Guided ion beam mass spectrometry has been used to examine the kinetic energy dependence of reactions of the second-row transition-metal cations, Ru+, Rh+, Pd+, and Ag+, with molecular hydrogen and its isotopologues. By using a meter long flow tube ion source, we are able to create Ru+, Rh+, Pd+, and Ag+ ions that are believed to be in their electronic ground state terms and primarily in the lowest spin-orbit levels. Corresponding state-specific reaction cross sections are obtained. Analysis of the cross section data yields 0 K bond dissociation energies of D-0(Ru+-H) = 1.62 +/- 0.05 eV, D-0(Rh+-H) = 1.67 +/- 0.04 eV, D-0(Pd+-H) = 2.07 +/- 0.04 eV, and D-0(Ag+-H) = 0.41 +/- 0.06 eV. This thermochemistry is compared with theoretical calculations and previous experimental measurements. Periodic trends in these bond dissociation energies and the bonding character of these metal hydride ions are discussed. Results for the HD reactions indicate that Rh+, Ru+, Pd+, and Ag+ ions react via direct mechanisms. The reaction mechanisms and reactivity differences among these ions are explained using simple molecular orbital concepts.