The energy required to form and remove vacancies on metal surfaces mediates the rate of mass transport during a wide range of processes. These energies are known to be sensitive to environmental conditions. Here, we use electronic structure density functional theory calculations to show that the surface vacancy formation energy of silver changes markedly in the presence of adsorbed and dissolved oxygen. We found that adsorbed atomic oxygen can reduce the surface vacancy formation energy of the Ag(111) surface by more than 30%, whereas surface vacancy formation becomes exothermic in the presence of pure subsurface oxygen. We went on to show that the total directionality of the topologically defined bond paths can be used to understand these changes. The resulting structure-property relationship was used to predict the behavior of silver in different atmospheres. We show that the surface vacancy formation energy decreases when electronegative elements are adsorbed on the surface, but that it can increase when electropositive elements are adsorbed.