Assuming the radius of diatomic molecules is approximately 2.3 ×10-10 m for what pressure in Pa will the mean free path in room-

Question

2 years ago

5

Assuming the radius of diatomic molecules is approximately 2.3 ×10-10 m for what pressure in Pa will the mean free path in room-

temperature (20°C) nitrogen be 0.027 m? The Boltzmann constant is 1.38 × 10-23 J/K, Avogadro’s number is 6.02 × 1023 molecules/mole, and the ideal gas constant is R = 8.315 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

Physics

1 answer:

shutvik [7] · Answer 1 · 2022-10-26T12:11:56+03:00

For a radius of diatomic molecules is approximately 2.3 ×10-10 m, the pressure in Pa is mathematically given as

P=0.134Pa

<h3>What pressure in Pa will the mean free path in room-temperature (20°C) nitrogen be 0.027 m?</h3>

Generally, the equation for the ideal gas is mathematically given as

PV=nRT

Therefore

$P=\frac{1kT}{\sqrt{2}\pi(p)d^2}$

$P=\frac{1.38*10^-23*293}{\sqrt{2}\pi*(2*1.3*10^{-10})^2)*0.1}$

P=0.134Pa

In conclusion, Pressure

P=0.134Pa