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Question

The mean free path of a gas molecule is 6 × 10⁻⁷ m at 0.5 atm. What will it be at 1 atm if temperature remains constant?

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Explanation

**Dalton's law of partial pressures** total pressure P_total = Σ P_i, P_i = X_i P_total, X_i mole tion, each gas exerts pressure as if alone, ideal gas mixture P_i V = n_i R T, partial pressure proportional to mole tion, e.g., air 79% N₂ 21% O₂ P_N₂=0.79 atm P_O₂=0.21 atm at 1 atm total. l ∝ (1)/(n), n ∝ P. If P doubles, n doubles, l halves.New l = 6 × 10⁻⁷/2 = 3 × 10⁻⁷ m. Substituting values gives 3.0 × 10⁻⁷ m, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V

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