In this paper, we revisit a turbulent mixing of gas and air in a gas burner with computational fluid dynamics (CFD) models. The quality of such a turbulent mixture is based on temperature, pressure, and velocity distributions as well as the distributions of different molecules, turbulent kinetic energy, and turbulent dissipation rate. In order to identify a precise combination of a gas and air mixture in a gas burner, which directly influences the quality of the combustion flame and reduces the amount of carbon monoxide (CO) emission in flue gases, thermodynamic principles are utilized based on the balancing ratio of molecular weights and the balancing ratio of mass flows between gas and air. Moreover, input parameters, such as volume flow rates, pressure, mass ratio, temperature, turbulent kinetic energy, and turbulent dissipation rate, are judiciously chosen with proper boundary conditions for both axisymmetric two-dimensional and three-dimensional models. It is confirmed that the effectiveness of gas and air mixture and combustion depends on the gas burner model, more specifically, on the sizes and locations of gas and air inlets and outlets as well as operation conditions.