The Stokes-Einstein law for diffusion in solution

Source abstract

Abstract Einstein has shown that the relation between molecular movement and diffusion in a liquid may be expressed by the following equation, when the particles move independently of each other:— D=͞Δ2/2t, (1) D being the diffusion constant and ͞Δ2 the mean square of the deviation in a given direction in time t. Further, if it be assumed that the particles possess the same mean kinetic energy as gas molecules at the same temperature, the following equation holds ͞Δ = 2RT/N . t/C (2) where R is the gas constant, N Avogadro’s number, T the absolute temperature, and C a constant, which we might call the frictional resistance of the molecule. Hence, D = RT/N .1/C. (3) Under the foregoing assumptions equations (2) and (3) hold equally well for dissolved molecules and particles of greater dimensions.