Studies of the reaction of H atoms with Cl chemisorbed on Au(111) reveal two dynamically distinct mechanisms. Some reactions occur on essentially a single gas-surface collision, by way of a so-called Eley-Rideal (ER) mechanism. Others occur between accommodated H and Cl atoms, by way of a so-called Langmuir-Hinschelwood (LH) mechanism. The dynamics of these processes has been characterized by combining molecular beam techniques with quantum-state-specific detection. Specifically, I have used molecular beam time-of-flight (TOF) techniques to determine angular and velocity distributions of the HCl product, and I have used resonance-enhanced multiphoton ionization to determine rotational and vibrational state distributions. The TOF and angular distributions provide clear evidence for the ER mechanism. This mechanism yields a fast (early) peak in the TOF distributions and a narrow angular distribution that is asymmetric with respect to the surface normal. Moreover, the peak in the angular distribution moves further away from the normal in the direction of the specular angle as the energy of the incident H atom is increased from 0.07 to 0.3 eV. The mean energy of the ER product is about 0.6 eV, but increases slightly with increasing incidence energy. In contrast, the LH mechanism yields a relatively slow (late) TOF component that approximately follows a Boltzmann distribution at the surface temperature (T-s) and disappears at T-s<170 K. The form of the angular distribution of this LH component is close to a cosine function. The fast (ER) TOF component is itself found to be composed of at least two contributions, assigned to HCl product formed in upsilon=0 and upsilon=1 (with some contribution from upsilon=2). The rotational state distribution for the HCl(upsilon=0) product of the ER mechanism is found to be distinctly non-Boltzmann, with a mean rotational energy of about O.11 eV, or about 5% of the available energy. The rotational distributions obtained for upsilon=1 and upsilon=2 are similar to those for upsilon=0. The relatively small fraction of energy channelled into rotation is a consequence of the low II-atom mass. In contrast, the rotational distributions for HCl(upsilon=0) due to the LH mechanism are consistent with Boltzmann distributions at T-s. The vibrational state distribution for the ER process peaks in upsilon=1. The form of this distribution varies slightly with T-s, with about 30% in upsilon=0, 55% in upsilon=1, and 15% in upsilon=2 states at T-s=600 K. The mean vibrational energy for the ER component is thus about 0.32 eV, or similar to 14% of the available energy. This vibrational distribution is inconsistent with a simple attractive potential energy surface, which would lead to higher vibrational excitation. Either a large fraction of the energy is released as repulsion between the HCl and the surface, or vibrational energy is quenched, possibly by coupling between the departing molecule and the surface. The mean total energy carried away in the HCl product is only about half of that theoretically available. The total yield of the ER reaction increases rapidly with T-s, reaching a cross section of about 2X10(-16) cm(2) per Cl atom at T-s=600 K.