States of Matter

At constant V and T, P ∝ n.
Initial: P1 = 2 atm, moles of X = nX.
After adding Y: P2 = 6 atm, total moles = nX + nY.
(nX + nY)/nX = P2/P1 = 6/2 = 3 ⇒ nY = 2nX.

Given mX = 10 g, mY = 80 g.
Mx = 10/nX, My = 80/nY = 80/(2nX) = 40/nX ⇒ My = 4Mx.

u(rms) ∝ 1/√M, so uX/uY = √(My/Mx) = √4 = 2.
Ratio uX : uY = 2 : 1.

• Volume, V = 1 L
• Temperature, T = 27°C = 300 K
• Mass of CH₄ = 4 g, Molar mass = 16 g/mol → Moles, n₁ = 4/16 = 0.25 mol
• Mass of CO₂ = 4.4 g, Molar mass = 44 g/mol → Moles, n₂ = 4.4/44 = 0.1 mol
• Total moles, n = 0.25 + 0.1 = 0.35 mol
• Gas constant, R = 0.0821 L atm K⁻¹ mol⁻¹

Using the ideal gas equation:
PV = nRT
P × 1 = (0.35) × (0.0821) × (300)
P = 8.62 atm