Question

The average distance between collisions for atoms in a real gas is known as the mean free path (see pp. 298-9 in McKay). Which of the answers below best represents the mean free path for gas molecules at STP with atomic radii on the order of 1.0 x 10-10 m? The average distance between collisions for atoms in a real gas is known as the mean free path (see pp. 298-9 in McKay). Which of the answers below best represents the mean free path for gas molecules at STP with atomic radii on the order of 1.0 x 10-10 m?

A. 30 nm
B. 3000 nm
C. 300 nm
D. 3 nm

Answer 1

Answer:

300 nm

Explanation:

R = Gas constant = 8.314 J/molK

r = Atomic radii = $1\times 10^{-10}\ m$

d = Atomic diameter = $2r=2\times 10^{-10}\ m$

At STP

T = Temperature = 273.15 K

P = Pressure = 100 kPa

$N_A$ = Avogadro's number = $6.022\times 10^{23}$

The mean free path is given by

$\lambda=\frac{RT}{\sqrt2d^2N_AP}\\\Rightarrow \lambda=\frac{8.314\times 273.15}{\sqrt2 \pi \times (2\times 10^{-10})^2\times 6.022\times 10^{23}\times 100000}\\\Rightarrow \lambda=2.12165\times 10^{-7}\ m=212.165\times 10^{-9}\ m=212.165\ nm$

The answer that best represents the mean free path for gas molecules is 300 nm