In this study, the reclamation of a calcareous sodic soilwith the exchangeable sodium percentage (ESP) value of 26.6 % was investigated using the cheap and readily available chemical and organicmaterials including natural bentonite and zeolite saturated with calcium (Ca2+), waste calcite, three metal oxide nanoparticles functionalized with an acidic extract of potato residues, and potato residues. Chemical amendments were added to the soil at a rate of 2%, while potato residues were applied at the rates of 2 and 4 % by weight. The ESP in the amended soils was reduced in the range of 0.9–4.9 % compared to the control soil, and the smallest and the largest decline was respectively observed in treatments containing waste calcite and 4 % of potato residues. Despite the reduction in ESP, the values of this parameter were not below 15 % at the end of a 40-day incubation period. So, the effect of solutions of varying sodium adsorption ratio (SAR) values of 0, 5, 10, 20, 30, 40, and 50 on sodium (Na+) exchange equilibria was evaluated in batch systems. The empirical models (simple linear, Temkin, and Dubinin-Radushkevich) fitted well to experimental data. The relations of quantity to intensity (Q/I) revealed that the potential buffering capacity for Na+ (PBCNa) varied from 0.275 to 0.337 ((cmolc kg−1) (mmol L−1)−1/2) in the control soil and amended soils. The relationship between exchangeable sodium ratio (ESR) and SAR was individually determined for the control soil and amended soils. The values of Gapon selectivity coefficient (KG) of Na+ differed from the value suggested by U.S. Salinity Laboratory (USSL). The PHREEQC, a geochemical computer program, was applied to simulate Na+ exchange isotherms by using the mechanistic cation exchange model (CEM) along with Gaines-Thomas selectivity coefficients. The simulation results indicated that Na+ exchange isotherms and Q/I and ESR-SAR relations were influenced by the type of counter anions. The values of KG increased in the pre