A chemical kinetic model is presented which fits the uptake kinetics of both steady-state and time-resolved heterogeneous reactions of D2O, HCl, HBr, and HOBr with ice substrates that have been studied in a Knudsen flow reactor. The salient feature of the model is the existence of two precursors to adsorption that explain the observed negative temperature dependence, as well as the absence of saturation, of the rate of uptake at the experimental conditions met in the Knudsen flow-reactor studies. From the temperature dependence of the fitted rate constants, enthalpy diagrams have been obtained in which the loosely bound precursor state has a binding energy on ice of 7.6-8.0, 6.4, 3.9, and 6.9 kcal/mol for D2O, HCl, HBr, and HOBr, respectively. The mass accommodation coefficients alpha at 200 K were 0.43 (D2O, B = bulk ice), 0.34 (D2O, C = condensed ice), 0.67 (HOBr, B-type ice), 0.36 (HCl, B-type ice), and 0.38 (HBr, B-type ice) and show a negative temperature dependence as well. The chemical kinetic model describes the transition between submonolayer Langmuir adsorption at low to multilayer adsorption at high doses or partial pressures.