Chapter 43: Diffusion – Molecular Motion

Diffusion – Molecular Motion delves into the kinetic theory of gases applied to non-equilibrium situations, focusing on transport phenomena that describe how gases move and transfer quantities like charge, mass, and energy. The analysis begins by quantifying the fundamental molecular interactions through the concept of collisions between molecules, defining the average time between collisions (τ). This average time is used to show that the probability of a molecule traveling a certain time without interacting decays exponentially. This collision frequency directly determines the mean free path (l), which is the average distance a molecule travels between collisions, and this path length is inversely related to the number density of scattering particles and the molecular collision cross section. The text then examines the slow, directed movement of molecules, called the drift speed, which is a small velocity superimposed on the much faster, random thermal motion, resulting from an external force (like an electric or gravitational field). The mobility (μ) of a particle is introduced as a key quantity, describing the constant proportionality linking the drift speed to the applied force. This concept is first applied to model ionic conductivity, calculating the macroscopic electric current that arises from ions drifting under an electric field. The discussion expands to molecular diffusion, which is the flow of particles driven by a spatial gradient in concentration or density rather than an external force. The rate of diffusion is quantified by the diffusion coefficient (D), which relates the particle flow to the density gradient. Crucially, the chapter establishes a fundamental connection between the two seemingly distinct processes of mobility and diffusion, demonstrating that the diffusion coefficient is directly proportional to the product of the particle's mobility and the absolute temperature. Finally, the principles of kinetic theory are extended to study thermal conductivity, the transfer of heat due to a temperature gradient, revealing the rather surprising theoretical prediction that the thermal conductivity rate of a gas is independent of its density.