One of the challenges in utilizing hydrogen gas (H-2) as a sustainable fossil fuel alternative is the inhibition of H-2 oxidation by carbon monoxide (CO), which is involved in the industrial production of H-2 sources. To solve this problem, a catalyst that selectively oxidizes either CO or H-2 or one that co-oxidizes H-2 and CO is needed. Recently, a NiIr catalyst [(NiCl)-Cl-II(X)(IrCl)-Cl-III(eta(5)-C5Me5)], (X = N,N'-dimethyl-3,7-diazanonane-1,9-dithiolate), which efficiently and selectively oxidizes either H-2 or CO depending on the pH, has been developed (Angew. Chem. Int. Ed. 2017, 56, 9723-9726). In the present work, density functional theory (DFT) calculations are employed to elucidate the pH-dependent reaction mechanisms of H-2 and CO oxidation catalyzed by this NiIr catalyst. During H-2 oxidation, our calculations suggest that dihydrogen binds to the Ir center and generates an Ir(III)-dihydrogen complex, followed by subsequent isomerization to an Ir(V)-dihydride species. Then, a proton is abstracted by a buffer base, CH3COO-, resulting in the formation of a hydride complex. The catalytic cycle completes with electron transfer from the hydride complex to a protonated 2,6-dichlorobenzeneindophenol (DCIP) and a proton transfer from the oxidized hydride complex to a buffer base. The CO oxidation mechanism involves three distinct steps, i.e., (1) formation of a metal carbonyl complex, (2) formation of a metallocarboxylic acid, and (3) conversion of the metallocarboxylic acid to a hydride complex. The formation of the metallocarboxylic acid involves nucleophilic attack of OH- to the carbonyl-C followed by a large structural change with concomitant cleavage of the Ir-S bond and rotation of the COOH group along the NiIr axis. During the conversion of the metallocarboxylic acid to the hydride complex, intramolecular proton transfer followed by removal of CO2 leads to the formation of the hydride complexes. In addition, the barrier heights for the binding of small molecules (H-2, OH-, H2O, and CO) to Ir were calculated, and the results indicated that dissociation from Ir is a faster process than the binding of H2O and H-2. These calculations indicate that H-2 oxidation is inhibited by CO and OH- and thus prefers acidic conditions. In contrast, the CO oxidation reactions occur more favorably under basic conditions, as the formation of the metallocarboxylic acid involves OH- attack to a carbonyl-C and the binding of OH- to Ni largely stabilizes the triplet spin state of the complex. Taken together, these calculations provide a rationale for the experimentally observed pH-dependent, selective oxidations of H-2 and CO.