Debye-Huckel theory with non-polar solvents

I want to calculate the activity coefficients of mixed solvent salt solutions. I am seeing very strange behavior when I try calculating the activity coefficient of salts in non-polar solvents using Debye-Huckel theory though and its messing up my down-stream calculations.


In a simple example, let's compare the activity of NaCl in hexane and water:


Inputs: (hexane / water)


* Density: 654 / 1000 kg/m^3
* Dielectric constant: 1.89 / 80.4
* Temperature: 293 K
* Molarity = 0.1 mol/L


Calculations:


* $A = consts \frac {\sqrt {\rho}} {(\epsilon \* T)^{1.5}} = $ 230 / 1
* $I = \frac12 \sum\_{ions} cz^2 =$ 0.1 / 0.1
* $ln(\gamma) = -Az^2\sqrt I = $ -73 / -0.32
* $\gamma = 10^{-32}$ / 0.72


In equilibrium the salt activity should be the same in each phase, $\gamma\_{aq}x\_{aq} = \gamma\_{org} x\_{org}$, which would imply that the salt should all be flying over to the organic phase. That clearly makes no sense.


Why does this give such totally wrong behavior in a limiting case?


