We want to compare the accuracy of various equations to predict the diffusivity of different solutes at infinite dilution in solvents with varying viscosity. The following values are given:

(a) Estimate the values of for  these conditions using the Stokes–Einstein and the Wilke–Chang equations and calculate the error relative to the experimental value given.

(b) Note that these equations become less accurate for small solutes in very viscous solvents. In these cases, the Gainer–Metzner equation is recommended. This equation gives:

where k_B is the Boltzmann constant, N is Avogadro’s number, is the number of nearest neighbors (usually between 6 and 8), and  isthe difference in activation energy for viscosity and diffusivity. The latter can be estimated from molecular properties using equations in Gainer and Metzner (1964) and Gainer (1994). The values of  are 1,940cal/mol for the water–glycerol system and 1,310 cal/mol for the n-hexanol–glycerol system. Estimate the corresponding diffusivities and calculate the error relative to the experimental value using this equation.

Transcribed Image Text:

Solute (A) Ethylene glycol Water Solvent (B) Water T r.B (C) (g/mol) 20 18 Water n-Hexanol Glycerol M Ethylene glycol Glycerol 20 92 0 92 20 62 VA g (cp) (cm/mol) 1.0 67 20 19 1410 19 12100 153 V (cm/mol) 19 67 110 110 Do exp. A,B (cm/s) 1.04 x 10-5 1.0 x 10-6 1.33 x 10-7 1.37 x 10-8