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.

\[D\left(\frac{m^{2}}{s}\right) \propto \frac{T}{\mu \bar{V}^{1 / 3}}\]

Where \(T\) is the absolute temperature \((\mathrm{K}), k_{b}\) is Boltzmann's constant, \(\mu\) is the viscosity in \(\mathrm{Pa} \cdot \mathrm{s}\) and \(\bar{V}\) is the molar volume of the gas in \(\mathrm{m}^{3} / \mathrm{kgmol}\). 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 \(30^{\circ} \mathrm{C}\) where the density of condensed carbon dioxide is \(600 \mathrm{~kg} / \mathrm{m}^{3}\).

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 \(\mathrm{CO}_{2}\) in these fluids (i.e., derive a correlation for the diffusivity as a function of viscosity?)

Transcribed Image Text:

Ionic Liquid Cyphos 101 Viscosity (Pa's) CO, Diffusivity x100 m/s 1.316 3.0 Cyphos 105 0.213 3.0 Cyphos 109 0.243 6.2 Cyphos 169 0.207 3.5 Cyphos 201 3.011 1.7