Amorphous ice has long been invoked as a means for trapping extreme volatiles into solids, explaining the abundances of these species in comets and planetary atmospheres. Experiments have shown that such trapping is possible and have been used to estimate the abundances of each species in primitive ices after they formed. However, these experiments have been carried out at deposition rates which exceed those expected in a molecular cloud or solar nebula by many orders of magnitude. Here we develop a numerical model which reproduces the experimental results and apply it to those conditions expected in molecular clouds and protoplanetary disks. We find that two regimes of ice trapping exist: `burial trapping where the ratio of trapped species to water in the ice reflects that same ratio in the gas and `equilibrium trapping where the ratio in the ice depends only on the partial pressure of the trapped species in the gas. The boundary between these two regimes is set by both the temperature and rate of ice deposition. Such effects must be accounted for when determining the source of trapped volatiles during planet formation.
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