Achieving control of the surface chemistry of colloidal quantum dots (CQDs) is essential to fully exploit their properties in solar cells, but direct measurement of the chemistry and electronic structure in the outermost atomic layers is challenging. Here we probe the surface oxidation and passivation of cation-exchanged PbS/CdS core/shell CQDs with sub nm-scale precision using synchrotron-radiation-excited depth-profiling photoemission. We investigate the surface composition of the topmost 1-2.5 nm of the CQDs as a function of depth, for CQDs of varying CdS shell thickness, and examine how the surface changes after prolonged air exposure. We demonstrate that the Cd is localized at the surface of the CQDs. The surface-localized products of oxidation are identified, and the extent of oxidation quantified. We show that oxidised sulfur species are progressively eliminated as Cd replaces Pb at the surface. A sub-monolayer surface 'decoration' of Cd is found to be effective in passivating the CQDs. We show that the measured energy-level alignments at PbS/CdS colloidal quantum dot surfaces differ from those expected on the basis of bulk band offsets, and are strongly affected by the oxidation products. We develop a model for the passivating action of Cd. The optimum shell thickness (of around 0.1 nm, previously found to give maximised power conversion efficiency in PbS/CdS solar cells) is found to correspond to a trade-off between the rate of oxidation and the introduction of a surface barrier to charge transport.