Boron-based two-dimensional materials showcase promise in variety of fields like hydrogen storage, fabrication of electronic devices and catalytic applications. These materials have garnered interest owing to their unique properties such as high electron mobility, high gravimetric capacity for hydrogen especially after metal decoration, thermal conductivity and tensile strength amongst others. However, for sustained operations of the devices involving these materials, their chemical stability against oxygen is of paramount importance. Especially in the applications involving exposure of the material to air. Abundance of oxygen in the air and its high reactivity increases the likelihood of oxidation of the material. In this work, chemical stability of hydrogen passivated 2D Boron structures; Borophane and 2D Boron Hydride against oxygen were analysed. First-principles calculations reveal that Borophane and 2D Boron Hydride have a less negative binding energy thus indicating that the oxygen binds less strongly to compared to Borophene which does not possess surface passivation by hydrogen. Experimental studies in the literature involving synthesis of 2D Boron Hydride reported presence of vacancies. The effect of vacancy site towards the reaction with oxygen was therefore analysed to maintain consistency with the synthesized materials. The simulations were performed on Borophane and 2D Boron Hydride by introducing a Boron vacancy in the system. The DFT simulation of defect containing Borophane revealed that oxygen binds less strongly in the physisorbed state and more strongly in the chemisorbed state, relative to the values obtained for Borophane without any defects. In case of 2D Boron Hydride it was observed that the vacancies provide a stable site for oxygen, for both physisorbed and chemisorbed state. From these simulations we can conclude that presence of vacancies in Boron based 2D materials generally leads to a stable site for oxygen.