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).