We have talked about the diffusivity in liquids and how the Stokes-Einstein formulation works reasonably well. Ionic liquids are a relatively recent class of liquids useful as replacements for many...

We have talked about the diffusivity in liquids and how the Stokes-Einstein formulation works reasonably well. Ionic liquids are a relatively recent class of liquids useful as replacements for many toxic organic solvents. The diffusivity of gases in these liquids is of interest. We can write a version of Stokes-Einstein using the molar volume of the solute.

Where T is the absolute temperature (K), kb is Boltzmann’s constant, μ is the viscosity in Pa∙s and V is the molar volume of the gas in m³/kgmol. The data below show diffusivities as a function of solvent viscosity for carbon dioxide in a variety of ionic liquids. All data is taken at 30°C where the density of condensed carbon dioxide is 600 kg/m³.

a. Plot the data on log-log coordinates and see if the Stokes-Einstein relationship holds.

b. Based on your result from part (a), what is the actual relationship between diffusivity and viscosity for CO2 in these fluids (i.e., derive a correlation for the diffusivity as a function of viscosity?)