Our computational study presents embedded cluster models of the hydrated electron focusing on its reactivity with the hydrated proton and the nitrous oxide molecule leading to formation of a hydrogen atom in the former case and a nitrogen molecule plus hydroxyl radical and hydroxide anion in the latter case. We show using ab initio calculations combined with the nudged elastic band method for determining minimum energy paths that carefully chosen cluster models with no more than six water molecules embedded in a polarizable continuum are able to capture the essential features of the reactive processes of the hydrated electron.