Chapter 33, Problem 33.31NP

(a)

Interpretation Introduction

Interpretation: The single-particle collisional frequency and mean free path for ${\text{N}}_{\text{2}}$ at ${10}^{-3}$ torr pressure and 298 K need to be determined.

Concept Introduction:

The single-particle collisional frequency can be calculated as follows:

  $Z_{11}=\sqrt{2}\left(\frac{P{N}_A}{RT}\right)\sigma {\left(\frac{8RT}{\pi M}\right)}^{1/2}$

Here, P is pressure, $N_A$ is Avogadro’s number, R is Universal gas constant, T is temperature, M is molar mass, and $\sigma$ is collision diameter.

The formula for collision diameter is as follows:

  $\sigma =\pi {\left(r_1+r_2\right)}^2$

Here, r is radius of atoms colliding together.

(b)

Interpretation Introduction

Interpretation: The collision frequency and mean free path for ${\text{N}}_{\text{2}}$ at ${10}^{-10}$ torr pressure and 298 K need to be determined.

Concept Introduction:

Collision frequency can be calculated as follows:

  $\text{Collision frequency}=\frac{v_{\text{rms}}}{l}$

Here, $v_{\text{rms}}$ is the root mean square velocity and l is the mean free path.

Here, root mean square velocity can be calculated as follows:

  $v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

Here, R is the Universal gas constant, T is temperature and M is molar mass.