Advanced telescopes, such as ALMA and JWST, are likely to show that the chemical universe may be even more complex than currently observed, requiring astrochemical modelers to improve their models to account for the impact of new data. However, essential input information for gas-grain models, such as binding energies of molecules to the surface, have been derived experimentally only for a handful of species, leaving hundreds of species with highly uncertain estimates. We present in this paper a systematic study of the effect of uncertainties in the binding energies on an astrochemical two-phase model of a dark molecular cloud, using the rate equations approach. A list of recommended binding energy values based on a literature search of published data is presented. Thousands of simulations of dark cloud models were run, and in each simulation a value for the binding energy of hundreds of species was randomly chosen from a normal distribution. Our results show that the binding energy of H$_{2}$ is critical for the surface chemistry. For high binding energy, H$_{2}$ freezes out on the grain forming an H$_{2}$ ice. This is not physically realistic and we suggest a change in the rate equations. The abundance ranges found are in reasonable agreement with astronomical ice observations. Pearson correlation coefficients revealed that the binding energy of HCO, HNO, CH$_{2}$, and C correlate most strongly with the abundance of dominant ice species. Finally, the formation route of complex organic molecules was found to be sensitive to the branching ratios of H$_{2}$CO hydrogenation.
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