We have investigated the adsorption of H2O onto the A and B type steps on an Ag single crystal by temperature programmed desorption. For this study, we have used a curved crystal exposing a continuous range of surface structures ranging from [5(111) × (100)] via (111) to [5(111) × (110)]. LEED and STM studies verify that the curvature of our sample results predominantly from monoatomic steps. The sample thus provides a continuous array of step densities for both step types. Desorption probed by spatially-resolved TPD of multilayers of H2O shows no dependence on the exact substrate structure and thus confirms the absence of thermal gradients during temperature ramps. In the submonolayer regime, we observe a small and linear dependence of the desorption temperature on the A and B step density. We argue that such small differences are only observable by means of a single curved crystal, which thus establishes new experimental benchmarks for theoretical calculation of chemically accurate binding energies. We propose an origin of the observed behavior based on a "two state" desorption model.