Question

A 1 L closed flask contains a mixture of 4 g of methane and 4.4 g of carbon dioxide. The pressure inside the flask at 27\degree C is (Assume ideal behaviour of gases):

• A. 8.6 atm
• B. 2.2 atm
• C. 4.2 atm
• D. 6.1 atm

Hint:

The ideal gas equation \( PV = nRT \) is fundamental in calculating pressure, volume, and temperature relationships in gas mixtures.

Answer 1

The Correct Option is A

Step 1: {Calculate the number of moles of each gas}
The number of moles of methane \( CH_4 \) is given by: \[ n_1 = \frac{{Mass of } CH_4}{{Molar mass of } CH_4} = \frac{4}{16} = 0.25 { mol} \] Similarly, the number of moles of carbon dioxide \( CO_2 \) is: \[ n_2 = \frac{{Mass of } CO_2}{{Molar mass of } CO_2} = \frac{4.4}{44} = 0.1 { mol} \] Step 2: {Total number of moles}
Total number of moles, \( n_T \) is: \[ n_T = n_1 + n_2 = 0.25 + 0.1 = 0.35 { mol} \] Step 3: {Applying the ideal gas equation}
Using the ideal gas equation: \[ PV = nRT \] where \( R = 0.0821 \) atm L mol\(^{-1}\)K\(^{-1}\), \( T = 300 \) K, and \( V = 1 \) L, we get: \[ P = \frac{0.35 \times 0.0821 \times 300}{1} = 8.6 { atm} \] Thus, the correct answer is (A).

Answer 2

Step 1: Use the ideal gas law
The ideal gas equation is:
\( PV = nRT \)
Where:
- \( P \) = pressure (atm)
- \( V \) = volume (L)
- \( n \) = number of moles
- \( R \) = ideal gas constant = 0.0821 L·atm/mol·K
- \( T \) = temperature in Kelvin

Step 2: Convert temperature to Kelvin
Given: \( T = 27\degree C = 27 + 273 = 300 \) K

Step 3: Calculate moles of each gas
Molar mass of methane (CH₄) = 12 + 4 = 16 g/mol
Moles of CH₄ = \( \frac{4}{16} = 0.25 \) mol

Molar mass of carbon dioxide (CO₂) = 12 + 2×16 = 44 g/mol
Moles of CO₂ = \( \frac{4.4}{44} = 0.10 \) mol

Total moles of gas, \( n \) = 0.25 + 0.10 = 0.35 mol

Step 4: Apply the ideal gas equation
Given: \( V = 1 \) L, \( T = 300 \) K, \( R = 0.0821 \)
\( P = \frac{nRT}{V} = \frac{0.35 \times 0.0821 \times 300}{1} \)
\( P = 8.63115 \approx 8.6 \) atm

Step 5: Final Answer
The pressure inside the flask is:
8.6 atm