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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?

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  • $\begingroup$ I've never applied Debye-Huckel theory outside of aqueous solutions, but does the ionic strength equation really apply directly to hexane in the same way as water? I would imagine the actual concentration to be taken into account would be the equilibrium concentration of the dissolved ions in the hexane phase; in reality, practically all the salt would precipitate out of the hexane, so $\rm{ln(\gamma )}$ would be very close to zero. $\endgroup$ – Nicolau Saker Neto May 1 '15 at 2:58
  • $\begingroup$ @NicolauSakerNeto I agree. In theory, the solubility is derivable from activity so I was really hoping for a robust way to (roughly) predict solubility without any pre-sorting. It would be nice if the limiting case worked but you may be right that the ionic strength equation just doesn't make sense. $\endgroup$ – ericksonla May 1 '15 at 12:55

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