Trends in the chemical reactivity of transition-metal surfaces have been studied at the example of the dissociative adsorption of hydrogen on the (100) surfaces of Rh, Pd, and Ag. Detailed calculations of the six-dimensional potential-energy surfaces have been performed using density-functional theory. The adsorption dynamics has been investigated by solving the time-independent Schr\"odinger equation via a coupled-channel technique. The results are discussed in the light of current concepts for a reactivity theory.