Measuring the ratio of aqueous diffusion coefficients between 6 Li + Cl - and 7 Li + Cr - by osmometry

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Osmotic equilibrium is a singular occurrence in the evolution of an osmotic cell because at this event the net solution flux is zero such that . At this juncture, the diffusion coefficient of the solute through the membrane ( ) equals the solute flux ( J s ) divided by the osmotic pressure ( ). Because the solute permeability coefficient ( ) is related to the Fickian diffusion coefficient ( D ) through the gas constant, temperature, and the membrane's thickness and tortuosity, the ratio of values for individual isotopic species equals the ratio of D values for the same isotopic components. A 0.9450 molal LiCl solution was placed within sealed dialysis tubing and osmoted against a kilogram of deionized water at 22°C. Osmotic equilibrium occurred at 164 ± 10 min. The ratio of 6 Li + Cl - / 7 Li + Cl - was measured to be 1.011 ± 0.003--a value close to the square root of the mass ratio between 7 LiCl and 6 LiCl (= 1.012) as calculated by Graham's Law. The measured diffusion coefficient ratio was used to predict the degree of hyperfiltration-induced fractionation of Li isotopes as a function of membrane ideality. When a membrane's exceeds 0.95 (as is likely for low-porosity shales) the 6 Li / 7 Li ratio on the high-pressure side of the membrane can theoretically vary by more than 0.0017.

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