Pressure‐composition‐temperature absorption isotherms have been determined for the Pd1‐xREx (RE = Dy, Gd, Sm, and Y; x = 0.05 and 0.08) solid solution face centered cubic alloys in the pressure and temperature ranges 2 ≦ P(H2)/mbar ≦ 1000 and 473 ≦ T/K ≦ 873 using the manometric method. The partial molar enthalpy of solution of hydrogen at infinite dilution (ΔH̄0H) becomes more exothermic with increasing content of RE. The partial molar excess entropy of hydrogen solution at infinite dilution (ΔS̄E.0H) decreases with xRE. A correlation of the atomic diameter (dRE) of the substituting rare‐earth metals when in solution in palladium with ΔH̄0H and with the metal‐hydrogen interaction shows that the increase in the exothermicity of the Pd1‐xREx solid solution alloys is due to the lattice expansion and an attractive metal‐hydrogen interaction. From the correlation of ΔH̄0H with dRE of Pd1‐xREx (x = 0.05 and 0.075), ΔH̄0H of Pd1‐xREx (RE = Yb, Ho, and Eu; x = 0.05 and 0.075) solid solution alloys have been predicted. The dependence of ΔH̄0H of the “expanded” and “contracted” Pd1‐xMx alloys on the size of the octahedral interstitial hole sites (rh) occupied by hydrogen atoms is discussed.