A stainless steel chamber contains Ar gas at a temperature T and pressure 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 molecules 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)?

Option 3 : P’ = P/2

CONCEPT:

• Ideal gas: It is a hypothetical gas, consisting of molecules that are having negligible volume and their collision is perfectly elastically (means no loss of energy) and obeys gas law.
• The properties of an ideal gas are:
  • They are having negligible volume, point size molecules.
  • There is no attractive or repulsive force between the particles of gas
  • The collision between the gases and the walls of the container should be perfectly elastic (there is no loss of energy).
• The Equation of State is an equation that connects all the state variables of a system.

The Equation of State for an ideal gas is given by:

⇒ PV= μRT

Where μ is the number of moles of gas, Pressure(P), Temperature(T), and Volume(V) is the state variables, R is the gas constant.

EXPLANATION:

• Both Ar and CO₂ are ideal gases. So we will apply the ideal gas equation.
• For Ar – the temperature is T, the pressure is P and the number of molecules is n, and volume (V) is the same for both the gases.
• Use the ideal gas equation:

⇒ PV = nRT        ---- (1)

• For CO₂ – The temperature is T, Pressure is P’, the number of molecules is n/2, and Volume (V)
• Apply the Ideal gas equation: 

⇒ P’V = (n/2) RT        ---- (2)

Equation (2) divided by (1):

⇒ P’/P = n/2