The new ruthenium hydride complexes CpRuH(L) (L = PR2CH2CH2PR2, R = p-CF3C6H4 (dtfpe) or R = p-MeOC6H4 (dape) were prepared by reaction of NaOMe with CpRuCl(L), which were obtained by treating CpRuCl(PPh3)2 with L. Similarly, Cp*RuH(L) (L = dppm, (PMePh2)2) were prepared from the reaction of NaOMe with Cp*RuCl(L) obtained from the reaction of Cp*RuCl2 with L in the presence of Zn. Protonation of CpRuH(L) (L = dtfpe, dape) and Cp*RuH(dppm) with HBF4.ET2O produces mixtures of [CpRu(H)2(L)]+ and [CpRu(eta-2-H-2)(L)+, and [Cp*Ru(H)2(dppm)]+ and [Cp*Ru-(eta-2-H-2)(dppm)]+. The pK(a) values of the dihydrogen/dihydride complexes [CpRuH2(L)]+ (L = dtfpe, dppm, dppe, (PPh3)2, dppp, dape) and [Cp*RuH2(L)+ (L = dppm, (PMePh2)2) are determined by studying acid/base equilibria by H-1 and P-31 NMR spectroscopy in both CH2Cl2 and THF. The electrochemical properties of the monohydrido complexes CpRuH(L) and Cp*RuH(L) are reported. Peak potentials for oxidation of these monohydrides and pK(a) values of the cationic complexes are linearly related for all the complexes with a dihydrogen form: pK(a)(Ru(H-2)+) = 10.7E(pa)(RuH+/RuH) + 13.0. As expected eta-2-H-2 acidity decreases as the parent hydride becomes easier to oxidize. The related complexes with just a dihydride form, [CpRu(H)2(L)]+ (L = (PPh3)2, dppp) and [Cp*Ru(H)2(PMePh2)2]+, give a similar trend. Acidity constants have been determined for both tautomers when they observed; the pK(a) of the eta-2-H-2 form is approximately 0.3 pK(a) unit less (more acidic) than that of the (H)2 form for the complexes with L = dtfpe, dppe, and dape but is 0.4 unit greater for [Cp*RuH2(dppm)+. The acidities of the two tautomers are similar because their concentrations are similar and they have the same monohydrido conjugate base. Other trends in pK(a), 1J(HD), and delta-Ru(H-2) values of dihydrogen complexes and ratio of dihydride to dihydrogen tautomers and the peak potentials for oxidation of the monohydrido complexes are presented. These correlations are shown to be of value in explaining/predicting the propensity of dihydrogen to undergo heterolytic cleavage. Extremes in pK(a) values of such cyclopentadienylruthenium(II) complexes are expected for [Cp*RuH2(dmpe)]+ (pK(a) approximately 12) and [CpRuH2(Co)2]+ (pK(a) approximately -6).