This study focuses on the evaluation of isotherm models for the precise prediction of adsorption equilibrium and breakthrough dynamics. For this, the evaluation was performed using pure $N_2$, $CO_2$ and their binary mixture gas with an activated carbon (AC, Norit RB3) as an adsorbent. Both BET and breakthrough experiments were conducted at various conditions of temperature and pressure. The corresponding uptake amount of pure component adsorption was experimentally determined, and parameters of the four different isotherm models, Langmuir, Langmuir-Freundlich, Sips, and Toth, were estimated from experimental data. Then, the predictive power of each isotherm model was also evaluated with the binary experimental results of binary $N_2/CO_2$ mixtures, by means of sum of square errors (SSE). As a result, the Toth model was the most precise isotherm model in describing $CO_2$ adsorption equilibrium on the AC. Based on the breakthrough experimental result from the binary mixture adsorption, non-isothermal modeling for the adsorption bed was performed. A process simulator was used for examining breakthrough results for all of the isotherm models to precisely predict its adsorption dynamics and the Toth model was the most accurate model of all four isotherm models.