A comprehensive thermodynamic analysis has been performed for the Ga/N/H/C/O system. Apriori process-property relationships of the metal organic chemical vapor deposition (MOCVD) of Gallium Nitride (GaN) are thus obtained. The parameter space for pure GaN growth is studied for system water vapor levels of 0.1 ppb – 10 ppm, system pressure between 10-6- 106 Torr, N/Ga feed ratios of 1 - 100,000, C/Ga feed ratios of 0 – 100, and H2/Ga feed ratios of 100 – 10,000. Higher growth temperatures for pure GaN are predicted at high operating pressures (for pressures greater than 0.1 Torr), low C/Ga feed ratios, high carrier gas flow rates, and mostly at low N/Ga feed ratios. Because relative C/Ga, N/Ga and H2/Ga feed ratios have been considered, the predictions in this study are applicable to any multiple and single precursor systems. Such analyses can be easily extended to the molecular beam epitaxy of GaN, when the feed ratio C/Ga = 0. Experimental data reported on the growth of GaN are found to be in good agreement with our theoretical predictions, for many systems that have included different source species.