Question

0.10 mol of argon gas is admitted to an evacuated 40 cm3 container at 20 ∘ C. The gas then undergoes an isothermal expansion to a volume of 100 cm3 . What is the final pressure of the gas?

Answer 1

Universal gas constant = R = 8.314 J/(mol.K)

Number of moles of the argon gas = n = 0.1 mol

Volume of the container = Initial volume of the gas = V₁ = 40 cm³ = 40 x 10^-6 m³ = 4 x 10^-5 m³

Initial temperature of the gas = T₁ = 20 ^oC = 20 + 273 K = 293 K

Initial pressure of the gas = P₁

P₁V₁ = nRT₁

P₁(4x10^-5) = (0.1)(8.314)(293)

P₁ = 6.09 x 10⁶ Pa

Final pressure of the gas = P₂

Final volume of the gas = V₂ = 100 cm³ = 100 x 10^-6 m³ = 1 x 10^-4 m³

The process is isothermal therefore the temperature remains constant.

P₁V₁ = P₂V₂

(6.09x10⁶)(4x10^-5) = P₂(1x10^-4)

P₂ = 2.436 x 10⁶ Pa

Final pressure of the gas = 2.436 x 10⁶ Pa