Question

Nitrogen and oxygen of volumes one litre each at atmospheric pressure are mixed in a closed container of volume three litres. If the process is isothermal, the ratio of final pressure of the mixture and atmospheric pressure is

• A. 2/3
• B. 3/2
• C. 2
• D. 1

Hint:

For mixing non-reacting gases isothermally: $P_{mix} V_{mix} = P_1 V_1 + P_2 V_2 + \dots$ Here: $P_{mix} (3) = P_0(1) + P_0(1) \Rightarrow 3 P_{mix} = 2 P_0$.

Answer 1

The Correct Option is A

Step 1: Concept - Boyle's Law and Dalton's Law:
Since the process is isothermal ($T$ constant), $P_1 V_1 = P_2 V_2$ applies for each gas. The total pressure is the sum of partial pressures.
Step 2: Calculate Partial Pressures:
Let $P_0$ be the atmospheric pressure.

• Nitrogen: Initial ($P_0, 1$ L) $\rightarrow$ Final ($P_{N_2}, 3$ L). \[ P_0 \times 1 = P_{N_2} \times 3 \Rightarrow P_{N_2} = \frac{P_0}{3} \]
• Oxygen: Initial ($P_0, 1$ L) $\rightarrow$ Final ($P_{O_2}, 3$ L). \[ P_0 \times 1 = P_{O_2} \times 3 \Rightarrow P_{O_2} = \frac{P_0}{3} \]

Step 3: Total Pressure:
\[ P_{final} = P_{N_2} + P_{O_2} = \frac{P_0}{3} + \frac{P_0}{3} = \frac{2P_0}{3} \]
Step 4: Ratio:
\[ \frac{P_{final}}{P_{atm}} = \frac{2P_0/3}{P_0} = \frac{2}{3} \]