Stokes-Einstein Equation for Dilute Solutions

The Stokes-Einstein equation can be used to calculate diffusion coefficients in liqnids  

Equation (9.26) is valid when the molecule reaches a steady-state velocity. This is when the net force acting on the molecule is zero. The solution is assumed to be ideal and dilute. 

For dilute solutions, the concentration of the second species, Cg, far exceeds the solute concentration and can be taken as constant. The gradient at constant temperature, then is 

Comparing Equation (9.29) with Tick s law of molecular diffusion, the Stokes-Einstein relationship of Equation (9.24) results. 

Equation (9.32) is the generalized Tick s law of diffusion that accounts for the acceleration regime of the molecule as well as the steady-state regime. An expression for the relaxation time for molecular diffusion falls out of the analysis that is, 

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