A stainless steel chamber contains Ar gas at a temperature T and press P. The total number of Ar atoms in the chamber is n. Now Ar gas in the chamber is replaced by CO2 gas and the total number of CO2 moleucules in the chamber is n/2 at the same temperature T. The pressure in the chamber now is P'. Which one of the following relations holds true? (Both the gases behave as ideal gases)

The behavior of the gases in the stainless steel chamber is governed by the Ideal Gas Law, expressed as PV = nRT or PV = NkT, where P is pressure, V is volume, n is the number of moles (or N is the number of molecules), T is temperature, and R (or k) is the gas constant. In the first scenario, the chamber contains n atoms of Argon at pressure P and temperature T. When Argon is replaced by CO2, the volume V and temperature T remain constant. The ideal gas law assumes that all gas molecules behave identically regardless of their chemical identity. Since the number of CO2 molecules is n/2, the pressure P' is directly proportional to the number of particles. Therefore, P' = (n/2) / n * P, which simplifies to P' = P/2. Note: Option 3 is selected as it represents P' = P/2 (assuming a typo in the provided options where 2 and 3 are identical).

Sources

1. [1] https://www.khanacademy.org/science/chemistry/gases-and-kinetic-molecular-theory/ideal-gas-laws/v/ideal-gas-equation-pv-nrt