Kinetic-Theory Deviations from Blanc's Law of Ion Mobilities

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Abstract
Ion mobilities in gas mixtures are investigated by rigorous kinetic theory. It is shown that the Einstein relation between mobility and diffusion coefficient is exact in higher approximations, contrary to previous conjectures, and an explicit expression for the deviations from Blanc's law for ions in a binary gas mixture is obtained in second Chapman–Enskog approximation. Numerical calculations show that deviations from Blanc's law are usually small, as expected, but that systems with large deviations are possible. The results apply generally to any tracer diffusion, and are not limited to ions.