General relationship between salt concentration and x-ray absorption for binary electrolytes

We derive a general relationship between salt concentration and x-ray absorption for binary electrolytes. Volume and mass conservation are considered. The relationship can be used to measure salt concentration profiles via x-ray absorption imaging during cell polarization and relaxation. In conjunction with concentrated solution theory, the derived relationship is as a powerful tool to accurately determine transport coefficients such as cation transference number in ion battery electrolytes and to test thermodynamic models. The relationship is electrolyte-agnostic, as long as the product between mass attenuation coefficient, inverse partial molar volume, and molar mass of the solvent and that of the salt are not equal.