Chapter 16: Molecules in Motion

Fick's first law provides the mathematical framework for understanding diffusion as a process driven by concentration gradients, quantifying the flux of matter in response to compositional variations. Transport in liquids presents distinct challenges because strong intermolecular forces and high molecular density invalidate many assumptions valid for gases, necessitating alternative approaches such as examining electrical conductivity in electrolyte solutions to understand ion mobilities and effective particle sizes. The chapter explores diffusion through complementary theoretical perspectives: the thermodynamic approach treats diffusion as a response to internal driving forces and develops the diffusion equation governing how concentration profiles evolve over time, while the statistical approach reframes diffusion as random molecular displacement, connecting microscopic step characteristics to the overall diffusion coefficient through the Einstein-Smoluchowski relationship. A critical insight emerges through the Stokes-Einstein relation, which unifies the treatment of diffusion and frictional resistance, demonstrating that diffusion coefficients depend on molecular shape, solvent viscosity, and thermal energy. Together, these frameworks enable prediction and interpretation of how molecules redistribute themselves through space and how energy propagates through matter, essential concepts for understanding processes ranging from chemical reactions to biological transport across membranes.