The catalyst is the heart of a reaction process that transforms an original substance into a usable product. To rationally design practical catalysts with high selectivity and reactivity, it is necessary to understand the fundamental mechanisms behind these transformations. In this dissertation, I will describe my research project, focusing on the catalytic surface reactions involving N2 and CO molecules. The Density Functional Theory (DFT) approach is utilized to carefully examine the binding energies and vibrational characteristics of potential surface adsorbates across various transition metals. A comparison of nitrogen-containing species produced during N2 plasma exposure unravels the complexity of surface metastable speciation and the influence of trace CO molecules. A DFT-parameterized microkinetic model is employed for the plasma-assisted N2 oxidation reaction to study product selectivity and sensitivity, showing dependence on catalyst material and experimental temperature. Lastly, we explored the CO binding energies on Pd and Pd77Ag23 surfaces, revealing that CO inhibits H2 permeation on Pd and Pd77Ag23 foil membranes by occupying surface Pd atoms and subsequently influencing H2 dissociation.