Adsorption of gold and palladium species containing chlorine ion species onto commercial N-(2-[bis(2-aminoethyl)amino)-ethyl] aminomethyl-polystyrene polymer beads (TRIS) was investigated. The influence of the pH, initial metal ion concentration, and contact time on the adsorption performance was examined in a batch adsorption experiment. To examine and discuss both the theoretical character of the metal ion adsorptions, Langmuir, modified Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and nonlinear solutions of modified Langmuir and Redlich-Peterson isotherm models variables are calculated. The modified Langmuir monolayer adsorption capacities of the Pd(II) and Au(III) chlorine ions species were found to be 206.93 and 173.18 mg/g, respectively. The two metal adsorption kinetics fit the pseudo-second-order kinetic models. In thermodynamic calculations, the choice of different equilibrium constants with having a dimension is an important problem in the field. To overcome these problems, the modified Langmuir isotherm equilibrium constant was used for determination of thermodynamic parameters. Adsorption mechanism steps were characterized using Fourier transform infrared (FTIR), scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDS). The adsorbent is made to interact with each metal ion in the HCI solution electrostatic interaction and surface complex formation between the amine groups. The calculation of the thermodynamic parameters using the dimensionless modified Langmuir equilibrium constant was found to be more satisfying and reliable. Adsorptions of Pd(II) and Au(III) on TRIS beads were exothermic and endothermic spontaneous processes, respectively.