Chapter 14.4, Problem 45LC

Interpretation Introduction

Interpretation: To explain why the rate of diffusion of nitrogen gas and carbon monoxide is almost identical at the same temperature.

Concept Introduction: The capacity of gas to pass through a small aperture is known as effusion. The capacity of gases to mingle with one another, typically without the presence of a barrier, is known as diffusion.

Answer to Problem 45LC

Due to their almost identical molecular weights, nitrogen gas and carbon monoxide gas diffuse at very almost identical rates at the same temperature.

Explanation of Solution

The mass of nitrogen = 28 g/mol

The mass of carbon monoxide = 28 g/mol

It is known that the rate will be inversely proportional to the molar mass. It can be expressed as:

  $\text{Rate=}\frac{1}{\sqrt{\text{Molar}\text{mass}}}$

  $\begin{array}{c}\frac{{\left(\text{Rate}\right)}_{{\text{N}}_{\text{2}}}}{{\left(\text{Rate}\right)}_{\text{(CO)}}}\text{=}\sqrt{\frac{{\text{(Molar}\text{mass)}}_{\text{(CO)}}}{{\text{(Molar}\text{mass)}}_{{\text{(N}}_{\text{2}}\text{)}}}}\\ \frac{{\left(\text{Rate}\right)}_{{\text{N}}_{\text{2}}}}{{\left(\text{Rate}\right)}_{\text{(CO)}}}\text{=}\sqrt{\frac{\text{28}\text{g/mol}}{\text{28}\text{g/mol}}}\\ {\left(\text{Rate}\right)}_{{\text{N}}_{\text{2}}}\text{=}{\left(\text{Rate}\right)}_{\text{(CO)}}\end{array}$

Due to the similarity between the molar mass of nitrogen ( ${\text{N}}_{\text{2}}$ ) and carbon mono-oxide $\left(\text{CO}\right)$ . They will have identical rates of diffusion.