Abstract: The leaching of ionic rare earth is a process of rebalancing the electric double layer, and the ion size effects have an important influence on the cation and potential distribution in the electric double layer. This article coupled the nonlinear Boltzmann equation considering ion size effects with the Poisson equation (sPB) by taking into account the influence of ion size on the system's electrostatic free energy, based on the Gouy-Chapman-Stern double-layer model. This coupling equation was used to study the effects of ion size on the distribution of ions and electric potential in the double layer. Combined with the results of cup leaching experiments, the calculation results were compared and analyzed with the classical Poisson Boltzmann equation (cPB). The results showed that there were differences in the adsorption of NH₄⁺ and La³⁺ on the surface of montmorillonite, and the measured saturated adsorption amounts were 0.635 mmol/g and 0.305 mmol/g, respectively. Based on the cPB equation, the calculated adsorption amounts of NH₄⁺ and La³⁺ were about 17 times and 11 times the actual adsorption amounts, respectively. However, according to the sPB equation, they were about 1.75 times and 1.25 times, respectively. The Stern potential calculated by the sPB equation was significantly lower than that by the cPB equation, and the variation of the Stern potential calculated by the sPB equation with concentration was not significant. Ionic hydration had little effect on ion adsorption capacity and Stern potential. Overall, the sPB equation considering ion size could better describe the distribution of cations and electric potential within the electric double layer.