# 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?

• 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. – Nicolau Saker Neto May 1 '15 at 2:58
• @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. – ericksonla May 1 '15 at 12:55