  The chemical inventory of protoplanetary midplanes is the basis for forming
planetesimals. Among them, solid-state reactions based on CO/CO$_2$ toward
molecular complexity on interstellar dust grains have been studied in
theoretical and laboratory work. In this work, the erosion of C dust grains
induced by X-ray irradiation of H$_2$O ice was systematically investigated for
the first time. The work aims to provide a better understanding of the reaction
mechanism using selectively isotope-labeled oxygen/carbon species in kinetic
analysis. Ultrahigh vacuum experiments were performed to study the interstellar
ice analog on sub-$\mu$m thick C dust at $\sim$13~K. H$_2$O or O$_2$ ice was
deposited on the pre-synthesized amorphous C dust and exposed to soft X-ray
photons (250--1250~eV). Fourier-transform infrared spectroscopy was used to
monitor in situ the newly formed species as a function of the incident photon
fluence. Field emission scanning electron microscopy was used to monitor the
morphological changes of (non-)eroded carbon samples. The X-ray processing of
the ice/dust interface leads to the formation of CO$_2$, which further
dissociates and forms CO. Carbonyl groups are formed by oxygen addition to
grain surfaces and are confirmed as intermediate species in the formation
process. The yields of CO and CO$_2$ were found to be dependent on the
thickness of the carbon layer. The astronomical relevance of the experimental
findings is discussed.
