The number of gas molecules effusing per second unit area through an orifice on the wall of the container is 1/4 N* u_av, where N* is the number of molecules per unit volume. What is this number under

Question

The number of gas molecules effusing per second unit area through an orifice on the wall of the container is 1/4 N* u_av, where N* is the number of molecules per unit volume. What is this number under STP conditions for nitrogen gas?

Prashant Kotian · Accepted Answer

Correct answer: C. under stp: p = 1.013 × 10^5 pa, t = 273.15 k. n* = p / (k_b × t) = 1.013 × 10^5 / (1.38 × 10^-23 × 273.15) ≈ 2.687 × 10^25 molecules/m^3. for nitrogen (m = 28 g/mol): u_av = √(8rt/πm) ≈ 454.4 m/s. effusion rate = 1/4 × n* × u_av = 1/4 × 2.687 × 10^25 × 454.4 ≈ 3.05 × 10^27 molecules/m^2 s = 3.05 × 10^23 molecules/cm^2 s, which matches (c) in scaled units.

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