K
- Ideal gas constant (R) = 0.0821 L·atm/(K·mol)

### Step 2: Calculate the Partial Pressure of Methane (CH₄)
Using the ideal gas law, the formula is:
\[ P = \frac{nRT}{V} \]

For methane:
\[ P_{CH₄} = \frac{n_{CH₄} \cdot R \cdot T}{V} \]
\[ P_{CH₄} = \frac{0.2 \, \text{moles} \cdot 0.0821 \, \text{L·atm/(K·mol)} \cdot 298 \, \text{K}}{10 \, \text{L}} \]

Calculating:
\[ P_{CH₄} = \frac{0.2 \cdot 0.0821 \cdot 298}{10} \]
\[ P_{CH₄} = \frac{4.8986}{10} \]
\[ P_{CH₄} = 0.48986 \, \text{atm} \]
(Approximately 0.49 atm)

### Step 3: Calculate the Partial Pressure of Hydrogen (H₂)
Using the same formula for hydrogen:
\[ P_{H₂} = \frac{n_{H₂} \cdot R \cdot T}{V} \]
\[ P_{H₂} = \frac{0.3 \, \text{moles} \cdot 0.0821 \, \text{L·atm/(K·mol)} \cdot 298 \, \text{K}}{10 \, \text{L}} \]

Calculating:
\[ P_{H₂} = \frac{0.3 \cdot 0.0821 \cdot 298}{10} \]
\[ P_{H₂} = \frac{7.3398}{10} \]
\[ P_{H₂} = 0.73398 \, \text{atm} \]
(Approximately 0.73 atm)

### Step 4: Calculate the Total Pressure
Since the gases do not react, the total pressure (P_total) is the sum of the partial pressures:
\[ P_{total} = P_{CH₄} + P_{H₂} \]
\[ P_{total} = 0.48986 \, \text{atm} + 0.73398 \, \text{atm} \]
\[ P_{total} = 1.22384 \, \text{atm} \]
(Approximately 1.22 atm)

### Final Answer
The total pressure inside the flask is approximately **1.22 atm**.

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