Model core potentials with scalar-relativistic effect at the third order Douglas-Kroll level combined with the first-order Douglas-Kroll for spin-orbit coupling are developed for the 25 p-block elements, B-Tl, with the valence space starting at (n-1)p(n-1)d, except group 13, where (n-1)s is also included because its importance was clearly demonstrated for Tl. All of the comparisons between model core potential and all-electron calculations of atomic and ionic term and level energies and the spectroscopic constants of monohydrides and cationic dimers indicate the chemical accuracy of our new potentials in reproducing all-electron properties. The applications of the new potentials to the cationic dimers show that polyatomic calculations with model core potential atoms are accurate. The periodic trends in the spectroscopic properties of cationic dimers and hydrides are discussed. The timing study demonstrates the extent of the computational savings. These new sets of model core potentials and basis sets, which we call ZFKn-DK3, have been implemented in the the widely used quantum chemistry program package GAMESS-U.S.