We report the results of density functional calculations on the reactivity of a series of coordinatively unsaturated mixed phosphine/N-heterocyclic carbene complexes of ruthenium of the type Ru(CO)(IR)3-n(PH 3)n, where n = 1-3 and R = H (1,3-imidazol-2-ylidene) and R = Me (1,3-dimethylimidazol-2-ylidene). The oxidative addition reactions of H2 and CH4 and the C-C bond activation of C 2H6 have been studied. For all three processes, substitution of PH3 by IH results in minimal changes in the reaction energetics. In all cases H2 oxidative addition is barrierless and is downhill by around 120 kJ/mol. With CH4 activation barriers of around 75 kJ/mol are computed and the reaction is approximately thermoneutral. With C2H6 activation barriers increase to around 260 kJ/mol and the reaction is disfavored by about + 35 kJ/mol. Introduction of the IMe ligand disfavors oxidative addition, especially for the C2H6 reaction, and this trend is linked to increased steric bulk of the IMe ligand compared to IH. Computed Ru-PH3 and Ru-IR bond strengths and CO stretching frequencies indicate that PH3/IR substitution does create a more electron-rich metal center, and yet this does not facilitate oxidative addition with these Ru species. A fragment analysis reveals that, as expected, PH3/IH substitution enhances the Lewis basicity of the metal reactant. However, a more important effect is a reduction in Lewis acidity, and this factor lies behind the similar reaction energetics computed for analogous PH3- and IH-containing species.