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 moles of each gas}
Moles of methane ($ CH_4 $) are calculated as: \[ n_1 = \frac{{Mass of } CH_4}{{Molar mass of } CH_4} = \frac{4}{16} = 0.25 { mol} \] Moles of carbon dioxide ($ CO_2 $) are calculated as: \[ n_2 = \frac{{Mass of } CO_2}{{Molar mass of } CO_2} = \frac{4.4}{44} = 0.1 { mol} \] Step 2: {Determine total moles}
The total number of moles, $ n_T $, is the sum of individual moles: \[ n_T = n_1 + n_2 = 0.25 + 0.1 = 0.35 { mol} \] Step 3: {Apply ideal gas law}
The ideal gas equation is given by: \[ PV = nRT \] With $ R = 0.0821 $ atm L mol\(^{-1}\)K\(^{-1}\), $ T = 300 $ K, and $ V = 1 $ L, the pressure ($ P $) is: \[ P = \frac{0.35 \times 0.0821 \times 300}{1} = 8.6 { atm} \] The correct answer is (A).