The influence of potassium adatoms on the adsorption and desorption kinetics of hydrogen on the Pt(111) single-crystal surface has been studied by temperature-programmed desorption (TPD). We report measurements of the dissociative sticking coefficient for H-2 on Pt(111) over the entire range of coverages of H(a) and K(a) between zero and monolayer coverage. Small amounts of potassium strongly reduce the dissociative sticking coefficient for H-2 on Pt(111) and eliminate the influence of a precursor in the adsorption kinetics. For example, when the K coverage, theta-K, is 0.043 (defined relative to the Pt(111) surface atom density) the initial sticking coefficient of H-2 on Pt(111) at 150 K is reduced by a factor of 20. However, hydrogen adatoms on the K-modified surface are thermally stabilized compared to Pt(111). The peaks observed during H-2 TPD occur at temperatures up to 150 K higher on the K-modified surface than for equivalent hydrogen coverages on K-free Pt(111). Comparisons with the Bi-modified surface demonstrate that the influence of K(a) exceeds local site blocking effects. We explain these observations in terms of a model in which K(a) modifies the electronic structure of the surface Pt atoms in nearby sites. This has two effects: (i) destabilization of the bonding of H-2(a) to the surface and (ii) stabilization of the bonding of H(a) to the surface. The weaker interaction between H-2(a) and the Pt(111) surface caused by K(a) decreases the role of aa H-2(a) precursor in the adsorption kinetics, lowers the initial dissociative sticking coefficient for H-2, and causes an increase in the activation energy for dissociative adsorption of H-2. While a slightly increased Pt-H bond strength due to K(a) could lead in principle to an enhancement of dissociative H-2 adsorption, we find that the former effects on H-2(a) dominate to strongly reduce the dissociative sticking coefficient for H-2 on Pt(111) modified by K adatoms.