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Question:

A 25 × 10⁻³ volume cylinder is filled with 1 mol of O₂ gas at room temperature (300K). The molecular diameter of O₂, and its root mean square speed, are found to be 0.3nm, and 200m/s, respectively. What is the average collision rate (per second) for an O₂ molecule?

≈10¹³

≈10¹⁰

≈10¹¹

≈10¹²

Solution:

Correct option is C. ≈10¹⁰
v = V_avλ
λ = RT/(2πσ²NAP)
σ = 2 × 0.3 × 10⁻⁹
P = RT/V ⇒ λ = V/(2πσ²NA√2)
V_av = (8/3π) × Vrms
∴ v = 200 × (2πσ²NA)/(25 × 10⁻³ × (8/3π))
= 200 × 2π × (0.6 × 10⁻⁹)² × 6.022 × 10²³ / (25 × 10⁻³ × (8/3π))
= 17.68 × 10⁸/sec = 1.768 × 10¹⁰/sec ≈ 10¹⁰