Multiple choice

One litre of oxygen at a pressure of $1 atm$ and two litres of nitrogen at a pressure of $0.5 atm$, are introduced into a vessel of volume $1 L$. If there is no change in temperature, the final pressure of the mixture of gas (in atm) is

  1. $1.5$
  2. $2.5$
  3. $2$
  4. $4$
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C Correct answer
Explanation

Using Boyle's Law (P1V1 = P2V2) for each gas in the new volume (1L): Oxygen: 1 atm * 1 L = P_O2 * 1 L => P_O2 = 1 atm. Nitrogen: 0.5 atm * 2 L = P_N2 * 1 L => P_N2 = 1 atm. Total pressure = 1 + 1 = 2 atm.

AI explanation

Because the temperature is constant, we use Boyle's law (P1 V1 equals P2 V2) to find the final partial pressure of each gas in the 1 L vessel. The oxygen pressure becomes (1 atm)(1 L) divided by 1 L, which is 1 atm, and the nitrogen pressure becomes (0.5 atm)(2 L) divided by 1 L, which is 1 atm. According to Dalton's law of partial pressures, the final total pressure is the sum of these partial pressures, giving 2 atm.

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